Lowe Compare PHM Algorithms Interpack 2013

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1 Copyright © 2013 by ASME

Proceedings of the 12th

International Technical Conference and Exhibi tion on Packaging and Integration ofElectronic and Photonic Microsystems

InterPACK 2013July 16-18, 2013, Burlingame, CA, USA

InterPACK2013-73252

COMPARISON OF PROGNOSTIC HEALTH MANAGEMENT ALGORITHMS FOR ASSESSMENT OF ELECTRONIC INTERCONNECT RELIABILITY

Pradeep Lall Auburn University

NSF-CAVE3 Electronics Research Center Auburn, Alabama, USA

Ryan Lowe Air Force Research Laboratory

Eglin, Florida, USA

Kai GoebelNASA Ames Research CenterMoffett Field, California, USA

ABSTRACTThis paper compares three prognostic algorithms applied to the

same data recorded during the failure of a solder joint in ball

grid array component attached to a printed circuit board. Theobjective is to expand on the relative strengths and weaknesses

of each proposed algorithm. Emphasis will be placed on

highlighting differences in underlying assumptions required for

each algorithm, details of remaining useful life calculations,and methods of uncertainty quantification. Metrics tailored

specifically for Prognostic Health Monitoring (PHM) are presented to characterize the performance of predictions. The

relative merits of PHM algorithms based on a Kalman filter,extended Kalman filter, and a particle filter all demonstrated on

the same data set will be discussed. The paper concludes by

discussing which algorithm performs best given the informationavailable about the system being monitored.

INTRODUCTIONPreviously a measurement technique known as resistancespectroscopy [1],[2],[5][6] has been demonstrated to effectively

provide advanced warning of failure in electronics as they are

subjected to a variety of harsh environments such as drop/shock

[7], vibration [8], and simultaneous vibration and temperature[13]. The techniques ability to quantify damage prior to failure

in a solder joint allows insight into the health of components

attached to a circuit board to be monitored and mitigatingaction to be planned in the event of an impending failure. While

crucial to PHM for electronics, the data measured by the

resistance spectroscopy technique is inherently noisy due to the

dynamic environment that electronics systems operate in.

Prognostic algorithms process the noisy data and forecast theexpected time of failure of the device under test. It is

convenient to assign a name to an algorithm based on adistinguishing feature of the algorithm. For prognostic

algorithms based on recursive filters, typically the algorithm is

named by the tracking part of the algorithm. But it is importantto note that tracking is only half of the PHM algorithm, model

based forecasting techniques use smoothed estimates of noisy

data from the tracking algorithm to predict failures.

The first method described is based on a Kalman filter[9][10][19],[19], which is a widely used tracking algorithm

The Kalman filter assumes a system of ordinary differentiaequations can be used to model the system being tracked and

that noise in both the model and measurement system isGaussian in nature. In this paper the tracking is applied to

damage of electronics. The extended Kalman filter [11] allows

non-linear differential equations to be used to describe thesystem being tracked. Lastly the particle filter [3],[4],[12],[16]

is a generalization of both the Kalman and extended Kalman

filters and is completely general. Any manner of non-linear

equation can be implemented in the particle filter with any

arbitrary contribution of non-Gaussian noise. The particle filteris considered state of the art in non-linear filtering, but is also

the most complicated. In the following three sections PHM

algorithms based on each of the filters will be described andtheir results quantified. The paper will conclude by comparingthe merits of the three algorithms and providing guidance for

choosing the best algorithm based on the available information.

EXPERIMENTAL PROCEDUREA set of test boards with multiple package architectures were

used for experimental measurements. The test board includes

package architectures such as plastic ball-grid arrays, chiparray 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. The package parameters of this board are shown in

Table 1. Representative sample of the test board is shown inFigure 1.

Figure 1: Test Board

Table 1: Package architectures on test board

6 m m

T a p e A r r a y

7 m m

C h i p A r r a y

1 0 m m

T a p e a r r a y

1 5 m m

P B G A

1 6 m m

F l e x B G A

2 7 m m

P B G A

I/O 64 84 144 196 280 676

Pitch(mm)

0.5 0.5 0.8 1 0.8 1

Die Size

(mm)4 5.4 7 6.35 10 6.35

Substrate

Thick

(mm)

0.36 0.36 0.36 0.36 0.36 0.36

Pad Dia.

(mm)0.28 0.28 0.30 0.38 0.30 0.38

Substrate

Pad NSMD NSMD NSMD SMD NSMD SMD

Ball Dia.

(mm) 0.32 0.48 0.48 0.5 0.48 0.63

The test assemblies were subjected to vibration testing on a

LDS Model V722 vibration table. A step stress profile was

used to gradually ramp up the stress level to induce damage

(Figure 2). The individual random stress profiles used in the

step stress are shown in Figure 3. The next section will discusshow the transient response of a package during random

vibration testing was monitored for a leading indicators of

failure.

Figure 2: Step stress profile for vibration testing that fatiguesinterconnects to failure.

Figure 3: Random vibration profile at varying g levels

corresponding to the step stress profile outlined in Figure 2

A. Relating Damage to Resistance

The daisy chained resistance of a package was used as a leading

indicator of failure. The observed history of the resistance ofthe package during vibration testing is shown in Figure 4.

Figure 4: Raw resistance data. The data used as aninput data vector is shown in the brackets




At approximately 5.8 hours the package experiences its first

intermittent open event. In the following plots large resistance

values have been truncated for clarity. The resistance of an

open event of 300 or more makes it difficult to discuss mili-

ohm changes on a plot. Additional details quantifying theapplicability of the measurement system for capturing

intermittent events in advance of the traditional definition of

failure can be found in [5]-[8].

Figure 5: Zoomed view of resistance data between 2hrs and failure

The failure criteria for resistance change outlined in industry

standards JESD22-B103 [JEDEC 2006], and IPCSM785 [IPC1992] for the number, duration, and severity of intermittent

events is used as the definition of failure. It should be noted that

the smaller step increases of 0.05 Ω during the first 90 minutesof the test are experimental noise which can be reproduced by

motion of the system connections during shock and vibration.Resistance data two-hours after the initiation of the test till

failure has been studied for the construction of a feature vectorfor identification of impending failure. A subset of the

resistance data has been used since field data will often involve

electronic assemblies with accrued damage and not involve

pristine assemblies. Figure 5 shows a zoomed view of the input

data highlighting the experimental noise between two hours andfailure. The experimental noise is due in part to the challenges

with overcoming the variance in contact resistance in the

presence of transient dynamic motion in shock or steady-statevibration. Step changes in the resistance data can be seen at 2.8

and 4.9 hours respectively. However, the distinctive increase of

about 25 mΩ during the vibration test is easily discernible evenin the presence of experimental noise. The change in resistanceis attributed to change in geometry, since the resistivity of the

solder interconnect is expected to stay constant. Since the

material properties and geometry of a solder ball are non-linear,

a finite element simulation (FEM) was used to map the changein resistance of an interconnect to the state of plastic strain that

the interconnect was feeling [5]-[8]. Ultimately a failure

threshold of 3.125 was established.

RESISTANCE SPECTROSCOPY

The resistance spectroscopy (RS) technique provides the

experimental foundation for the work presented in this

document. Essentially the technique is a very narrow band pass

filter, but is implemented in an unexpected manner compared totraditional noise filters. The ability of the filter to reject noise a

frequencies not related to the signal makes the technique very

robust. Application of the RS method is described in extensivedetail in [5]-[8]. The RS method for prognostics has been

applied to a variety of interconnect alloys ([5]-[8]: SAC305

SnPb, HiPb), interconnect geometries (copper collumns [5]-[8]HiPb collumns/micro-coils [14]), and Molex computer

connectors [15]. In this paper the system being studied is

SAC305 ball grid array interconnects.

I. K ALMAN FILTER BASED PHM ALGORITHM

For the Kalman filter based algorithm the resistance of the

solder joint, measured using spectroscopy, was assumed tomost closely be described by a quadratic model. Based on this

assumption the system of equations relating the resistance, R, to

its derivatives, and is shown in (1). This equation alsoallows the prorogation of the system forward by time step The index K represents the state of the system at the curren

time step, while K-1 represents the state of the system at the

previous time step.

1 0.5T0 1 0 0 1

R R T 0.5R TR R T

R

1

The second derivative of a quadratic system is a constant

which is represented by the relationship . There

are two free parameters in the Kalman filter which affect theimportance given to measured data and the system model. The

first free parameter, the measurement noise term, is set by

estimating the amount of noise in the experimental setup before

testing starts. The second parameter, the process noise term, is

related to the belief that the system model is accurate. Based onobservations and experience the parameters were respectively

set to 5x10-5 and 1x10-9.

To forecast remaining useful life in the electronics beingmonitored it is necessary to use the Kalman filter to estimate

the state of the system, and then using the model defined in

equation (1) forecast when the system will propagate to the

failure threshold, . Using the failure threshold as the fina

state of the system allows calculation of the remaining usefu

life as in equation (2).R R R t 0.5R t 2

The uncertainty of each prediction was quantified using the

posterior error covariance estimated by the Kalman filter. As an

engineering approximation the uncertainty is calculated using a




straight line approximation. Then the uncertainty from the

linear approximation is superimposed on the failure prediction

obtained from (2). This is a trade off in accuracy, for the benefit

of algorithm simplicity.

Assuming that the feature vector and its first derivative arenormal random variables (Gaussian), then a straight line

approximation of the time to failure can be

t R R 3where tRUL is the time to failure, R f is the failure threshold,

is the estimated state of the system (resistance) and is theestimate of the first derivative. The numerator will have a

variance equal to the variance of the position estimate, which is

directly available in the posterior error covariance matrix as

P(1,1). The denominator will have a variance equal to the

variance of the first derivative estimate, directly available asP(2,2). If σ P1,1 4

σ P2,2 5then it is demonstrated in [Swanson 2001] that the non-

Gaussian distribution resulting from the ratio of two normal

distributions with variances of and can be integrated to

find the equivalent 68.4% probability range around the mean.

σ 1.86 σσ 6

The mean of the distribution from the straight line

approximation is disregarded since better methods are available

to solve for the predicted RUL. The uncertainty estimate around

the RUL prediction includes a number of simplifying

assumptions about the nature of the system and should only betaken as a rough estimate.

Figure 6: Prediction snapshot at 3.75 Hrs into the test.

At this point there has not been sufficient trend for the Kalmanfilter based PHM algorithm to converge.

The Kalman filter based PHM algorithm is a combination ofa tracking filter defined by equation (1), a prediction of

remaining useful life in equation (2), and an uncertainty

prediction from equation (6). The next set of figures show three

prediction snapshots from the Kalman filter based PHM

algorithm. In each figure the top section shows the information

that was available at the time the prediction was made. The

lower section shows a superposition of the prediction on top of

the full data set. Only because we are simulating our ability to predict failure based on previously recorded data can we show

the lower plot as a reference to the reader. In practice the lower

plot is not available. Three snapshots are shown, but remaininguseful life was predicted after each new data point was

processed. In practice the recursive nature of the Kalman filter

based algorithm would be beneficial due to its ease oimplementation and low computational overhead. At no poin

would the full time history of recorded data need to be stored.

Figure 7: Prediction snapshot at 4.25 Hrs into the test.

With more data available the Kalman filter based PHM

algorithm prediction is better.

Figure 8: Prediction snapshot near the end of the test.

It is particularly evident that the quadratic model is a poor

description of the underlying process at this final stage of the

components life.

Using PHM metrics which are specifically designed to quantify

accuracy and precision of predictions [18] a quantitative

description of results can be determined. The alpha lambda plois a summary of all of the predictions and the associated

uncertainty. The beta metric is a measure of precision, and

relative accuracy is an accuracy metric that is more sensitive to




errors closer to the actual failure. In the plots the pink shaded

region is a goal region for the predictions and represents +/-

20% of the actual remaining useful life.

Figure 9: Alpha-Lamb metric for the Kalman filter based PHM

algorithm summarizing all predictions and the uncertainty inthe predictions

Figure 10: Beta metric quantifying precision. In general the

predictions were both not accurate or precise which is

demonstrated in this result

Using results from the beta metric and relative accuracy metric

a single number can be used to quantify the overall

performance of the predictions. A cost function, defined in

[11],[12], is a weighted average of the beta metric and relativeaccuracy metric for each prediction step. In this implementation

the cost function was evaluated as 0.843. A perfect score on the

cost metric is zero, and the worst possible score is one.

Figure 11: Relative accuracy metric quantifying the

performance of the Kalman filter based PHM algorithm

EXTENDED KALMAN FILTER BASED PHM ALGORITHMFor the extended Kalman filter based algorithm the resistance

of the solder joint, measured using resistance spectroscopy, was

assumed to most closely be described by an exponential modelBased on this assumption the system of equations relating the

resistance, R, to its derivatives, and is shown in thefollowing equations. The model parameter b is also estimated

inside the filter which is known as online parameter estimation

or model adaption. 7

8 9

10 11

Exponential term ‘b’ can be adapted to more efficiently

represent the underlying process that is damaging the

electronics. When using non-linear equations there is no longerconvenient closed form methods for propagating system states

into the future to determine remaining useful life as there was

with equation (2) for the Kalman filter algorithm. Repeatedapplications of Euler integration is implemented using

equations (10) and (11) until the resistance of the packageunder test is predicted to break the failure threshold. The length

of the time step used for the prediction was set at 0.01 hourswhere the error due to linearization is expected to be about 1%

per step. Unfortunately choosing noise terms with the extended

Kalman filter requires more experience with the data set. In this

implementation artificial noise was added to the filter to

improve performance. This approach is commonly used whendesigning filters for practical applications to achieve smoother




state estimates [19]. The process noise and measurement noise

was both set as 1x10-3 Ω for the extended Kalman filter

implementation. The ‘b’ term is initialized as a value of 0.9.

The extended Kalman filter based PHM algorithm is a

combination of a tracking filter with a system model defined byequations (7) through (9). Remaining useful life predictions are

calculated with the repeated application of equations (10) and

(11). Prediction uncertainty is quantified in the same manner asthe Kalman filter using equation (6). Prediction snapshots are

shown in Figure 12 through Figure 14 and can be compared to

Figure 6 through Figure 8. Three snapshots are shown, butremaining useful life was predicted after each new data point

was processed. In practice the recursive nature of the extended

Kalman filter based algorithm would be beneficial due to its

ease of implementation and low computational overhead. The

model adaption capability of this implementation is expected tomake the algorithm robust to changing loads and stresses. The

ability to implement system models with non-linear equations

makes incorporating physically realistic models into thealgorithm easier.

Figure 12: Prediction snapshot at 3.75 Hrs into the testusing the extended Kalman filter based PHM algorithm. This

result is much better than the regular Kalman filter prediction

shown in Figure 6.

Figure 13: Prediction snapshot at 4.25 Hrs into the testusing the extended Kalman filter based PHM algorithm.

Figure 14: Prediction snapshot at 5.5 Hrs into the testusing the extended Kalman filter based PHM algorithm.

Figure 15: Alpha-Lamb metric for the extendedKalman filter based PHM algorithm summarizing all

predictions and the uncertainty in the predictions

Figure 16: Beta metric quantifying precision for the

extended Kalman filter based PHM algorithm.




Figure 17: Relative accuracy metric quantifying the

performance of the extended Kalman filter based PHM

algorithm

PHM metrics for the extended Kalman filter implementation

demonstrate that the implementation converges quicker, and is both more accurate and precise than the regular Kalman filter

algorithm. The cost function summarizing the total performance

of the algorithm is significantly better with a value of 0.520.

PARTICLE FILTER BASED PHM ALGORITHMThe same system dynamics are assumed for the Particle filter

based PHM algorithm as is used in the extended Kalman filter.

Online parameter estimation is also performed in the particle

filter, but using different methods than the extended Kalman

filter. In the particle filter an initial distribution is assumed for

the ‘b’ parameter and allowed to randomly walk during tracking[3]. The random walk method of model adaption is the simplest

approach known to the authors. The reader is directed to [17]

for a detailed discussion of different approaches for adaptingmodel terms in the particle filtering framework.

Euler integration is also used to propagate system states

forward in time in the particle filter, but there is the addition of

noise terms that slightly alter predictions using small levels ofrandom noise. For example the resistance of the package is

propagated forward in time using a relationship similar to

equation (10), with the addition of a noise term. The noise is

assumed to be Gaussian in nature and is centered around zero.

The standard deviation of the added noise is denoted as

. The

additive noise is roughly analogous to the process noise in theKalman family of filters. 0, 12As described in [12] the particle filter estimates the state of a

system using a series of discrete particles that approximate a

probability distribution. The significance of each weight

associated with an individual particle is updated after each

measurement. In this implementation a Gaussian kernel is

utilized for the weight update step.

f x 1w√ 2π expR z

2w 13

The Gaussian kernel shown in (12) has a mean value centered

at the most recent noisy measurement of the system. The

estimated position of particle at time step is denoted as The standard deviation of the kernel is denoted as noise term.The standard deviation of the Gaussian kernel is analogous

to the measurement noise term in the Kalman family of filters

When the estimated state of the system and the measured state

of the system are relatively close to each other the Gaussian

kernel is a larger value. When the state estimate andmeasurement differ significantly, the Gaussian kernel is a

smaller value. In this implementation the process noise like

term was set as 2x10-2 and the noise term similar tomeasurement noise was set as 3x10-4. The particle population

was set as 30 particles.

Figure 18: Prediction snapshot at 3.75 Hrs into the test

using the particle filter based PHM algorithm. This result is

much better than the regular Kalman filter prediction shown inFigure 6, and the method of uncertainty quantification is an

improvement over Figure 12.

Figure 19: Prediction snapshot at 4.25 Hrs into the testusing the particle filter based PHM algorithm.




The particle filter based PHM algorithm is a combination of a

tracking filter with a system model defined by equations (7)

through (9). Remaining useful life predictions are calculated

with the repeated application of equation (12) for each separate

particle representing the state of the system. In effect the prediction step becomes similar to a Monte Carlo simulation.

Prediction uncertainty is quantified based on the predicted

distribution generated during the RUL calculation. Unlike withthe Kalman filters the resulting RUL prediction distribution is

almost always non Gaussian in nature. Prediction snapshots are

shown in Figure 18 through Figure 20 and can be compared toFigure 6 through Figure 8 and Figure 12 through Figure 14.

Figure 20: Prediction snapshot at 5.5 Hrs into the test

using the particle filter based PHM algorithm.

Figure 21: Alpha-Lamb metric for the particle filter

based PHM algorithm summarizing all predictions and theuncertainty in the predictions

Three snapshots are shown, but remaining useful life was predicted after each new data point was processed. In practice

the recursive nature of the particle filter based algorithm would

be beneficial, but unlike the Kalman family of filters

implementation is more difficult and in some cases computationoverhead could be a burden depending on the situation.

Figure 22: Beta metric quantifying precision for the

particle filter based PHM algorithm.

Figure 23: Relative accuracy metric quantifying the performance of the particle filter based PHM algorithm

Figure 24:Failure prediction distributions from the particle filter PHM algorithm. Darker lines represent

predictions closer to the end of the test




Figure 25: Due to the variable nature of the particle

filter implementation the performance of the algorithm can vary

significantly. This histogram shows the results of 30 runs of thealgorithm on the same data set.

The model adaption capability of this implementation is

expected to make the algorithm robust to changing loads andstresses, but due to the inherent randomness in the algorithmresults may vary. The ability to implement system models with

any manner of non-linearity makes the filter a powerful choice

for representing physical phenomena. PHM metrics for the particle filter implementation demonstrate that the

implementation converges quicker, and is both more accurate

and precise than the regular Kalman filter algorithm. The costfunction summarizing the total performance of the algorithm is

the best reported in this paper with a value of 0.263.

SUMMARY AND CONCLUSIONSThe performance of three PHM algorithms based on the

Kalman filter, extended Kalman filter and particle filter have been demonstrated on the same data set. Differences in the

quadratic model used in the Kalman filter, and the exponential

model used in the extended Kalman filter and particle filter

have been highlighted. Differences in the remaining useful life

prediction portion of the algorithms has also been discussed.The Kalman family of filters uses a rough approximation to

quantify prediction uncertainty, while the particle filter has a

robust method for representing uncertainty as a generic

probability distribution. The repeatability of the particle filterwith the implementation in this paper was shown to have some

variability, but also was capable of the best performance. The

extended Kalman filters use of non-linear models and modeladaption gives it better performance than the simpler regular

Kalman filter. The tradeoff between computation burden and

performance is summarized in Table 1.

Table 2: Performance and Computational Cost

FilterCost Function

(lower is better)ExecutionTime (s)

Kalman 0.843 39

Extended Kalman filter 0.521 194

Particle filter 0.263 304

In summary no filter implementation is better than another, but

rather the best choice of filter depends on the specifics of your

application domain. The availability of run to failure data and

high resolution failure models is an important criterion for

selecting the best implementation. A large number of filteringand PHM algorithms exist, some with names that may be

ambiguous as to the details of the algorithm, and two

practitioners implementation are not necessarily identicalWithout a set of baseline validation data sets like those used in

machine learning or hurricane forecasting it is difficult to

quantify the absolute performance between PHM algorithms.

ACKNOWLEDGMENTSThe research presented in this paper has been supported by

NSF-FRS-1127913 and members of NSF-CAVE3 Electronic

Research Center

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Lowe Compare PHM Algorithms Interpack 2013