Approaches to Health Monitoring of the CAT 7 

Diesel Engine

by Andrew J. Bayba, David N. Siegel, Kwok Tom, and Canh Ly

ARL-TR-5677 September 2011

Approved for public release; distribution unlimited.
NOTICES

Disclaimers

The findings in this report are not to be construed as an official Department of the Army position 

unless so designated by other authorized documents.

Citation of manufacturer’s or trade names does not constitute an official endorsement or 

approval of the use thereof.

Destroy this report when it is no longer needed. Do not return it to the originator.
Army Research Laboratory

Adelphi, MD 20783-1197

ARL-TR-5677 September 2011

Approaches to Health Monitoring of the CAT 7 

Diesel Engine

Andrew J. Bayba, David N. Siegel, Kwok Tom, and Canh Ly

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
ii

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 

OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

September 2011

2. REPORT TYPE

Final

3. DATES COVERED (From - To)

October 2010 to July 2011

4. TITLE AND SUBTITLE

Approaches to Health Monitoring of the CAT 7 Diesel Engine

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Andrew J. Bayba, David N. Siegel, Kwok Tom, and Canh Ly

5d. PROJECT NUMBER

1NE6KK

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

U.S. Army Research Laboratory

ATTN: RDRL-SER-E

2800 Powder Mill Road

Adelphi MD 20783-1197

8. PERFORMING ORGANIZATION

 REPORT NUMBER

ARL-TR-5677

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT

This study consists of an evaluation of health assessment approaches for the CAT 7 diesel engine. The report presents the 

processing method and results from two potential approaches for monitoring ground vehicle engine health. This work is based 

on data acquired from seeded fault testing performed on the engine by the U.S. Army Tank and Automotive Research, 

Development and Engineering Center (TARDEC) from May–August 2010. Correlation analysis and principal component 

analysis were performed on the data and the results are presented. The results show detection of the presence of the majority of 

the faults. It is anticipated that through the application of various processing techniques such as these, a better assessment of

engine health, in particular, the early detection of subsystems faults, is possible.

15. SUBJECT TERMS

Health monitoring, diesel engine health, CAT Y diesel engine, diesel engine prognostics and diagnostics

16. SECURITY CLASSIFICATION OF: 

17. LIMITATION

 OF 

 ABSTRACT

UU

18. NUMBER

 OF

 PAGES

34

19a. NAME OF RESPONSIBLE PERSON

Andrew J. Bayba

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified

19b. TELEPHONE NUMBER (Include area code)

(301) 394-0440

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
iii

Contents

List of Figures iv

List of Tables iv

1. Introduction 1

2. Experimental 1

3. Data for Analysis 3

4. Modeling Approaches 5

4.1 Single Parameter Monitoring ..........................................................................................6

4.2 Correlation Analysis........................................................................................................7

4.3 Principal Component Analysis......................................................................................12

5. Discussion 23

6. Conclusion and Recommendations 23

7. References 24

List of Symbols, Abbreviations, and Acronyms 25

Distribution List 26
iv

List of Figures

Figure 1. Instrumented CAT 7 engine in the TARDEC test cell.....................................................2

Figure 2. Engine control, instrumentation, and data flow................................................................2

Figure 3. Typical stepped control of engine speed for a performance run. .....................................3

Figure 4. Exhaust stack temperature for an exhaust restriction of 50% compared with 

baseline data...............................................................................................................................7

Figure 5. Correlation difference matrices for baseline runs (left) 3 and (right) 6. ..........................9

Figure 6. Correlation difference matrix for a 46% exhaust restriction (run 36)............................10

Figure 7. ROC curve for the correlation-based FOM....................................................................11

Figure 8. Correlation FOM for all runs The first eight are baseline runs and the remainder are 

by test number from table 2. The plot excludes training runs. ................................................12

Figure 9. Percent of variability explained by each principal component (Regime 4). ..................14

Figure 10. Regime 1 SPE health values for each run. ...................................................................16

Figure 11. Regime 1 T2 health values for each run........................................................................17

Figure 12. Regime 2 SPE health values for each run. ...................................................................17

Figure 13. Regime 2 T2 health values for each run........................................................................18

Figure 14. Regime 3 SPE health values for each run. ...................................................................18

Figure 15. Regime 3 T2 health values for each run........................................................................19

Figure 16. Regime 4 SPE health values for each run. ...................................................................19

Figure 17. Regime 4 T2 health values for each run........................................................................20

Figure 18. SPE contribution plot, showing the relative contribution of each signal (50% 

exhaust restriction)...................................................................................................................22

List of Tables

Table 1. Baseline performance runs.................................................................................................4

Table 2. Seeded fault performance runs. .........................................................................................4

Table 3. Signals recorded from CAN and dyno...............................................................................5

Table 4. Advantages and disadvantages for each modeling approach identified for the CAT 7 

data.............................................................................................................................................6

Table 5. Operating regimes for PCA analysis. ..............................................................................13

Table 6. Results of SPE and T2......................................................................................................16
v

Table 7. Signal contribution to fault detection from T2 calculation...............................................21

Table 8. Signal contribution to fault detection from SPE calculation. ..........................................22
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction

There is a great deal of interest in the U.S. military in monitoring the health of assets in operation 

in the field. The primary motivation is so that timely, efficient, and effective decision making can 

be made both for operations and logistical support. With this in mind, the U.S. Army Research 

Laboratory (ARL) has teamed with the U.S. Army Tank and Automotive Research, 

Development and Engineering Center (TARDEC) to investigate approaches for assessing the 

health of diesel engines (Technology Program Annex TA-SE-2010-5). Seeded fault testing was 

executed with the assistance of Millennium Integrated Services (MIS) 2000/Global Defense 

under ARL contract W911NF-09-2-0036. The focus of this report is to present progress in this 

area, and specifically, to review the efficacy of algorithms that can detect anomalous conditions 

intentionally imposed on the system (seeded faults) and then identify the source of the variation 

that caused the anomaly. It is also anticipated that the effort in this particular subject will be 

applicable to other areas of interest in ARL’s prognostics and diagnostics (P&D) program.

2. Experimental

A military version of the CAT 7 diesel engine (Model C7 DITA) was installed and instrumented 

in a dynamometer (dyno) test cell at TARDEC’s facilities in Warren, MI (figure 1). The basics of 

the setup and data collected are described here; for a detailed description of the experiment, see 

reference 1. The setup was designed so that the engine could be operated and controlled without 

the presence a vehicle. The test stand supported provision of fuel, coolant, inlet air, and 

exhausting of the engine as well as a load (eddy current dyno, computer controlled). Data were 

collected from a variety of sources including existing sensors on the engine through the 

controller-area network (CAN) vehicle bus standard, several sensors in the test cell recorded by 

the cell data acquisition system (DAQ), and a few “add-on” sensors that were recorded at a 

higher rate (referred to as “analog data”). A small portion of the data that is referred to as “digital 

data” is primarily used for timing. There were also sensors inserted and data collected by the 

Pennsylvania State University (Penn State) Applied Research Laboratory. Both the CAN and 

dyno data were collected at a relatively low rate and provided to ARL at 1 Sample/s, and could 

be monitored continuously during a test run. The analog data were collected at 10 kiloSamples/s 

and, due to the high rate, “snapshots” of data of between 1 and 30 s were collected at select times 

during a test run. The Penn State data were collected independently without time synchronization 

of the TARDEC data at 102.4 kiloSamples/s. A diagram of the engine control, instrumentation,

and data flow is shown in figure 2.
2

Figure 1. Instrumented CAT 7 engine in the TARDEC test cell.

Figure 2. Engine control, instrumentation, and data flow.
3

Test runs were performed with various seeded faults and no fault cases. A test run consisted of 

running the engine through a stepwise sequence of designated speeds for a short time at each 

speed, as shown in figure 3; all with either no fault or a particular seeded fault. The engine 

speeds with associated duration were duplicated for all the tests. As can be seen, there are six 

speeds with duration of between 1 and 3 min each; the time duration at a given speed set point 

was not precisely controlled. 

Figure 3. Typical stepped control of engine speed for a performance run.

3. Data for Analysis

The current focus is on the performance test data since these files have several baseline runs 

along with several seeded fault runs. Baseline runs are test sequences at the beginning of a test 

day in which there was no fault but the standard test sequence was followed, and as such are 

viewed as “healthy states.” Table 1 shows the 15 baseline runs that were identified. For principal 

component analysis (PCA) and autoassociative neural network based methods (AANN), training 

data is required; the first column of table 1 shows the runs that were selected for training (50% of 

the runs, using a random number generator). Table 2 shows the 33 seeded fault performance 

runs; however, three of these test runs are considered a baseline condition since their gain was 
4

set to 1.0, which is the nominal value. As a note, several files contained more than one run, 

where the additional runs were various levels of the same fault type.

Table 1. Baseline performance runs.

Table 2. Seeded fault performance runs.

Baseline Performance Test # Date MatLAB File Name Run # in File Train (0) or Test (1) 

Training 1 May 27, 2011 PerfM3_JP8_May27_ext 1 0

Training 2 May 27, 2011 PerfM3_JP8_May27_ext 2 0

Test 1 June 1, 2011 Perf_Jun1_ext 1 1

Training 3 June 3, 2011 Perfor_Jun3_ext 1 0

Training 4 June 8, 2011 Perfor_Jun8_par 1 0

Test 2 June 10, 2011 Perfor_Jun10_ext 1 1

Training 5 June 15, 2011 Perfor_Jun15_ext 1 0

Test 3 June 16, 2011 Perfor_Jun16_ext 1 1

Test 4 June 22, 2011 Perfor_C_Jun22_ext 1 1

Test 5 June 29, 2011 Perfor_jun29_ext 1 1

Test 6 July 1, 2011 Perf_Jul1_ext 1 1

Training 6 July 6, 2011 Perfor_Jul6_ext 1 0

Training 7 July 8, 2011 Perfor_Jul8_ext 1 0

Test 7 July 27, 2011 Perfor_Jul27_ext 1 1

Test 8 August 3, 2011 Perfor_ext3_ext 1 1

Test # Date MatLAB File Name Fault Type Run in File Severity

9 May 27, 2011 PerfM3_IntRestr_May27_ext IntakeAir Restric Test 1 Pos # 4

10 May 27, 2011 PerfM3_IntRestr_May27_ext IntakeAir Restric Test 2 Pos # 6

11 June 8, 2011 PerfM3_OilP_Jun8_par OilPress High Gain 1 Gain 1.0

12 June 8, 2011 PerfM3_OilP_Jun8_par OilPress High Gain 2 Gain 0.7

13 June 8, 2011 PerfM3_OilP_Jun8_par OilPress High Gain 3 Gain 1.3

14 June 10, 2011 PerfM3_AirChgT_Jun10_ext Air Charge Temperature Increase 1 Increased by 20o

F

15 June 10, 2011 PerfM3_AirChgT_Jun10_ext Air Charge Temperature Increase 2 Increased by 30oF

16 June 10, 2011 PerfM3_AirChgT_Jun10_ext Air Charge Temperature Increase 3 Increased by 50oF

17 June 15, 2011 Perfor3_AirRestr_Jun15_ext AirRestriction Low 1 Pos # 2

18 June 15, 2011 Perfor3_AirRestr_Jun15_ext AirRestriction Low 2 Pos # 3

19 June 15, 2011 Perfor3_AirRestr_Jun15_ext AirRestriction Low 3 Pos # 4

20 June 15, 2011 Perfor3_B_AirRestr_Jun15_ext AirRestriction High 1 Pos #5

21 June 15, 2011 Perfor3_B_AirRestr_Jun15_ext AirRestriction High 2 Pos #6

22 June 15, 2011 Perfor3_C_AirChgT_high_Jun15_ext AirChgHigh 1

23 June 15, 2011 Perfor3_C_AirChgT_high_Jun15_ext AirChgHigh 2

24 June 16, 2011 PerforM3_AirChg_low_Jun16_ext AirCharge 1

25 June 16, 2011 PerforM3_AirChg_low_Jun16_ext AirCharge 2

26 June 16, 2011 PerforM3_AirChg_low_Jun16_ext AirCharge 3

27 June 29, 2011 PerfM3_B_AirIntRes_Jun29_ext IntRestriction 1 Pos #5

28 June 29, 2011 PerfM3_B_AirIntRes_Jun29_ext IntRestriction 2 Pos #6

29 June 29, 2011 PerfM3_B_AirIntRes_Jun29_ext IntRestriction 3 Pos #7

30 July 6, 2011 PerforM3_B_BoostG_Jul6_ext Boost 1 Gain 0.85

31 July 6, 2011 PerforM3_B_BoostG_Jul6_ext Boost 2 Gain 0.95

32 July 6, 2011 PerforM3_B_BoostG_Jul6_ext Boost 3 Gain 1.00

33 July 13, 2011 PerforM3_ExhRestr_Jul13_ext ExhRestr 1 60%

34 July 13, 2011 PerforM3_ExhRestr_Jul13_ext ExhRestr 2 55%

35 July 13, 2011 PerforM3_ExhRestr_Jul13_ext ExhRestr 3 50%

36 July 13, 2011 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 1 42%

37 July 13, 2011 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 2 46%

38 July 13, 2011 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 3 50%

39 August 3, 2011 PerforM3_InjPresG_ext3_ext InjPress 1 Gain 1.0

40 August 4, 2011 PerforM3_InjPresG_ext3_ext InjPress 2 Gain 0.9

41 August 5, 2011 PerforM3_InjPresG_ext3_ext InjPress 3 Gain 1.1
5

From the data described, it was determined to initially work with the 45 signals from the CAN 

and dyno. Working with this set of low-cost sensor and CAN bus signals provides a path for a 

practical onboard implementation, and thus, is conducted first prior to considering vibration and 

other signals for developing health models. They also have been interpolated and aligned to the 

same 1 Sample/s acquisition rate, so were in a format that was ready to process. The CAN and 

dyno signals are identified in table 3. The 32 signals highlighted in orange were used in the 

analysis. The other 13 signals were not included because they are either operating conditions or 

have a low amount of variability.

Table 3. Signals recorded from CAN and dyno.

4. Modeling Approaches

Modeling approaches identified for the CAT 7 data, in order of complexity, included single 

parameter monitoring, correlation analysis, PCA monitoring methods, and AANN residual 

methods. Each of these methods has its advantages and disadvantages; table 4 lists each method 

along with important trade-offs. For the present study, only correlation analysis and PCA 

monitoring were undertaken. Single parameter modeling is very simple and can be done in real 

time; however, it requires extensive experience for setting thresholds for each variable, thus only 

an example of its application is presented at this time. The AANN method is well suited for this 

data and is being considered for future work. 
6

Table 1. Advantages and disadvantages for each modeling approach identified for the CAT 7 data.

Method Training 

Requirements Threshold Setting Positive/Negative

Single parameter 

monitoring

None

Experience or 

requires historical 

data

Simple but does not take into 

account relationship among 

variables

Correlation analysis Multiple baseline data 

sets

Experience or 

requires historical 

data

Takes into account variable 

interaction but a less 

established method than PCA

PCA monitoring Multiple baseline data 

sets

Established 

statistical limits

Well-established method but 

does not account for nonlinear 

interaction between variables

AANN method

Multiple baseline data 

sets and more 

computation

Statistical limits

Handles nonlinear variable 

interaction but requires more 

computation for training

4.1 Single Parameter Monitoring

Single parameter monitoring assumes that degradation in engine performance can be evaluated 

by one or more of the signals independently. It appears likely that this method can be applied to 

this data, but as mentioned, fault thresholds for a signal must be expertly set. Here we present 

only an example of how this method could be applied. First, it is noted that when the exhaust was 

restricted, the exhaust gas temperature is seen to be increased above baseline runs, as shown in 

figure 4. If it was known that an exhaust stack temperature above 1100 °F at an operating speed 

of 1450 RPM indicated that there was a blockage in the exhaust stack, then the faulted condition 

could be identified. Note that our example does not take into account what other variables might 

cause the exhaust stack temperature to increase.
7

Figure 4. Exhaust stack temperature for an exhaust restriction of 50% compared with baseline data.

4.2 Correlation Analysis

The main concept of this approach is to look for correlation changes with respect to a template 

file. The seven baseline runs identified for training in table 1 were used as the template. The list 

of processing steps follows: 

1. Select the regime and signal subset.

2. Perform the correlation matrix calculation for the baseline/template.

3. Perform the correlation matrix calculation for the test run.

4. Calculate the correlation difference matrix with respect to the template file.

5. Calculate a figure of merit (FOM) for the test run.

6. Health classification using a FOM threshold from the receiver operating characteristic 

curve (ROC curve)

The initial step includes the option of considering a particular operating regime or signal subset. 

A FOM value is calculated and provides a single indicator that can be used to assess the health 

condition of the engine. Additionally, searching the correlation difference matrix for maximum 

800 1000 1200 1400 1600 1800 2000 2200

750

800

850

900

950

1000

1050

1100

1150

1200

Time (s)

T-ExhStack

Time Plot of T-ExhStack

Base June 3

Base August 3

ExHRestr 50%
8

changes provides a way of identifying which signals are contributing to the anomalous 

performance. 

1. Signal Subset and Operating Regime

The correlation analysis focused on the 32 signals highlighted in table 3. Only data that 

were in the operating regime with engine speed above 1500 RPM and engine load above 

80% were considered; this included all of the standard run data, but cuts out deviations 

from the standard run that are in the actual data. 

2. Correlation and Correlation Difference Matrix

Correlation between two signals, si and sj, is defined as the covariance between those two 

signals normalized by the variance of each signal ssi and sj, as shown in equation 1.

i j s s

i j

ij

Cov s s

r

σ σ

( , ) = , (1)

where covariance is defined as the expected value expression in the numerator (equation 2). 

Note that the correlation is calculated for each signal pair and provides a matrix that is 

N x N in size, where N is the number of signals (2).

[( )( )]

i j

i j

s s

i s j s

ij

E s s

r

σ σ

− μ − μ = (2)

The correlation difference matrix is generated by subtracting the elements of the correlation 

matrix for the run data from the template and squaring it to produce a magnitude (equation

3).

( )

2 d r _ Run r _Template ij = ij − ij

(3)

Correlation difference matrix plots are shown in figures 5 and 6. Figure 5 shows difference 

plots for two of the baseline runs (healthy) and indicates a low level of variation in healthy 

sets. Figure 6 is for an exhaust restriction run and shows distinct differences in correlation 

from the healthy template, particularly, in the T-ExhStack sensor compared with almost 

every other sensor.
9

Figure 5. Correlation difference matrices for baseline runs (left) 3 and (right) 6.
10

Figure 6. Correlation difference matrix for a 46% exhaust restriction (run 36).

FOM Calculation and Health Assessment

For each test run, a FOM value based on the correlation difference matrix was calculated. The 

FOM was defined as the summation of the values of the correlation difference matrix (equation 

4):

∑∑= =

=

n

i

n

j

FOM dij

1 1

(4)

To evaluate health of the system based on this FOM, there needs to be a threshold established 

above which the engine will be considered to be in a faulted state. The receiver operating 

characteristic curve (ROC curve) is a common way of showing classification/detection results as 

a function of false positives and false negatives as a threshold is varied (3). Figure 7 shows the 

ROC curve for the FOMs of this data. In this case, a threshold of approximately 44.6 for the 

FOM value offers the best trade-off. This provides a false alarm rate of 5.56% and a missed 

detection of 46.7%. 
11

Figure 7. ROC curve for the correlation-based FOM.

The FOM health values are shown along with the threshold in figure 8. For the baseline runs, 10 

of the 11 runs were classified correctly as healthy (9.1% false alarm rate). Note that three 

additional baseline runs were added and given a later test number since these are from the files in 

which the gain was varied, but for these runs the gain was 1.0. For the seeded fault runs, 14 of 

the 30 were misclassified as healthy. The missed detection rate is quite high and highlights that 

this method has difficulty in detecting lower levels of degradation (associated with the lower 

levels of particular faults). There is some implication, however, that some lower fault levels may 

not degrade engine performance, and it may not be correct to call them “unhealthy.” In general, 

this method is detecting the more severe induced faults but not the lower levels of the same fault.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X: 0.05556

Y: 0.5333

False Positive Rate

True Positive Rate

Correlation Figure of Merit ROC Curve
12

Figure 8. Correlation FOM for all runs The first eight are baseline runs and the remainder are by test 

number from table 2. The plot excludes training runs.

4.3 Principal Component Analysis

The primary concept is to extract useful information from the data set by projecting the data into 

a new set of orthogonal coordinates. PCA does this by performing an eigenvalue/eigenvector 

calculation on the covariance matrix (4). Its use for data analysis is diverse; for health 

monitoring, the application here, its use for dimension reduction (5) is applied and it is also used 

to calculate monitoring statistics (6). Specifically, the statistics T2 and square prediction error 

(SPE) are calculated for the block of data in each operating regime. The mean of the health value 

in that block is used to decide on the health status based on thresholds derived from statistical 

theory. If any values are above those thresholds, contribution plots are used to further identify 

the source of the fault. Listed below are the steps that were followed. Details of the basic PCA 

calculations are omitted, and the reader is referred to references 4–8 for specifics on the use of 

PCA and formulae used:

1. Select the regime and signal subset

2. Normalize the data and calculate the covariance matrix for the training set.

3. Perform eigenvalue/eigenvector calculation of the covariance matrix.

4. Save PCA baseline models with normalization and eigenvalue/eigenvector information.

5. Normalize and project data from the monitored engine using baseline models.
13

f. Calculate the T2 and SPE health statistics and calculate the mean of these for the block of 

data.

g. Calculate the top contributors for each fault. 

The initial step is to select operating regimes and the signal list. The signals were the same as 

those used for the correlation analysis. Four regimes were selected, which represent steady state 

operating points in the performance test runs, as shown in table 5. To avoid transient effects, the 

first and last 20 s in a particular operating regime were not included in the calculations.

Table 2. Operating regimes for PCA analysis.

Regime No Engine RPM Engine Load Pedal %

1 1620–1820 60–100 80–100

2 1820 – 2020 60–100 80–100

3 2020–2200 60–100 80–100

4 2220–2420 60–100 80–100

After calculating the principal components, its is seen that the first few principal components can 

explain most of the variation seen in the data. The typical approach for determining the number 

of principal components to retain is to look at the eigenvalues (ranked in decreasing order) and 

select the ones that explain a high percentage of the variability in the data. In this analysis, the 

percentage was set to 85%. As an example, in the case of Regime 4, the top principal component 

accounts for 37% of the variability in the data set and the first eight account for 85%. Figure 9 

shows the decay in the variability for the first 10 signals; the variability continues to decay for 

the remaining 22. 
14

Figure 9. Percent of variability explained by each principal component (Regime 4).

Critical to the use of PCA for health monitoring are the calculation of the monitoring statistics T2 

and SPE, which are defined here with a full description available in reference 7. The T2 

calculation is similar to Mahalanobis distance, but is performed with the principal components, 

in our case, retained principal components, instead of the original data matrix (equation 5).

{ } [ ] { }

T

xr rxr xr T u u 1

1

1

2 − = ∑ , (5)

where r is the number of retained principal components,{ } xr u 1 are the retained principal 

components, and Σrxr are the retained eigenvalues 

The residuals, E, are calculated, which are essentially the difference between the model and 

actual data values (equation 6):

{ } { } { } [ ]

T

xn n xn u xr P nxr E x 1 = 1 − 1 , (6)

where, n are the number signals, { } xn x 1 are the actual signal values, and T P nxr [ ] are the retained 

eigenvectors.

SPE is the sum of the residuals (summed from residuals for each sensor) (equation 7):

∑=

=

n

i

SPE Ei

1

(7)
15

To make health assessments based on T2 and SPE values, thresholds were calculated using 

commonly accepted techniques described below (8, 9). The thresholds for T2 is calculated using 

equation 8, where r is the number of principal components retained, m is the number of samples 

in the training data set, a is the confidence level, and F is the F value from the F-distribution 

table:

( ) α , ,α

2 1 Fr m r m r

r m T − −

− = . (8)

The SPE thresholds calculation is provided in equation 9. It is quite involved because the 

distribution of SPE is a summation of Chi-square distributions. See reference 9 for more details.

Ca is the Z-value corresponding to a given confidence level (Normal Distribution Table) and l

are the eigenvalues calculated from the training data set:

(9)

PCA Results

Based on calculations for a 99% confidence level, the detection results are very good for most 

cases; the detection rates are shown in table 6. The results, in general, improve with engine 

speed. The false alarm rate is zero in all regimes except Regime 1. Even so, the two false alarms 

in Regime 1 had values that were only slightly above the detection threshold. Plots of SPE and 

T2 for each regime along with the thresholds are presented in figures 10–17. Note that the x-axes 

are the original test numbers and that the y-axes are on a logarithmic scale (this is because of the 

large range in values). As a significant note, the majority of the missed detections were for air 

intake restrictions. For example, four of the five missed detections in Regime 4 occurred for the 

air intake seeded fault; this unfortunately significantly reduces the overall detection rate. Also of 

value, the monitoring statistics show a correlation with fault severity, in that faults of increasing 

severity had higher (more degraded) health values.

( ) 0

1

2

1

2 0 0

1

2

2 0

1

1 1

2 hc h h h SPE 













 − = + +

θ

θ

θ

θ θ α

α

: , i 1,2,3

1

= ∑ = = +

n

j r

i Where θ i λ j

2

2

1 3

0 3

2

: 1

θ

θ θ and h = −
16

Table 3. Results of SPE and T2.

Regime Fault Detection Rate 

(SPE)

False Alarm 

Rate (SPE)

Fault Detection 

Rate (T2)

False Alarm 

Rate (T2)

1 80% 18.18% 73.33% 0.00%

2 80% 0.00% 70.00% 0.00%

3 83.33% 0.00% 73.33% 0.00%

4 83.33% 0.00% 83.33% 0.00%

Figure 10. Regime 1 SPE health values for each run.
17

Figure 11. Regime 1 T2 health values for each run.

Figure 12. Regime 2 SPE health values for each run.
18

Figure 13. Regime 2 T2 health values for each run

Figure 14. Regime 3 SPE health values for each run.
19

Figure 15. Regime 3 T2 health values for each run.

Figure 16. Regime 4 SPE health values for each run.
20

Figure 17. Regime 4 T2 health values for each run.

It is of interest to know which signals had the greatest contribution for a particular fault. The T2

and SPE contribution values for each of the signals are calculated using equations 7 and 8 (9). 

The results are presented in tables 7 and 8. An additional benefit from this study is that the 

contribution plot results could provide insight on what signals are important for single parameter 

monitoring.

(7)

(8)

where k varies from 1 to n for both equations 6 and 7.

In general, the top contributors for the SPE agree with a physical understanding of the engine 

and the faults that were seeded. For example, seeded faults with boost are showing that the boost 

sensor is the main contributor, and likewise seeded faults with exhaust restriction are showing 

that the exhaust pressure sensor is showing the most contribution. The contribution results from 

the T2 are more difficult to interpret in some instances, for example, the boost sensor is the top 

contributor for the higher exhaust restriction faults. The faults that were induced by adjusting a 

sensor gain gave virtually the same contribution results for both T2 and SPE; however, the 

mechanical faults based on restricting airflow resulted in different top contributors. Whether this 

{ } { } [ ] ({ } [ ] )

T

contribue k xr rxr kcolumn x Pkrow xr T u x 1 1 1

1

1

− = ∑

{ }

∑=

= n

i

contribute k

i

k

E

E

SPE

1

2

2
21

is always the case would require further experimentation and study. Figure 18 shows a particular 

run, 50% exhaust restriction, with the relative contributions of each sensor from SPE. In this 

case, the exhaust pressure sensor has a much higher contribution than the others, with the second 

largest contributor being the exhaust gas temperature.

Table 4. Signal contribution to fault detection from T2 calculation.

 Test # MatLAB File Name Fault Type Severity T Contribution 1 T Contribution 2

9 PerfM3_IntRestr_May27_ext IntakeAir Restric Test Pos # 4 'P-ExhB4Turbo2' 'P-ExhB4Turbo1'

10 PerfM3_IntRestr_May27_ext IntakeAir Restric Test Pos # 6 'ECM1-Boost' 'Sensor-Boost'

12 PerfM3_OilP_Jun8_par OilPress High Gain Gain 0.7 'ECM1-OilPres' 'EngOilP'

13 PerfM3_OilP_Jun8_par OilPress High Gain Gain 1.3 'ECM1-OilPres' 'EngOilP'

14 PerfM3_AirChgT_Jun10_ext AirCharge Temp high Shift Increased by 20o

F 'Sensor-AirIntMani' 'ECM1-AirIntMani'

15 PerfM3_AirChgT_Jun10_ext AirCharge Temp high Shift Increased by 30oF 'IntManiAirT' 'Sensor-AirIntMani'

16 PerfM3_AirChgT_Jun10_ext AirCharge Temp high Shift Increased by 50oF 'IntManiAirT' 'Sensor-AirIntMani'

17 Perfor3_AirRestr_Jun15_ext AirRestriction Low Pos # 2 'Sensor-InjPres' 'ECM1-InjPres'

18 Perfor3_AirRestr_Jun15_ext AirRestriction Low Pos # 3 'InjCtrlP' 'Sensor-InjPres'

19 Perfor3_AirRestr_Jun15_ext AirRestriction Low Pos # 4 'P-ExhB4Turbo2' 'P-ExhB4Turbo1'

20 Perfor3_B_AirRestr_Jun15_ext AirRestriction High Pos #5 'P-ExhB4Turbo2' 'P-ExhB4Turbo1'

21 Perfor3_B_AirRestr_Jun15_ext AirRestriction High Pos #6 'ECM1-Boost' 'Sensor-Boost'

22 Perfor3_C_AirChgT_high_Jun15_ext AirChgHigh 'IntManiAirT' 'Sensor-AirIntMani'

23 Perfor3_C_AirChgT_high_Jun15_ext AirChgHigh 'T-IntAirMani' 'Sensor-AirIntMani'

24 PerforM3_AirChg_low_Jun16_ext AirCharge 'Sensor-AirIntMani' 'ECM1-AirIntMani'

25 PerforM3_AirChg_low_Jun16_ext AirCharge 'ECM1-AirIntMani' 'IntManiAirT'

26 PerforM3_AirChg_low_Jun16_ext AirCharge 'P-ExhB4Turbo2' 'InjCtrlP'

27 PerfM3_B_AirIntRes_Jun29_ext IntRestriction Pos #5 'P-ExhB4Turbo2' 'ECM1-EngCoolT'

28 PerfM3_B_AirIntRes_Jun29_ext IntRestriction Pos #6 'P-ExhB4Turbo2' 'T-ExhB4Turbo2'

29 PerfM3_B_AirIntRes_Jun29_ext IntRestriction Pos #7 'ECM1-Boost' 'Sensor-Boost'

30 PerforM3_B_BoostG_Jul6_ext Boost Gain 0.85 'ECM1-Boost' 'Boost'

31 PerforM3_B_BoostG_Jul6_ext Boost Gain 0.95 'Sensor-Boost' 'P-ExhB4Turbo2'

33 PerforM3_ExhRestr_Jul13_ext ExhRestr 60% 'P-ExhB4Turbo2' 'P-ExhStack'

34 PerforM3_ExhRestr_Jul13_ext ExhRestr 55% 'P-ExhB4Turbo2' 'P-ExhStack'

35 PerforM3_ExhRestr_Jul13_ext ExhRestr 50% 'ECM1-Boost' 'Sensor-Boost'

36 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 42% 'Sensor-Boost' 'ECM1-Boost'

37 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 46% 'Sensor-Boost' 'ECM1-Boost'

38 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 50% 'ECM1-Boost' 'Sensor-Boost'

40 PerforM3_InjPresG_ext3_ext InjPress Gain 0.9 'Sensor-InjPres' 'T-ExhB4Turbo2'

41 PerforM3_InjPresG_ext3_ext InjPress Gain 1.1 'Sensor-InjPres' 'T-ExhB4Turbo2'
22

Table 5. Signal contribution to fault detection from SPE calculation.

Figure 18. SPE contribution plot, showing the relative contribution of each signal (50% exhaust restriction).

 Test # MatLAB File Name Fault Type Severity Q Contribution 1 Q Contribution 2

9 PerfM3_IntRestr_May27_ext IntakeAir Restric Test Pos # 4 'P-ExhB4Turbo2' 'P-AirB4Mani'

10 PerfM3_IntRestr_May27_ext IntakeAir Restric Test Pos # 6 'AirFlow' 'T-ExhB4Turbo2'

12 PerfM3_OilP_Jun8_par OilPress High Gain Gain 0.7 'ECM1-OilPres' 'EngOilP'

13 PerfM3_OilP_Jun8_par OilPress High Gain Gain 1.3 'ECM1-OilPres' 'EngOilP'

14 PerfM3_AirChgT_Jun10_ext AirCharge Temp high Shift Increased by 20o

F 'T-IntAirMani' 'IntManiAirT'

15 PerfM3_AirChgT_Jun10_ext AirCharge Temp high Shift Increased by 30o

F 'T-IntAirMani' 'IntManiAirT'

16 PerfM3_AirChgT_Jun10_ext AirCharge Temp high Shift Increased by 50oF 'T-IntAirMani' 'IntManiAirT'

17 Perfor3_AirRestr_Jun15_ext AirRestriction Low Pos # 2 'T-ExhB4Turbo2' 'P-ExhStack'

18 Perfor3_AirRestr_Jun15_ext AirRestriction Low Pos # 3 'Torque' 'P-ExhB4Turbo1'

19 Perfor3_AirRestr_Jun15_ext AirRestriction Low Pos # 4 'P-ExhB4Turbo2' 'AirFlow'

20 Perfor3_B_AirRestr_Jun15_ext AirRestriction High Pos #5 'P-ExhB4Turbo2' 'AirFlow'

21 Perfor3_B_AirRestr_Jun15_ext AirRestriction High Pos #6 'AirFlow' 'P-ExhB4Turbo2'

22 Perfor3_C_AirChgT_high_Jun15_ext AirChgHigh 'T-IntAirMani' 'T-ExhB4Turbo2'

23 Perfor3_C_AirChgT_high_Jun15_ext AirChgHigh 'Sensor-AirIntMani' 'ECM1-AirIntMani'

24 PerforM3_AirChg_low_Jun16_ext AirCharge 'T-IntAirMani' 'ECM1-EngCoolT'

25 PerforM3_AirChg_low_Jun16_ext AirCharge 'Sensor-AirIntMani' 'ECM1-EngCoolT'

26 PerforM3_AirChg_low_Jun16_ext AirCharge 'P-ExhB4Turbo2' 'P-aftTurbo'

27 PerfM3_B_AirIntRes_Jun29_ext IntRestriction Pos #5 'P-ExhB4Turbo2' 'AirFlow'

28 PerfM3_B_AirIntRes_Jun29_ext IntRestriction Pos #6 'P-ExhB4Turbo2' 'AirFlow'

29 PerfM3_B_AirIntRes_Jun29_ext IntRestriction Pos #7 'AirFlow' 'P-ExhB4Turbo2'

30 PerforM3_B_BoostG_Jul6_ext Boost Gain 0.85 'ECM1-Boost' 'Sensor-Boost'

31 PerforM3_B_BoostG_Jul6_ext Boost Gain 0.95 'ECM1-Boost' 'Sensor-Boost'

33 PerforM3_ExhRestr_Jul13_ext ExhRestr 60% 'P-ExhStack' 'P-ExhB4Turbo2'

34 PerforM3_ExhRestr_Jul13_ext ExhRestr 55% 'P-ExhStack' 'P-ExhB4Turbo2'

35 PerforM3_ExhRestr_Jul13_ext ExhRestr 50% 'P-ExhStack' 'T-ExhStack'

36 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 42% 'P-ExhStack' 'T-ExhStack'

37 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 46% 'P-ExhStack' 'T-ExhStack'

38 PerforM3_B_ExhRestr_Jul13_ext ExhRestr 50% 'P-ExhStack' 'T-ExhStack'

40 PerforM3_InjPresG_ext3_ext InjPress Gain 0.9 'Sensor-InjPres' 'ECM1-InjPres'

41 PerforM3_InjPresG_ext3_ext InjPress Gain 1.1 'Sensor-InjPres' 'ECM1-InjPres'
23

5. Discussion

Several items of interest were discovered in this preliminary study including relative 

performance of the methods evaluated as well as salient characteristics of the results. First, when 

faults were applied, differences in the sensor outputs were detected. Therefore, it is reasonable to 

assume that single parameter modeling can be applied to health assessment of the engine. Again, 

the caveat of requiring expert knowledge to set signal thresholds inhibits our use of this method 

at this time. Although such information is difficult to come by, if it were to become available,

then this method would be simple to implement. Second, it is seen that PCA is better suited to 

detect faults in this data than correlation analysis. The primary drawback of correlation analysis 

here is its inability to detect lower-level faults. There are several items of interest with PCA on 

this data set. It is a curiosity that the results improve with engine speed and we speculate that the 

effects of the fault are exacerbated as the speed increases. It is a matter for further study why the 

faults that were induced by adjusting a sensor gain gave the same contribution results for both T2

and SPE, while the mechanical induced faults gave different top contributors. Finally, there is the 

matter that both methods could not detect the faults in all but the highest states of intake air 

restriction. At this time, we can only suggest that the lower states do not appear to have a 

significant effect on engine performance. This emphasizes a point regarding the nature of this 

testing; although named seeded faults, the runs may be more accurately described as 

perturbations in operating variables and are not faults in the traditional sense. These 

perturbations may or may not adversely affect engine performance. With this in mind, our work 

is on the detectability of the perturbations; and whether or not they are critical to the actual 

“health” of the engine is uncertain.

6. Conclusion and Recommendations

Single parameter monitoring, correlation analysis, and PCA with two independent statistics—T2

and SPE—all show applicability to this problem. As discussed, single parameter monitoring can 

be pursued further if thresholds in signals become available. Encouragingly, both PCA statistics 

and correlation analysis detect the majority of the faults. PCA by far outperformed correlation 

analysis, and between the two any further work should focus on PCA. For the PCA method, 

various model refinements can be done, such as adjusting how many principal components to 

retain, using a smaller sensor subset, or incorporating the analog and Penn State data in the 

analysis. Finally, it is recommended to evaluate the data using nonlinear PCA; AANN is a 

proven way of implementing this approach (11). The motivation for using the AANN approach 

is based on the belief that some of the sensors in the engine have a nonlinear

relationship/correlation.
24

7. References

1. MIS 2000, Final Report, “A Dynamic Neural Network Approach to CBM”, Cooperative 

Agreement W911-09-2-0036.

2. Montgomery, D. C.; Runger, G. C.; Hubele, N. F. Engineering Statistics, Second edition, 

New York, Wiley, 2001.

3. Zweig, M.; Campbell, G. Receiver-Operating Characteristics (ROC) Plots: A Fundamental 

Evaluation Tool in Clinical Medicine. Clinical Chemistry 39 (4), pp. 561–577

4. Abdi, H.; Williams, L. J. Principal component analysis, Wiley Interdisciplinary Reviews. 

Computational Statistics 2010, 2, 433–450.

5. Worden, K.; Staszewski, W. J.; Hensman, J. J. Natural computing for mechanical system 

research: A tutorial overview. Mechanical Systems and Signal Processing 2011, 25, 4–111.

6. Kano, M.; Nagao, K.; Hasebe, S.; Hashimoto, I.; Ohno, H.; Strauss, R.; Bakshi, B. 

Comparison of statistical process monitoring methods: application to the Eastman challenge 

problem. Computers and Chemical Engineering 2000, 24, 175–181.

7. Gallagher, V. B.; Wise, R. M.; Butler, S. W.; White, D. D.; Barna, G. G. Development and 

benchmarking of multivariate statistical process control tools for semiconductor etch 

process; improving robustness through model updating. In proceedings of ADCHEM 97, pp. 

78–83, 1997.

8. Antory, D. Application of a data-driven monitoring technique to diagnose air leaks in an 

automotive diesel engine: A case study. Mechanical Systems and Signal Processing 2007, 

21 (2), 795–808.

9. Jackson, J. E.; Mudholkar, G. S. Control procedures for residuals associated with principal 

component analysis. Technometrics 2979, 331–349.

10. Kano, M.; Hasebe, S.; Hashimoto, I.; Strauss, R.; Bakshi, B. R.; Ohno, H. Contribution plots 

for fault identification based on the dissimilarity of process data. In AIChe Annual Meeting, 

Technical Presentation, 2000.

11. Kramer, M. A. Nonlinear principal component analysis using autoassociative neural 

networks. AIChe Journal 37 (2), 233–243.
25

List of Symbols, Abbreviations, and Acronyms

AANN auto-associative neural network based methods

ARL U.S. Army Research Laboratory

CAN controller-area network

DAQ data acquisition system

dyno dynamometer 

FOM figure of merit 

MIS Millennium Integrated Services

P&D prognostics and diagnostics

PCA principal component analysis

Penn State Pennsylvania State University 

ROC receiver operating characteristic curve

SPE square prediction error

TARDEC U.S. Army Tank and Automotive Research, Development and Engineering Center
26

NO. OF

COPIES ORGANIZATION

1 DEFENSE TECHNICAL

(PDF INFORMATION CTR

ONLY) DTIC OCA

8725 JOHN J KINGMAN RD

STE 0944

FORT BELVOIR VA 22060-6218

1 DIRECTOR

US ARMY RESEARCH LAB

IMNE ALC HRR

2800 POWDER MILL RD

ADELPHI MD 20783-1197

1 DIRECTOR

US ARMY RESEARCH LAB

RDRL CIO LL

2800 POWDER MILL RD

ADELPHI MD 20783-1197

1 DIRECTOR

US ARMY RESEARCH LAB

RDRL CIO MT

2800 POWDER MILL RD

ADELPHI MD 20783-1197

4 DIRECTOR

US ARMY RESEARCH LAB

ATTN: RDRL SER E

ANDREW J BAYBA

DAVID N SIEGEL

KWOK TOM

CANH LY

2800 POWDER MILL RD

ADELPHI MD 20783-1197

3 DIRECTOR

(PDF US ARMY RESEARCH LAB

ONLY) ATTN: RDRL VTM M HAILE

ATTN: RDRL VTM A GHOSHAL

ATTN: RDRL VTM M MURUGAN

BLDG 4603

APG MD 21005

NO. OF

COPIES ORGANIZATION

1 NASA GLENN

(PDF US ARMY RESEARCH LAB

ONLY) ATTN RDRL VTP B DYKAS

BLDG 23 RM W121

CLEVELAND OH 44135-3191

1 NASA GLENN

(PDF US ARMY RESEARCH LAB

ONLY) ATTN RDRL VTP H DECKER

BLDG 23 RM W121

CLEVELAND OH 44135-3191

3 US ARMY TARDEC

(PDF ATTN RDTA RS C BECK

ONLY) ATTN RDTA RS K FISHER

ATTN RDTA RS S HUSSAIN

MS# 204

6501 E 11 MILE RD

WARREN MI 48397-5000

1 USAMSAA

(PDF ATTN T. S. KILBY

ONLY) 392 HOPKINS RD

APG MD 21005

TOTAL: 17 (10 ELEC, 7 HCS)