A Constant False Alarm Rate- (CFAR) Based Change 

Detection Approach to Helicopter Diagnostics 

by Kenneth Ranney, Hiralal Khatri, Jerry Silvious, Kwok Tom, 

and Romeo del Rosario 

ARL-TN-0310 April 2008 

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Army Research Laboratory 

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ARL-TN-0310 April 2008 

A Constant False Alarm Rate- (CFAR) Based Change 

Detection Approach to Helicopter Diagnostics 

Kenneth Ranney, Hiralal Khatri, Jerry Silvious, Kwok Tom, 

and Romeo del Rosario 

Sensors and Electron Devices Directorate, ARL 

Approved for public release; distribution unlimited. 
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A Constant False Alarm Rate- (CFAR) Based Change Detection Approach to 

Helicopter Diagnostics 

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6. AUTHOR(S) 

Kenneth Ranney, Hiralal Khatri, Jerry Silvious, Kwok Tom, 

and Romeo del Rosario 

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U.S. Army Research Laboratory 

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13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

We extend results obtained for fault detection and present a procedure for calculating condition indicators that is tailored to

detect a recently observed fault. We illustrate how it arises naturally from consideration of statistics commonly calculated as

part of constant false alarm rate (CFAR) target detection algorithms. 

15. SUBJECT TERMS

Constant False Alarm Rate, Diagnostics, Fault Detection 

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Kenneth Ranney 

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iii 

Contents 

List of Figures iv

List of Tables iv

1. Introduction 1

2. Technical Approach 2

2.1 Failure Mode and Description of Available Data ...........................................................2 

2.2 CFAR-based CI Definition..............................................................................................4 

3. Results 6

4. Summary 8

5. References 9

Acronyms 10

Distribution List 11
iv 

List of Figures 

Figure 1. Indication of spectral bands of interest in the stored spectral HUMS data for the fault 

of interest. ............................................................................................................................... 4 

Figure 2. FFT output from different test runs for fault 1. Red plot indicates faulted data. ......... 6 

Figure 3. Plots of CI1 for all aircraft (faulted and non-faulted). .................................................... 7 

List of Tables 

Table 1. Data available for fault diagnosis for Aircraft Tail number 5180. .................................. 2 
1 

1. Introduction 

The U.S. Army has recently invested substantial time and effort in developing a condition based 

maintenance (CBM) system for its helicopter fleet. This system detects nascent equipment faults 

before they can progress to catastrophic malfunctions that seriously increase aircraft downtime 

and reduce fleet readiness (1–3). Clearly, a completely effective CBM system could realize both 

time and cost savings and increase operator safety by indicating components that require 

replacement. This is especially true if a periodic inspection of the faulty component is not 

scheduled in the near future. 

Part of the CBM system development consists of determining suitable condition indicators (CIs) 

capable of detecting incipient faults. These CIs then serve as input features to statistical 

analysis/detection algorithms that, in turn, decide if the feature level exceeds an alarm threshold. 

If the alarm threshold is exceeded, then the diagnosed fault is reported, and it can be repaired at 

the earliest opportunity. 

The CI definitions are often formulated with the goal of detecting specific faults frequently 

encountered during an aircraft’s maintenance cycle. Experimental investigations have also been 

conducted to better understand the physical phenomena and manifestations of various failure 

modes (4). The results have enabled investigators to better understand the underlying problem 

and define new CIs as the need arises. Hence, there is a need for continued formulation of 

additional CIs as new faults are discovered and new maintenance data becomes available—CIs 

that are uncorrelated with the existing ones. 

The U.S. Army Research Laboratory (ARL) has also addressed the diagnostics problem, 

exploiting archived maintenance records collected by the Health and Usage Monitoring System 

(HUMS) installed on specific Apache helicopters. We have obtained failure dates and failure 

modes for these aircraft and examined the relevant sensor data. Based on this analysis, we have 

been able to formulate new definitions for CIs to detect the onset of the described failure modes. 

These definitionsare similar to the classical constant false alarm rate (CFAR) and change 

detection test statistic definitions so familiar to the radar community. This report describes our 

approach and presents experimental results obtained using HUMS data from several aircraft, the 

vast majority of which did not experience the failure mode targeted by the new CI. 
2 

2. Technical Approach 

As mentioned in section 1, we had access to certain maintenance records from two specific 

Apache helicopters together with the failure modes that were discovered as a result of 

maintenance inspections. (This information was provided by Dr. Jonathan Keller, U.S. Army 

Aviation and Missile Research Development and Engineering Command (AMRDEC).) The 

available HUMS data comprised a set of preprocessed spectra collected at variably, sometimes 

widely, spaced intervals around the indicated failure dates. It included only a single example of 

a specific failure mode with a small amount of maintenance history available for each example. 

This sparseness of the data set exhibiting the failure mode of interest, together with the small 

number of available samples (both failed and non-failed) suggest that this investigation be 

considered as preliminary. Additional data examples (both failed and non-failed) are required to 

place it on a sound statistical footing. Still, the samples separated in time from those closest to 

the time of failure appear relatively consistent to one another in a sense that we quantify below. 

In addition, we observed certain unique qualities of the spectra collected closest to the failure 

date, and we developed CI definitions intended to detect these qualities if present. 

2.1 Failure Mode and Description of Available Data 

The failure mode that we initially investigated was due to the failure of the primary hydraulic 

pump on the left-hand side of the main transmission. To our knowledge, this particular failure 

mode instance was not detected by the current set of CIs, and it was identified during a manual 

inspection. In what follows, we will denote this as “fault 1”. Spectral data records from the 

HUMS system were available for the aircraft as described in table 1; these data provided the 

basis for our development of a new CI definition. 

Table 1. Data available for fault diagnosis for Aircraft Tail 

number 5180. 

Date Time Condition 

Dec. 2, 2005 13:01 Before fault, Fault 1 

Dec. 2, 2005 15:45 Before fault, Fault 1 

Dec. 2, 2005 22:58 Before fault, Fault 1 

Dec. 3, 2005 01:35 Before fault, Fault 1 

Dec. 3, 2005 02:37 Before fault, Fault 1 

Dec. 3, 2005 02:50 Before fault, Fault 1 

Dec. 3, 2005 03:06 Before fault, Fault 1 

Dec. 3, 2005 03:17 Before fault, Fault 1 

Dec. 3, 2005 12:13 Before fault, Fault 1 

Dec. 4, 2005 00:28 Before fault, Fault 1 

Dec. 4, 2005 22:10 Before fault, Fault 1 
3 

Table 1. Data available for fault diagnosis for Aircraft Tail 

number 5180 (continued). 

Date Time Condition

Dec. 5, 2005 02:31 Before fault , Fault 1 

Dec. 5 , 2005 13:06 Before fault , Fault 1 

Dec. 5, 2005 21:58 Before fault , Fault 1 

Dec. 6, 2005 22:14 Before fault , Fault 1 

Dec. 17, 2005 23:11 After fault , Fault 1 

Dec. 17, 2005 23:27 After fault , Fault 1 

Dec. 18 , 2005 13:01 After fault , Fault 1 

Dec. 18 , 2005 15:40 After fault , Fault 1 

NOTES: 

Failure date: Dec. 9, 2005 

Table for fault 1 data 

Since we were interested in components in the vicinity of the main transmission (hydraulic 

pumps), we selected (out of the data collected by 15 different sensors) the outputs from sensors 

“#1 Main GB” and “#3 Main GB”. Stored spectra were available for all dates listed in the table, 

and sample spectra from the #1 Main GB obtained on Dec. 5, Dec. 6, and Dec. 18, 2005 (all 

from Fault 1 data) are shown in figure 1. We note that data for Dec. 6, the date closest to the 

failure, is qualitatively different than the other two. (We assume that the defect was corrected 

before the Dec. 18 measurement.) In particular, we notice the spectral bands indicated in the 

figure by the red box. A similar plot for #3 Main GB yields another spectral band of interest as 

indicated by the red box and oval in the plots of figure 2. In each case, the x-axis denotes Fast 

Fourier Transform (FFT) bin number. 
4 

 (a) Spectra from “#1 MainGB” (b) Spectra from “#3 Main GB” 

Figure 1. Indication of spectral bands of interest in the stored spectral HUMS data for the fault of interest. 

Notes: 

1. Dec. 6 is the date closest to component failure. 

2. Units on the x-axis are FFT bin number. 

2.2 CFAR-based CI Definition 

Researchers have proposed several different CI (feature) definitions that capture anomalous 

behavior similar to that observed in figure 1. Some approach the problem using statistical 

techniques (5), others combine statistical approaches and physics-based data observations (1), 

while still others create physical models of the system in an effort to understand various faults 

(6). The CFAR-based approach that we propose is closest in spirit to the data-based methods 

because it relies on a set of training data to decide what is normal and abnormal system behavior. 

That is, a training set is used to set various algorithm parameters, in particular the detection 

threshold. 

Like many of the CIs developed to date, the resulting definition is highly tailored to the specific 

failure mode of interest. Our goal is to develop a feature that will detect a specific, newly 

identified defect while maintaining an acceptably low probability of false alarm (Pfa); it is this 

philosophy that leads us to refer to the CI definition as CFAR-based. 

We propose the following CI definitions based on empirical observations of data from 

#1 Main GB: 

CI1 (for fault 1): 

( )

∑ ∑

−

=

−

=

+ + +

− + = 1

0

1

0

2

2 2

2

2

1 1

1

0 0

1 1 2

( : ) 1 ( : ) 1

max ( : )

M

i

M

i

test test

test

F n n i

M

F n n i

M

F n B n B

CI , (1) 
5 

where Ftest(·) is the HUMS spectrum for the test data, n0 indicates the FFT bin number 

manifesting the fault, B is a small bandwidth allowing for frequency drift, n1 indicates the 

starting FFT bin number for background region 1, n2 indicates the starting FFT bin for 

background region 2, and M1 and M2 indicate the length of the spectral band (in bins) for 

background region 1 and background region 2, respectively. We base the selection of these 

frequencies of interest on the data sets enumerated in table 1 and illustrated to some extent in 

figure 1. The actual parameter values are determined empirically, utilizing a classical radarbased CFAR paradigm (7). Under these guidelines, n1 and n2 are selected to be “close” to n0

while still allowing a “guard band” to provide some degree of separation. Thus, the quantity in 

the denominator of equation 1 represents a background average that also serves as a 

normalization factor, and the size of spectral peaks are measured relative to the local spectral 

background. This also enables our selected threshold value to be independent, to some extent, of 

differences in scale between different data sets. As a result, an empirically determined threshold 

value should suffice to achieve relatively low false alarm rates. 

Based on initial experiments, we have determined that the values of M1=150, M2=150, n0=3080, 

n1=2800, n2=3150, and B=20 (corresponding to approximately 60 Hz) provide acceptable results. 

It must be stressed, however, that these numbers are based on an FFT length of 8192 points, and 

a total available spectrum of approximately 24 kHz. If the total spectrum bandwidth and FFT 

length were to change, then the corresponding bin numbers and frequency band lengths 

(expressed in units of FFT bin) would also have to change. In addition, it should also be stressed 

that data collected in the Survey mode and FPG101 state were used for this analysis. It would be 

necessary to verify that the same phenomenology is evident before the same algorithm is applied 

to data collected in different data collection states (i.e., different from FPG101). 

As a final note on the algorithm parameter definition and selection, we consider the motivation 

for including both the bandwidth, B, and the guard band around the test frequency bin. This 

decision is best understood by considering figure 2 below. The plots in figure 2 show that 

certain frequency bands may drift slightly from one data collection to the next; hence the 

maximum required by the numerator of equation 1 may not appear in the same bin from one data 

collection to the next. Hence, we need to include several bins around the frequency bin of 

interest to ensure that we capture the spike if it is present. Similarly, we include a guard band to 

ensure that we do not include sidebands due to the fault in our calculation of the spectral 

background. 
6 

Figure 2. FFT output from different test runs for fault 1. Red plot 

indicates faulted data. 

We have calculated feature values using all of the data from the faulted aircraft as well as unfaulted data from several other aircraft. These statistics are plotted and discussed in section 3. 

3. Results 

Figure 3 shows the feature values calculated for the faulted aircraft together with those calculated 

for a collection of non-faulted aircraft. The different aircraft are depicted by different line styles 

and colors, and for each of the aircraft the sample number increases with the date. That is, in 

figure 3(b), for example, sample 0 corresponds to Dec. 2, 2005, while sample 18 corresponds to 

Dec. 18, 2005. Note that there is no relationship between the data collection dates for the various 

aircraft, and the number of samples varies considerably from one aircraft to the next. 

We can see from the plots that a threshold could be chosen such that none of the non-faulted 

aircraft would produce false alarms while the “faulted” aircraft would still be flagged before the 

failure date. In addition, there are several early measurements (taken before those closest to 

failure) that indicate a potential problem. This indicates that the weight of evidence could be 

brought to bear to increase confidence in the final decision. 

We must note here that all of this analysis is based on a single failure example and utilizes field 

data collected as part of a specified operational testing procedure. By definition the amount of 

data available from such a collection protocol will be sparse. Hence, all of these results must be 

considered preliminary and doubtful until a statistically significant number of failure exemplars 

become available. 
7 

 (a) Plot of all CI1 values for 11 aircraft (including the faulted aircraft). The solid black lines indicate CI values 

from the faulted aircraft, while the different colors and line styles indicate other aircraft. 

(b) Plot of CI1 values for faulted aircraft. The dashed red line indicates the mean of all CIs from other aircraft, 

and the blue line indicates the maximum CI1 from all other aircraft. 

Figure 3. Plots of CI1 for all aircraft (faulted and non-faulted). 

Measurement number 

Faulted aircraft (solid black) 

CI value 

Sample number 

CI Value 

Max. of un-faulted 

Avg. of un-faulted 

Assumed 

closest to 

failure 
8 

4. Summary 

We have presented a method for calculating condition indicators based on CFAR automatic 

target detection (ATD) concepts. This development yields a ratio test that—since it is a ratio of a 

test cell magnitude to a RMS background average—allows the user to set a threshold limiting the 

number of false alarms. We have exercised the algorithm using several fault-free data sets and 

observed that we could, indeed, set a threshold that detected the fault while avoiding false 

alarms. Since we only had access to a single example of the failure mode, these results must be 

viewed as preliminary. 
9 

5. References 

1. Keller, J.; Branhof, R.; Dunaway, D.; Grabill, P. Examples of Condition Based Maintenance 

with the Vibration Management Enhancement Program. Proceedings of American 

Helicopter Society 61st Annual Forum, American Helicopter Society, Grapevine, Texas, June 

2005. 

2. Roemer, M.; Byington, C.; Kacprzynski, G.; Vachtsevanos, G. An Overview of Selected 

Prognostic Technologies with Application to Engine Health Management. Proceedings of 

GT2006 ASME Turbo Expo 2006: Power for Land, Sea, and Air, American Society of 

Mechanical Engineers, Barcelona, Spain, May, 2006. 

3. Brotherton, T.; Grabill, P.; Wroblewski, D.; Friend, R.; Sotomayer, B.; Berry, J. A Testbed 

for Data Fusion for Engine Diagnostics and Prognostics. Proceedings of the 2002 IEEE 

Aerospace Conference, Institute of Electrical and Electronics Engineers, Big Sky, Montana, 

March 2002. 

4. Chin, H.; Danai, K.; Lewicki, D. Pattern Classifier for Health Monitoring of Helicopter 

Gearboxes; NASA Technical Memorandum 106099, AVSCOM Technical Report 92-C-033; 

NASA Lewis Research Center: Cleveland, Ohio, 1993. 

5. Decker, H.; et al. Crack Detection for Aerospace Quality Spur Gears. Proceedings of the

American Helicopter Society 58th Annual Forum, American Helicopter Society, Montreal, 

Canada, June, 2002. 

6. Patrick-Aldaco, R. A Model Based Framework for Fault Diagnosis and Prognosis of 

Dynamical Systems with an Application to Helicopter Transmissions, Ph.D. Dissertation, 

Georgia Technical University, Atlanta, GA, August 2007. 

7. Skolnik, M. Radar Handbook; McGraw-Hill, Inc: 1990. 
10 

Acronyms 

AMRDEC U.S. Army Aviation and Missile Research Development and Engineering 

 Command 

ARL U.S. Army Research Laboratory 

ATD automatic target detection 

CBM condition based maintenance 

CFAR constant false alarm rate 

CI condition indicator 

FFT Fast Fourier Transform 

HUMS Health and Usage Monitoring System 

Pfa probability of false alarm 
11 

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