Donald L. Simon

Glenn Research Center, Cleveland, Ohio

Aidan W. Rinehart

Vantage Partners, LLC, Brook Park, Ohio

A Model-Based Anomaly Detection Approach 

for Analyzing Streaming Aircraft Engine 

Measurement Data

NASA/TM—2015-218454

January 2015

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Donald L. Simon

Glenn Research Center, Cleveland, Ohio

Aidan W. Rinehart

Vantage Partners, LLC, Brook Park, Ohio

A Model-Based Anomaly Detection Approach 

for Analyzing Streaming Aircraft Engine 

Measurement Data

NASA/TM—2015-218454

January 2015

GT2014–27172

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NASA/TM—2015-218454 1 

A Model-Based Anomaly Detection Approach for Analyzing 

Streaming Aircraft Engine Measurement Data 

Donald L. Simon 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Aidan W. Rinehart 

Vantage Partners, LLC 

Brook Park, Ohio 44142 

Abstract 

This paper presents a model-based anomaly detection 

architecture designed for analyzing streaming transient aircraft 

engine measurement data. The technique calculates and monitors 

residuals between sensed engine outputs and model predicted 

outputs for anomaly detection purposes. Pivotal to the 

performance of this technique is the ability to construct a model 

that accurately reflects the nominal operating performance of the 

engine. The dynamic model applied in the architecture is a 

piecewise linear design comprising steady-state trim points and 

dynamic state space matrices. A simple curve-fitting technique 

for updating the model trim point information based on steadystate information extracted from available nominal engine 

measurement data is presented. Results from the application of 

the model-based approach for processing actual engine test data 

are shown. These include both nominal fault-free test case data 

and seeded fault test case data. The results indicate that the 

updates applied to improve the model trim point information also 

improve anomaly detection performance. Recommendations for 

follow-on enhancements to the technique are also presented and 

discussed. 

Nomenclature 

C-MAPSS40k Commercial modular aero-propulsion system 

simulation, 40k 

FDI fault detection and isolation 

FOQA flight operations quality assurance 

PBM performance baseline model 

PWLM piecewise linear model 

RTSTM real-time self-tuning model 

WSSR weighted sum of squared residuals 

VIPR vehicle integrated propulsion research 

Introduction 

Aircraft operators rely on engine condition monitoring and gas 

path fault diagnostics to help ensure the safe and efficient 

operation of their gas turbine engine assets. A typical architecture 

depicting this functionality is shown in Figure 1. As shown, this 

architecture includes both on-board and ground-based 

functionality. On-board fault detection and isolation (FDI) logic 

continuously monitors control sensors and actuators. 

Additionally, automated data acquisition logic is applied to 

collect in-flight engine measurements. These engine 

measurements, along with any identified engine fault conditions 

identified by the on-board FDI logic, are transmitted off-board to 

fleet-wide ground stations that apply additional monitoring 

functionality. Conventionally, ground-based gas path diagnostic 

approaches are designed to analyze steady-state snapshot engine 

measurement data collected at a limited number of discrete 

operating points each flight. Early diagnosis of incipient fault 

conditions with minimal latency is challenging. However, 

advances in on-board processing and flight data recording 

capabilities are enabling the acquisition of full-flight streaming, 

or continuous, measurement data. This includes flight operation 

quality assurance (FOQA) and flight data monitoring programs 

implemented by airlines (Refs. 1 and 2). Such data span a broad 

range of aircraft flight conditions including transient engine 

operating scenarios. An example of aircraft engine flight data is 

shown in Figure 2. This figure shows full-flight data, which 

contains considerable transients, along with notional 

conventional snapshot measurement points. While this vastly 

expanded quantity of engine data presents new diagnostic 

opportunities, it also necessitates the development of new 

analysis approaches that account for the expanded quantity and 

dynamic content of the data. As the volume and availability of 

flight datasets continues to increase, the future emphasis on using 

these databases for performance and condition monitoring 

purposes is also expected to grow. 

In response to the need for new methods for analyzing aircraft 

flight data for health monitoring purposes, several research 

efforts in this area have been conducted within the aviation 

community. Chu and Gorinevsky have presented work on 

aircraft anomaly detection techniques applied for processing 

FOQA data (Refs. 3 and 4), and Das et al. have presented a data 

driven approach for anomaly detection in flight recorder data 

(Ref. 5).Merrington et al. applied analytical redundancy 

methods to process aircraft gas turbine engine transient 

measurement data (Ref. 6), and Kerr et al. (Ref. 7), Dewallef et 

al. (Ref. 8), and Borguet et al. (Ref. 9) have each proposed 

Kalman filter-based approaches for the on-line processing of 

aircraft engine measurement data for diagnostic purposes. 
NASA/TM—2015-218454 2 

Control

Logic

Gas Path Sensor

Measurements

Actuator

Commands

On-Board System

Ground-Based System

Ground

Station

Fleet-wide Trend 

Monitoring & Diagnostics

Transmission of “Snapshot” 

Reports and Engine Fault Codes

“Snapshot” Data

Acquisition Engine

Fault Codes

Fault Detection and

Isolation Logic

Figure 1.—Conventional aircraft engine condition monitoring and gas path 

fault diagnostic architecture.

Denotes notional “snapshot” measurement point

Altitude Fan Speed

Exhaust GasTemperature Fuel Flow

Figure 2.—Example commercial aircraft engine flight data.
NASA/TM—2015-218454 3 

Actuator Commands and 

Sensor Measurements

Fault Diagnostics

Real-Time Self-Tuning Model 

(Performance Trend Monitoring)

Performance 

Baseline Model

Aircraft Engine

Model Tuning Parameters

+

-

Compare Sensor Measurements 

to Baseline Model

u

y

yˆ

y

y

~

Figure 3.—Performance trend monitoring and gas path fault diagnostic architecture

Recently, NASA developed a unified approach for 

processing full-flight streaming engine data for performance 

estimation and fault diagnostic purposes (Refs. 10 and 11). This 

model-based approach is suitable for either post-flight or onboard processing of acquired engine flight data. Simulation 

studies have found this architecture to hold promise for 

analyzing streaming flight data either in real-time or post-flight. 

However, key to the performance of this or any other modelbased diagnostic technique is having a model that accurately 

reflects the nominal operating performance of the actual engine. 

Often, available engine models do not match the actual engine 

well due to modeling inaccuracies, or unaccounted 

enhancements, or configuration changes an engine design may 

undergo over its lifecycle. These issues can negatively impact 

the performance of model-based diagnostic approaches. In 

Reference 12, a hybrid modeling approach is applied 

combining analytical and empirical modeling to achieve 

improved model-to-engine matching. The empirical component 

of this hybrid model is based on a neural network trained to 

learn observed residuals between the engine and the model 

based on available engine measurement data. This has been 

shown to improve model-to-engine matching, but only 

addresses the portion of the engine operating envelope from 

which measurement data is available for training the neural 

network. The study presented in this paper addresses engine-tomodel inaccuracies by applying a simple curve fitting technique 

for updating the model based on steady-state information 

extracted from nominal engine measurement data. Furthermore, 

the identified curve fits can be readily extended (extrapolated) 

to additional portions of the operating envelope beyond that 

from which measurement data is available. This technique has 

been found to improve overall model accuracy and enable 

successful anomaly detection when implemented within the 

NASA-developed model-based diagnostic architecture. 

The paper is organized as follows. First, the NASAdeveloped model-based architecture for integrated aircraft 

engine performance estimation and fault diagnostics is 

presented. This is followed by a description of model 

enhancements made to improve engine-to-model matching 

based on available nominal engine measurement data. Next, the 

architecture is applied to analyze actual engine test data 

including both nominal and faulty engine operating scenarios. 

The architecture’s anomaly detection performance with and 

without the model enhancements are presented and compared. 

This is followed by a discussion of potential follow-on work 

and conclusions. 

Model-Based Architecture for Processing 

Streaming Aircraft Engine Measurement 

Data 

The NASA-developed model-based architecture for integrated 

aircraft engine performance estimation and fault diagnostics is 

shown in Figure 3. It contains two models designed to operate in 

parallel—a real-time self-tuning model (RTSTM) and a 

performance baseline model (PBM). The RTSTM is a self-tuning 

engine model based on a piecewise linear Kalman filter. It selftunes to account for performance deterioration that the engine 

may incur over time with usage. The RTSTM is capable of 

providing real-time estimates of measured and unmeasured 

engine performance parameters for condition monitoring 

purposes. The PBM is designed to provide a reference baseline 

of recent past engine performance. It incorporates a version of the 

same piecewise linear model used in implementing the RTSTM. 

The PBM accepts inputs consisting of actuator commands, u, and 

a parameter representative of engine power, yr, such as fan speed 

or engine pressure ratio. The PBM is driven to the power 

reference parameter to prevent the model from inadvertently 

diverging from the engine. In addition to receiving continuous 

inputs from the engine, the model also automatically receives 

periodically updated tuning parameter estimates from the 

RTSTM. This periodic update of the tuning parameters allows 

the PBM to adapt to normal performance deterioration that 

occurs gradually over time, but prevents the model from 

immediately adapting to rapid performance shifts caused by 
NASA/TM—2015-218454 4 

faults. The frequency of the periodic tuning parameter update is 

user-specified, but is recommended to be on the order of once per 

flight. Sensed engine outputs, y, and PBM predicted engine 

outputs, yˆ , are compared, and the resulting residual vector, y

~ , 

is analyzed for diagnostic purposes. Small residuals indicate that 

the engine is operating nominally, whereas large residuals 

indicate anomalous engine behavior. 

The subsections below will first discuss the construction of a 

piecewise linear model used to implement the RTSTM and PBM, 

followed by a description of the anomaly detection logic applied 

within the performance trend monitoring and gas path diagnostic 

architecture. This is followed by a description of the 

enhancements made to help improve model-to-engine matching. 

Piecewise Linear Model Implementation 

An aircraft engine piecewise linear model (PWLM) is created 

from an available transient nonlinear engine model, or cycle 

deck. Linear state space system point models are extracted from 

the nonlinear model and then combined and scheduled for 

interpolation based on engine operating point. In this fashion the 

PWLM is able to approximate the transient full-envelope 

nonlinear model response, while offering advantages over the 

more complex nonlinear model. A PWLM is usually less 

computationally intensive than its nonlinear equivalent, and the 

simpler structure allows for straightforward design of linear 

estimation approaches such as a Kalman filter. A detailed 

description of PWLM construction can be found in Reference 13, 

and is summarized below. 

The nonlinear model of an aircraft engine is assumed to be 

represented by the following equations 

( , , )

( , , )

y g x u h

x f x u h

 

 (1) 

where x and u represent the vectors of engine state variables and 

control command inputs, respectively. The vector h represents 

health parameters, such as efficiency or flow capacity, reflective 

of performance deterioration within the major rotating modules of 

the engine. For given input values, the nonlinear functions f and g

generate the vectors of state derivatives x , and sensed engine 

outputs y, respectively. By linearizing the engine model at a given 

operating point, the following state-space equations can be 

obtained: 

  

  

y C x D u M h

y y C x x D u u M h h

x A x B u L h

x A x x B u u L h h

h

ref

u

trim

x

trim

y

trim

h

ref

u

trim

x

trim

' '  '  '

     

 '  '  '

     

' ' ' '

' ' '

	
 	
 	
 	




	
 	
 	
 

( )

( )

(2)

Here, A, B, C, D, L, and M are the state-space matrices 

reflecting system dynamics. The trim vectors, denoted by the 

subscript “trim,” reflect the values of the state variables, 

commands, and sensed outputs when the model is at steadystate (i.e., x = 0) at the given operating point. Collectively, 

the trim vectors define what is referred to as a “trim point.” 

The vector href represents a reference health condition 

specified by the system designer. In Equation (2), parameter 

deviations relative to trim or reference conditions are denoted 

by the delta symbol ('). A block diagram illustration of the 

linear state space model implementation at a single operating 

point is shown in Figure 4. 

The initial step in creating this PWLM is the computation of 

linear state-space models from the nonlinear model at multiple 

operating points. These operating points serve as the interpolation 

scheduling parameters in the piecewise linear model. Figure 5 

shows a notional three-dimensional example of operating point 

specification using altitude, Mach number, and power setting as the 

scheduling parameters. The number of operating points and 

spacing between operating points, which does not have to be 

uniform, are design decisions left to the end user. 

L

D

A

B C u ++ +- +

+ ++

utrim ytrim

M

'u ਄ 'x 'y y

h

href

xtrim

x ++

-

+

+

s

1

Figure 4.—Linear state-space model implementation
NASA/TM—2015-218454 5 

Power

Reference

Parameter

Altitude

Mach

o denotes location in 3-dimensional 

space defining an operating point

Figure 5.—Example of three-dimensional piecewise linear 

model operating point scheduling.

Anomaly Detection 

Within the model-based diagnostic architecture, anomaly 

detection is performed by monitoring residuals between sensed 

engine outputs and those predicted by the PBM (see Figure 3). 

If no fault is present, the engine and PBM are expected to be in 

good agreement, in which case the residuals will be small. 

Conversely, in the event of a system fault impacting engine 

performance, the engine and PBM will diverge and the 

residuals will increase. Anomaly detection is performed by 

monitoring a weighted sum of squared residuals (WSSR), 

which is calculated as shown in Equation (3) 

y R y WSSR ~T 1~ (3) 

Here, y

~ is the vector of measurement residuals reflecting the 

difference between sensed engine outputs and PBM produced 

outputs and R is the sensor measurement covariance matrix. If 

necessary, the WSSR signal can be filtered to smooth the signal 

and eliminate any short-term outliers contained therein. The 

WSSR signal is compared against a defined threshold, and if 

that threshold is exceeded an anomaly is declared. 

Re-Trimming of Piecewise Linear Model 

As mentioned previously, a model’s ability to accurately 

reflect the sensed outputs of the actual engine is key in enabling 

effective model-based diagnostic methods based on that model. 

The step taken in this study to improve engine-to-model steadystate matching is to “re-trim” the PWLM based on nominal 

steady-state engine data extracted from engine flight data or test 

cell data. Re-trimming the model entails adjusting the utrim and 

ytrim vectors along with any sensed elements of the xtrim vector 

shown in Equation (2) to match the acquired steady-state data. 

The re-trimming process is envisioned to occur at relatively 

infrequent intervals, for example, when an engine first enters 

into service or undergoes a major overhaul. Additionally, for 

on-board applications this is not intended to occur on-board the 

aircraft. Rather, the intent is for the model to be re-trimmed offline (off-board), and then loaded into an on-board processor. 

The steps in the re-trimming process include identifying engine 

steady-state operating points over a range of power settings, 

applying a polynomial curve fit to that data, and adjusting the 

model trim vector information to match the polynomial curve 

fit. Each step is further discussed below. 

Identification of Engine Steady-State Operating Points 

In this study, steady-state engine operating performance is 

approximated based on streaming engine measurement data 

acquired under known nominal (fault-free) conditions from a 

single engine. A fixed-time length sliding window approach is 

applied to analyze the data and determine whether each 

individual sample of measurement data is reflective of steadystate engine operation. Several criteria must be met to satisfy 

the steady-state assumption. First, engine operating conditions 

(e.g., pressure altitude and Mach number) must remain within 

defined ranges over the past fixed-time window. Second, the 

standard deviation of select engine measurement parameters in 

the window must be below defined thresholds. Finally, the 

absolute difference between the current sample and the mean 

within the window for select engine measurement parameters 

must be below defined thresholds. If all of these criteria are met, 

the engine is assumed to be at steady-state and the current 
NASA/TM—2015-218454 6 

vector of measurement data is archived for subsequent use in 

obtaining the polynomial curve fits that will be used for retrimming the model. The sliding window is then advanced 

forward one time step and the process is repeated on the next 

data point. 

Polynomial Curve Fit 

Given the acquired engine steady-state data within a fixed 

pressure altitude and Mach number range, the next step is to 

apply a curve fit through each measured parameter plotted 

against the engine power reference parameter used in the 

PWLM. This power reference parameter is typically a 

parameter such as corrected fan speed or engine pressure ratio. 

At any arbitrary steady-state sample k, an nth order polynomial 

equation expressing a measured engine output, yi, as a function 

of the engine power reference parameter, yr, can be written as 

n

r k i n r k yi k pi pi yr k pi y p y , , 2

, , ,0  ,1 ,  ,2  (4) 

where pi,0, pi,1, pi,2, ..., pi,n are the polynomial coefficients. 

Assuming N steady-state samples have been identified, the 

polynomial equations for these samples can be concatenated as 

shown in Equation (5) 

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as 

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,

,2

,1

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, 2, ,

,2

2

,2 ,2

,1

2

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where Yi is an Nu1 vector of steady-state measurements for 

parameter yi, Pi is an nx1 vector of polynomial coefficients, and 

Hr is an Nun matrix relating Pi to Yi. An estimate of the vector 

of polynomial coefficients, Pi

ˆ , can be obtained applying a least 

squares solution as shown in Equation (7) 

  i T r r T Pi Hr H H Y 1 ˆ  (7)

A notional illustration of a polynomial curve fit through 

acquired steady-state data is shown in Figure 6. Here, a single 

engine output, yi, is plotted against the power reference 

parameter, yr. The red line represents the yi vs. yr curve based 

on trim point information contained in the original PWLM, the 

black “x’s” represent steady-state data points based on actual 

sensed engine data, and the blue curve is the polynomial curve 

fit through those steady-state points. Note that the polynomial 

curve fit provides a better representation of actual engine 

performance compared to that of the original model. It is noted 

that Equations (4) to (7) only illustrate the polynomial curve 

fitting process for a single element (i.e., the i

th element) of the 

sensed measurement trim vector, ytrim. Although not shown, an 

analogous set of equations are also produced and applied in 

order to construct unique curve fits for each additional element 

of the piecewise linear model ytrim vector, each element of the 

utrim vector, and any sensed elements of the xtrim vector. 

Furthermore, for an individual actuator command or state 

variable, the yi information shown in Equations (4) to (7) is to 

be replaced with ui or xi, respectively. 

A necessity for constructing accurate curve fits is the need for 

a suitable amount of steady-state data points distributed across 

a broad range of engine power settings. If most of the steadystate data points are concentrated in a narrow yr range it will be 

difficult to obtain curve fits that reflect the true performance of 

the engine. 

Adjusting Model Trim Points 

Once polynomial curve fits have been identified for each 

parameter, that information is used to adjust, or “re-trim,” the 

piecewise linear model trim points. This is illustrated in 

Figure 7. Here, the solid red and blue lines represent the original 

and the re-trimmed yi vs. yr curves for the given altitude and 

Mach number range where the steady-state data points were 

Figure 6.—Illustration of steady-state data polynomial curve fit

yr

yi

Original model

Engine steady-state data point

Steady-state data polynomial curve fit
NASA/TM—2015-218454 7 

yr

yi

Original model

Re-trimmed model

Step 1: Calculate 

scale factors and 

offsets representing 

separation between 

curves in the 

original model

Step 2: Apply 

obtained scale 

factors and offsets 

to generate 

additional curves in 

the re-trimmed 

model at operating 

conditions where 

steady-state data is 

unavailable

Figure 7.—Illustration of re-trimmed piecewise linear model

obtained. The lighter dashed lines represent curves at additional 

altitude and Mach numbers. If sufficient steady-state data is 

available, curve fits may be performed at different altitude and 

Mach number combinations. However, for those altitude and 

Mach numbers where steady-state data is limited or 

unavailable, yi vs. yr curves can be approximated based on a 

curve fit performed at another operating point. This is done by 

first applying a least squares calculation to determine a scale 

factor and offset reflecting the separation between two yi vs. yr

curves in the original model—specifically, the separation 

between a curve where steady-state data is available (solid red 

line in Figure 7) and a second curve at the altitude and Mach 

number where steady-state data is unavailable (a dashed red line 

in Figure 7). Next, the obtained scale factor and offset is applied 

to adjust the re-trimmed model yi vs. yr curve (solid blue line in 

Figure 7) by a proportionate amount, thus enabling the 

calculation of a re-trimmed model yi vs. yr curve at the 

corresponding altitude and Mach number (a dashed blue line in 

Figure 7). This process is repeated to calculate and apply a 

unique scale factor and offset adjustment for each yi vs. yr curve 

at each altitude and Mach number combination in the model. 

Application Example 

In this section, an example application of the model-based 

anomaly detection architecture processing actual engine test 

data is presented. This example demonstrates the processing of 

data acquired during the NASA Vehicle Integrated Propulsion 

Research (VIPR) test program—a ground test conducted at 

NASA Dryden Flight Research Center and the Edwards Air 

Force Base on a C-17 aircraft equipped with Pratt & Whitney 

F117 turbofan engines. An objective of the VIPR program is to 

develop and demonstrate engine health management 

technologies including advanced sensors and diagnostic 

algorithms. The VIPR program included both nominal (faultfree) and non-damaging seeded fault engine test scenarios. 

The engine gas path sensor measurements and actuator 

commands acquired during the VIPR testing are shown in 

Table 1 and Table 2, respectively. The model-based anomaly 

detection architecture, shown in Figure 3, was designed and 

applied for processing this data. This architecture was 

developed using the NASA C-MAPSS40k turbofan engine 

model (Ref. 14). While of the same thrust category as the Pratt 

& Whitney F117 turbofan engines used in the VIPR test, 

C-MAPSS40k is not the same engine and therefore notable 

engine-to-model mismatches exist. As such, updating of the 

model is necessary to achieve suitable matching with the 

engines. The subsections below will first discuss re-trimming 

of the piecewise linear model and then show anomaly detection 

and RTSTM Kalman filter tuning parameter estimation results 

obtained by updating the model. 

TABLE 1.—GAS PATH SENSOR MEASUREMENTS 

Symbol Description 

N1 Fan speed 

N2 Core speed 

Ps3 High pressure compressor exit static pressure 

T35 High pressure compressor exit total temperature 

P5 Low pressure turbine exit total pressure 

T5 Low pressure turbine exit total temperature 

TABLE 2.—ACTUATOR COMMANDS 

Symbol Description 

Wf Fuel flow 

VSV Variable stator vanes 

BLD25 Station 2.5 bleed valve 

BLD14 14th stage bleed valve 
NASA/TM—2015-218454 8 

Re-Trimming of Piecewise Linear Model 

The first step in re-trimming the model is to identify steadystate data points within the available nominal (fault-free) data. 

During the VIPR test, several fault-free “baseline” runs were 

conducted where the engine was operated over a range of power 

settings spanning idle to max power. Figure 8 shows the time 

history of one of the engine gas path measurement parameters 

acquired during a VIPR test baseline run. In this figure, and all 

other figures in this section of the paper, units have been 

omitted and y-axis parameter names are simply referred to as yi

to protect the proprietary nature of the data. As shown in 

Figure 8, the baseline run consists of a series of steady-state 

stair steps in power settings starting at idle, stepping up to 

max power, and then stepping back down to idle. The steadystate stair steps are then followed by a gradual 

acceleration/deceleration (idle-max-idle), and then a rapid 

acceleration/deceleration (idle-max-idle). In the figure, the blue 

line represents the acquired raw data and the red dots represent 

identified steady-state data points. Here, the steady-state criteria 

was defined as a data point where the standard deviation of both 

N1 and N2 is below 25 rpm based on a 100 sec window of past 

data and the absolute residual between the current data point 

and the mean value over past 100 sec window of N1 and N2 is 

less than 20 rpm. If these criteria are all met the engine is 

assumed to be at steady-state. 

Figure 9 and Figure 10 show example steady-state yi vs. yr

curves for two of the acquired engine gas path parameters. Here, 

corrected fan speed is used as the power reference parameter, yr, 

and the yi parameters are labeled as ya and yb in Figure 9 and 

Figure 10, respectively. Each figure shows the original 

C-MAPSS40k generated curves (red line), steady-state data 

points identified from VIPR nominal baseline runs (black “X’s”), 

and a fourth order polynomial curve fit through the acquired 

steady-state data points (blue line). The order of this curve fit was 

determined manually through trial and error. As seen in these 

figures, the original piecewise linear model based on 

C-MAPSS40k does not match the steady-state performance of 

the actual engine. However, the polynomial curve fit is able to 

match the steady-state data points fairly well. Since the VIPR test 

was a ground test all of the data was acquired at zero Mach and 

approximately the same pressure altitude. Figure 11 and Figure 

12 illustrate the extension of the data collected at this operating 

point to other altitude and Mach numbers for the purpose of retrimming the entire piecewise linear model. All parameters are 

shown as corrected parameters. Since the VIPR data exhibited no 

Mach number variation and limited pressure altitude variation, it 

was not possible to validate whether the re-trimmed model 

accurately matched the actual engine over the entire operating 

envelope. However, this will be assessed in future studies 

focused on the processing of actual engine flight data spanning a 

broad operating range of altitudes and Mach numbers. 

Figure 8.—Example of steady-state data points identified within 

a baseline run

Figure 9.—Original model and polynomial curve fit through 

steady-state data (parameter ya)

Figure 10.—Original model and polynomial curve fit through 

steady-state data (parameter yb)

Time

yi

Raw data

Steady-state data point

N1corrected

y

a

Original model

Engine steady-state data point

Steady-state data polynomial curve fit

N1corrected

y

b

Original model

Engine steady-state data point

Steady-state data polynomial curve fit
NASA/TM—2015-218454 9 

Figure 11.—Original and re-trimmed PWLM (parameter ya)

Figure 12.—Original and re-trimmed PWLM (parameter yb)

Figure 13.—Nominal baseline #1

Residual Calculation 

The model-based anomaly detection architecture was 

updated to use the re-trimmed piecewise linear model design. 

Then, both nominal and faulty data acquired during the VIPR 

testing was supplied as input to the architecture. Figure 13 and 

Figure 14 show the benefit of using the re-trimmed piecewise 

linear model compared to the original piecewise linear model 

for processing nominal fault-free data acquired during two of 

the VIPR baseline runs. The top half of each figure shows 

information for one of the engine sensed gas path parameters, 

yi, including the actual engine measurement (green line), the 

estimated value produced by the original PBM model (red line), 

and the estimated value produced by the re-trimmed PBM 

model (blue line). Note that the engine measurement (green 

line) is partially obscured by the re-trimmed PBM (blue line) in 

these plots. The bottom half of each figure shows the yi residual 

between the engine measurement and the original PBM (red 

line) and the re-trimmed PBM (blue line). For both of the 

baseline runs, the re-trimmed model provides much better 

matching with the actual engine, which is desired in these cases 

where no fault is present. Conversely, the original model 

exhibits a large amount of mismatch, which limits its utility for 

fault detection purposes. 

Figure 15 and Figure 16show residual results obtained by 

processing two of the bleed fault cases conducted during the 

VIPR testing. This includes a station 2.5 bleed fault case 

(Figure 15) and a 14th stage bleed fault case (Figure 16). In each 

case the bleed valves were failed open. The time of fault 

insertion is denoted by the red vertical arrows in each figure. 

Once again, the top half of each figure shows the engine 

measurement, the original model PBM produced estimate, and 

the re-trimmed PBM model produced estimate of yi while the 

bottom half of each figure shows the residual information for 

Figure 14.—Nominal baseline #2

N1corrected

y

a

Original model

Re-trimmed model

N1corrected

y

b

Original model

Re-trimmed model

yi

0 500 1000 1500 2000 2500 3000 3500

0

Time (s)

y

i residual

Engine measurement

Original PBM

Re-trimmed PBM

Original PBM

Re-trimmed PBM

yi

0 500 1000 1500 2000 2500 3000 3500 4000

0

Time (s)

yi residual

Engine measurement

Original PBM

Re-trimmed PBM

Original PBM

Re-trimmed PBM
NASA/TM—2015-218454 10 

the original model and the re-trimmed model. In cases such as 

these where a fault is present, it is necessary for the sensed 

engine outputs and the PBM produced estimated outputs to 

diverge in order for the anomaly to be readily detectable. While 

the original model still exhibits large residuals in these cases we 

can observe that the re-trimmed model also diverges from the 

measured engine output, albeit to a lesser extent. For the station 

2.5 bleed fault, shown in Figure 15, the engine and the PBM 

agree well at lower power conditions and do not noticeably 

diverge until the engine reaches higher power settings. This is 

expected as this is a modulated bleed valve and it is normally 

scheduled open at low power settings and modulates closed as 

the engine moves to higher power settings. As such, the engine 

and PBM agree at lower power settings and begin to diverge as 

the engine increases in power. For the 14th stage bleed fault, 

shown in Figure 16, the valve is normally closed under most 

operating conditions. For this fault case, a change in the 

residuals is immediately apparent as soon as the valve is failed 

open. 

Anomaly Detection 

The vector of engine sensed measurements versus PBM 

output residuals, y

~ , are used to construct a weighted sum of 

squared residuals (WSSR) as previously shown in Equation (3). 

The measurement residual matrix, R, applied within this 

equation was determined empirically by calculating the 

covariance in the residuals based on the available nominal 

baseline run data. The residuals used to produce the WSSR 

signal consist of all sensor measurements shown in Table 1, 

with the exception of the N1 measurement, which is used as a 

PBM input. Anomaly detection is then performed by comparing 

the WSSR signal against a defined anomaly detection threshold. 

If this threshold is exceeded, an anomaly is declared. 

The WSSR results obtained by processing the acquired VIPR 

data are shown in Figure 17 to Figure 20. Here, only re-trimmed 

PBM results are shown. When using the original PBM it was 

not possible to reliably distinguish between normal and 

anomalous engine behavior due to the large mismatch between 

the engine and the model. The top half of each figure shows a 

time history plot of one of the measured gas path parameters 

(denoted as yi) and the bottom half of the figure shows the 

corresponding WSSR information (blue line) and a threshold 

applied and monitored for anomaly detection purposes 

(magenta dashed line). This threshold was manually set to 

ensure that no false alarms were generated when processing the 

nominal (fault-free) engine data acquired during VIPR testing. 

Additionally, the WSSR signal was processed through a median 

filter (Ref. 15) to help smooth the signal and reduce noise. The 

median filtered WSSR signal is shown in the plots. For the two 

baseline runs, shown in Figure 17 and Figure 18, the filtered 

Figure 15.—Station 2.5 bleed valve fault

Figure 16.—The 14th stage bleed valve fault

Figure 17.—Nominal baseline run #1

yi

Engine measurement

Original PBM

Re-trimmed PBM

0 500 1000 1500 2000 2500 3000

0

Time (s)

yi residual

Original PBM

Re-trimmed PBM

Fault

Inserted

yi

Engine measurement

Original PBM

Re-trimmed PBM

0 500 1000 1500 2000 2500

0

Time (s)

yi residual

Original PBM

Re-trimmed PBM

Fault 

Inserted

y

i

0 500 1000 1500 2000 2500 3000 3500

WSSR

Time (sec)

Engine measurement

Re-trimmed PBM

WSSR

Anomaly detection threshold
NASA/TM—2015-218454 11 

Figure 18.—Nominal baseline run #2

Figure 19.—Station 2.5 bleed valve fault

Figure 20.—The 14th stage bleed valve fault

WSSR signal remains below the threshold throughout the entire 

test case although increases in the WSSR are evident during 

transients. The two bleed valve fault cases are shown in Figure 19 

and Figure 20. In each figure the time of fault insertion is denoted 

by the red vertical arrows. For the station 2.5 bleed fault case 

shown in Figure 19, the WSSR signal exceeds the anomaly 

detection threshold when the engine is taken to higher 

power settings in the 900 to 1000 sec timeframe, which is 

expected as this is where the valve would normally be partially 

or fully closed. It is noted that the WSSR anomaly detection 

threshold is not exceeded during the engine transients performed 

around the 2600 to 2800 sec timeframe even though the engine is 

taken to a power setting where off-nominal 2.5 bleed operation 

should be noticeable. This is due to the applied filtering of the 

WSSR signal and the magnitude of the fault-induced 

performance shift. 

For the 14th stage bleed fault case shown in Figure 20, the 

filtered WSSR signal exceeds the anomaly detection threshold 

soon after the fault is inserted and remains above the detection 

threshold throughout the remainder of the test case, including 

the transients towards the end of the test case. Comparing 

Figure 19 and Figure 20 it can be observed that the 14th stage 

bleed valve fault has a larger impact on engine performance 

than the station 2.5 bleed fault, making it more readily 

detectable. 

RTSTM Kalman Filter Tuning Parameter 

Estimation 

Like the PBM, the RTSTM was also updated to use the retrimmed piecewise linear model. The Kalman filter 

implemented within the RTSTM estimates model state 

variables plus six model tuning parameters. Figure 21 to 

Figure 24 show the RTSTM-produced tuning parameter 

estimates for the various test cases. In each figure the top 

subplot shows results using the original model and the bottom 

subplot shows results using the re-trimmed model. Although 

units have been removed, the y-axis scales are identical in all 

subplots. For the baseline runs, shown in Figure 21 to 

Figure 22, it is observed that the original model tuner estimates 

are larger and undergo notable variation as the engine 

transitions to different operating points. Conversely, the revised 

model tuning parameter estimates are mainly concentrated near 

zero, although they do exhibit variation when the engine 

undergoes a transient. These results demonstrate that the retrimmed model more accurately matches the steady-state 

performance of the actual engine, thus requiring smaller 

RTSTM tuning parameter adjustments. The station 2.5 and 14th

stage bleed fault cases are shown in Figure 23 and Figure 24, 

respectively. Again, the re-trimmed RTSTM produces smaller 

magnitude tuners with less variation compared to the original 

model. While the station 2.5 bleed valve fault results in minimal 

variation in the tuner estimates, changes in the tuner estimates 

associated with the 14th stage bleed valve fault are evident, 

again due to the fact that the latter fault has a larger impact on 

engine performance. The 14th stage bleed valve fault causes a 

distinct change in the estimates initiating at the time of fault 

insertion and remaining for the duration of the run. 

y

i

0 500 1000 1500 2000 2500 3000 3500 4000

WSSR

Time (sec)

Engine measurement

Re-trimmed PBM

WSSR

Anomaly detection threshold

y

i

Engine measurement

Re-trimmed PBM

0 500 1000 1500 2000 2500 3000

WSSR

Time (sec)

WSSR

Anomaly detection threshold

Fault

Inserted

y

i

Engine measurement

Re-trimmed PBM

0 500 1000 1500 2000 2500

WSSR

Time (sec)

WSSR

Anomaly detection threshold

Fault

Inserted
NASA/TM—2015-218454 12 

Figure 21.—Nominal baseline #1

Figure 22.—Nominal baseline #2

Discussion 

The model-based anomaly detection architecture has been 

shown to hold promise for the processing of streaming aircraft 

engine measurement data. However, future maturation and 

enhancements are warranted. One necessary enhancement is the 

need to further improve engine-to-model matching specifically 

during engine transients. Current work is ongoing to update 

metal temperature state dynamics contained in the model. 

It is also necessary to include and evaluate the full 

functionality of the architecture. The results presented in this 

paper exclusively focus on the anomaly detection performance 

achieved by updating the architecture to use a PWLM retrimmed to match nominal engine performance. Here, the 

Figure 23.—Station 2.5 bleed valve fault

Figure 24.—The 14th stage bleed valve fault

model-tuning parameters that the PBM periodically accepts 

from the RTSTM to reflect deterioration have been set to zero. 

Follow-on work is necessary to evaluate how the system will 

perform when the engine begins to experience performance 

degradation over time and model tuning parameter updates 

passing from the RTSTM to the PBM are necessary. 

Furthermore, the results presented in this paper only focus on 

anomaly detection capabilities. Follow-on work is ongoing to 

also include fault isolation logic that classifies the root cause 

for any detected anomalies. This will be performed by 

analyzing the observed residual vector present when any 

anomaly is detected, and then classifying the most likely root 

cause for the event. 

0

Tuners

Original RTSTM

0 500 1000 1500 2000 2500 3000 3500

0

Tuners

Time (s)

Re-trimmed RTSTM

Tuner 1

Tuner 2

Tuner 3

Tuner 4

Tuner 5

Tuner 6

0

Tuners

Original RTSTM

0 500 1000 1500 2000 2500 3000 3500 4000

0

Tuners

Time (s)

Re-trimmed RTSTM

Tuner 1

Tuner 2

Tuner 3

Tuner 4

Tuner 5

Tuner 6

0

Tuners

Original RTSTM

0 500 1000 1500 2000 2500 3000

0

Tuners

Time (s)

Re-trimmed RTSTM

Tuner 1

Tuner 2

Tuner 3

Tuner 4

Tuner 5

Tuner 6

Fault

Inserted

0

Tuners

Original RTSTM

0 500 1000 1500 2000 2500

0

Tuners

Time (s)

Re-trimmed RTSTM

Tuner 1

Tuner 2

Tuner 3

Tuner 4

Tuner 5

Tuner 6

Fault

Inserted
NASA/TM—2015-218454 13 

Summary 

This paper presented a model-based anomaly detection 

architecture designed for the processing of aircraft engine flight 

data either on-board or post-flight. The significance of this 

technique is that it enables processing of streaming engine 

measurement data and the detection of fault conditions with 

reduced latency. The architecture has been demonstrated for 

processing actual engine measurement data and found to avoid 

false alarms and correctly detect actuator bleed fault scenarios 

contained within the data. A method for re-trimming the model 

contained within the architecture was presented and found to be 

an effective means of addressing model-to-engine mismatch. 

This was performed by fitting a polynomial curve to identified 

nominal engine steady-state operating data, and then updating 

piecewise linear model trim point information. Follow on work 

is recommended to further improve the transient response 

matching of the model and to evaluate overall architecture 

performance when applied to additional aircraft engine 

datasets. 

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