Amy K. Chicatelli, Aidan W. Rinehart, and T. Shane Sowers

Vantage Partners, LLC, Brook Park, Ohio

Donald L. Simon

Glenn Research Center, Cleveland, Ohio

Investigation of Asymmetric Thrust Detection With 

Demonstration in a Real-Time Simulation Testbed

NASA/TM—2016-218925

January 2016

AIAA–2015–3987
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Amy K. Chicatelli, Aidan W. Rinehart, and T. Shane Sowers

Vantage Partners, LLC, Brook Park, Ohio

Donald L. Simon

Glenn Research Center, Cleveland, Ohio

Investigation of Asymmetric Thrust Detection With 

Demonstration in a Real-Time Simulation Testbed

NASA/TM—2016-218925

January 2016

AIAA–2015–3987

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NASA/TM—2016-218925 1 

Investigation of Asymmetric Thrust Detection With Demonstration 

in a Real-Time Simulation Testbed 

Amy K. Chicatelli, Aidan W. Rinehart, and T. Shane Sowers 

Vantage Partners, LLC 

Brook Park, Ohio 44142 

Donald L. Simon 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The purpose of this effort is to develop, demonstrate, and evaluate three asymmetric thrust detection 

approaches to aid in the reduction of asymmetric thrust-induced aviation accidents. This paper presents the 

results from that effort and their evaluation in simulation studies, including those from a real-time flight 

simulation testbed. Asymmetric thrust is recognized as a contributing factor in several Propulsion System 

Malfunction plus Inappropriate Crew Response (PSM+ICR) aviation accidents. As an improvement over 

the state-of-the-art, providing annunciation of asymmetric thrust to alert the crew may hold safety benefits. 

For this, the reliable detection and confirmation of asymmetric thrust conditions is required. For this work, 

three asymmetric thrust detection methods are presented along with their results obtained through simulation 

studies. Representative asymmetric thrust conditions are modeled in simulation based on failure scenarios 

similar to those reported in aviation incident and accident descriptions. These simulated asymmetric thrust 

scenarios, combined with actual aircraft operational flight data, are then used to conduct a sensitivity study 

regarding the detection capabilities of the three methods. Additional evaluation results are presented based 

on pilot-in-the-loop simulation studies conducted in the NASA Glenn Research Center (GRC) flight 

simulation testbed. Data obtained from this flight simulation facility are used to further evaluate the 

effectiveness and accuracy of the asymmetric thrust detection approaches. Generally, the asymmetric thrust 

conditions are correctly detected and confirmed. 

I. Introduction 

Asymmetric thrust is cited as the cause of several loss of control aviation incidents and accidents 

(Refs. 1 to 3). As noted in the propulsion system malfunction plus inappropriate crew response (PSM+ICR) 

reports, the detection of unintended asymmetric thrust conditions needs to be performed in a timely manner 

in order for there to be sufficient time for recovery. This effort was part of a feasibility study that evaluated 

three asymmetric thrust detection methods. This paper presents the results from that study which was 

conducted in simulation to demonstrate that asymmetric thrust conditions can be detected. In addition, to 

test effectively any proposed asymmetric thrust detection method, a realistic flight simulation environment 

is necessary. The NASA GRC flight simulation laboratory provides an opportunity to evaluate the 

effectiveness of the proposed methods with a pilot-in-the-loop. However, additional work would be 

necessary to address whether this information should be annunciated to the flight crew. 

The remainder of the paper is organized as follows. The paper begins with a section that provides the 

motivation for this work and describes the significance and improvement over state-of-the-art. Following 

that, the description of three developed asymmetric thrust detection methods is provided. Next, results from 

a simulation-based sensitivity study and the application of these methods in a real-time flight simulation 

laboratory are presented. Finally, a summary that outlines the effectiveness of the asymmetric thrust 

detection approaches is presented along with generalized concluding remarks about the research effort. 
NASA/TM—2016-218925 2 

II. Motivation 

A. Significance 

As previously noted, asymmetric thrust is cited as the cause of several Loss of Control aviation 

incidents and accidents. The sequence of events that lead to a PSM+ICR event can be described as 

follows. In a typical scenario, the aircraft’s autopilot is being used by the crew and the autothrottle control 

is engaged. Due to a failure, an unintended asymmetric thrust condition occurs while the autopilot and 

autothrottle are engaged. Due to the automated flight control systems, the asymmetric thrust condition is 

initially managed, but it progressively increases because the flight controls reach their limits of effective 

control. When the autopilot disengages and the crew takes over control, there may not be enough control 

authority for the crew to sufficiently control the aircraft. In addition, the crew’s response may be 

inappropriate and exacerbate the situation. 

If the flight crew is aware of the developing thrust asymmetry, they should be able to identify the 

cause and take preventive or corrective action. Therefore, the detection of the asymmetric thrust condition 

is needed, and the annunciation of asymmetric thrust may be beneficial in warning the flight crew. 

However, as indicated in the Federal Aviation Administration (FAA) report (Ref. 4) for indications of 

propulsion system malfunctions, there are risks associated with thrust asymmetry annunciation and the 

only time when annunciation may be practical is when the autopilot is engaged. Many of the reported 

incidents and accidents of thrust asymmetry by themselves were not so significant that they were not 

recoverable. In addition, aircraft are required to be controllable in extreme asymmetric thrust conditions 

throughout typical flight profiles. For the purposes of this effort, the asymmetric thrust condition that 

leads to aircraft upset and to loss of control is of interest. Typically that condition occurs due to the lack 

of reaction or from the inappropriate action of the flight crew. It is in this way that an asymmetric thrust 

condition can become unmanageable. 

B. Improvement Over State-of-the-Art 

The flight crew is responsible for recognizing and responding to unintended asymmetric thrust 

conditions. Today, this is done by the pilots monitoring available engine cockpit instrumentation such as 

rotor speeds or engine pressure ratio, which provide an indication of engine power. If an imbalance in the 

power produced by the aircraft’s engines is observed, the pilots must take appropriate action to address 

the issue. It is possible, when the autopilot is being used, the thrust imbalance can actually be 

exacerbated. If the flight control system is continually correcting for thrust asymmetry, the limits of 

control authority could be approached. In this case, recovery by the flight crew will be challenged by the 

suddenness of the event and the reduced margin for corrective action. Depending on its design, the 

autopilot will disengage at some point as it becomes unable to maintain the desired input flight conditions 

(i.e., heading, airspeed, altitude). When the autopilot disengages, the flight crew is given control of an 

aircraft that may have developed an unusual flight attitude with controls at or near their maximum 

deflection from the autopilot. In these situations, recovery depends on the proper response and skill of the 

flight crew. 

As noted above, asymmetric thrust conditions can be masked from the flight crew when the automatic 

controls are being used. In order to add an alert for asymmetric thrust conditions, the thrust imbalance 

must be detected and confirmed when these controls are being used. The results of the research presented 

in this paper, will show that the detection and confirmation of asymmetric thrust conditions is possible. 

The simulation studies and pilot-in-the-loop tests that were conducted under this effort will show that 

reliable automated real-time detection of asymmetric thrust conditions is feasible. 

 
NASA/TM—2016-218925 3 

III. Asymmetric Thrust Detection and Confirmation 

For this research effort, three asymmetric thrust detection approaches are developed and evaluated. 

The first two are based on producing an estimate of the engine thrust for each engine and comparing those 

values with each other in order to determine a mismatch in the thrust. The first two approaches include a 

Kalman filter-based thrust estimation approach and a two-dimensional table lookup thrust estimation 

approach. The third method takes a fundamentally different approach. Instead of a monitoring for a 

mismatch in estimated thrust between engines it monitors for a mismatch between the commanded and 

actual power produced by an individual engine. This is done by monitoring the primary engine control 

parameter (typically either corrected fan speed or engine pressure ratio (EPR)), which is a proxy for the 

amount of thrust produced by the engine. If an engine is detected to be producing more/less thrust than 

commanded, that serves as confirmation that an asymmetric thrust condition is likely. The three detection 

approaches are described in the following sections. 

A. Kalman Filter Approach 

A Kalman filter (KF) is an optimal linear estimator designed to estimate the unknown states of a 

dynamic system. It incorporates a dynamic model of the system and is designed to recursively update 

estimates by processing acquired system measurement data. Accounting for measurement noise and 

model uncertainty, the Kalman filter is designed to minimize the mean squared error in the estimated 

parameters. It is well suited for aircraft engine applications and several previous efforts have reported on 

the application of Kalman filters for onboard real-time aircraft engine performance estimation (Refs. 5 

and 6). In this study, an asymmetric thrust detection strategy based on Kalman filter estimation 

technology is considered. Here, a Kalman filter is designed and applied for each engine installed on the 

aircraft. To account for the nonlinear behavior inherent in an aircraft gas turbine engine, a piecewise 

linear Kalman filter design is applied. Individual linear Kalman filters are designed spanning the entire 

engine operating envelope and then combined and scheduled applying interpolation to account for 

changes in engine operating condition. In addition to estimating the dynamic states of the engine, the 

Kalman filter is also constructed to estimate states reflective of turbomachinery performance deterioration 

(Refs. 7 and 8). In this fashion, that Kalman filter is able to account for deterioration induced performance 

changes in the engine. Additional details on the Kalman filter formulation and implementation for 

asymmetric thrust detection are provided in the subsections below. 

1.Kalman Filter Formulation 

The nonlinear model of an aircraft engine can be represented by the following equations 

 

 

z g   x u h

y g x u h

x f x u h

z , ,

, ,

, ,





 

(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 modules of the engine. For given input values, the nonlinear functions f, g, 

and gz generate the vectors of state derivatives x , sensed engine outputs y, and unmeasured engine 

outputs such as net thrust denoted by z. By linearizing the engine model at a given operating point, the 

following state-space equations are obtained: 
NASA/TM—2016-218925 4 

     

    

    

z F x G u N h

z z F x x G u u N h h

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

z

trim

h

ref

u

trim

x

trim

y

trim

h

ref

u

trim

x

trim

      

      

      

      

     

     

   

   

  

   

   



   

(2) 

Here, A, B, C, D, F, G, L, M, and N 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 

measured and unmeasured outputs when the model is at steady-state (i.e., x = 0) at the given operating 

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 

(). Through algebraic manipulation, Equation (2) can be re-written to shift the health parameters to 

become state variables as shown in Equation (3): 

 

  G u

h

x z F N

D u

h

x

y C M

B u

h

A L x

h

x

  



 









 

  



 









 

  



 













 



  











0 0 



(3) 

Since engine performance deterioration evolves slowly in time, the health parameter states in Equation (3) 

are modeled without dynamics. Once the health parameters are augmented with the state variables, they 

can be estimated by applying a Kalman filter as long as the system is observable. However, a necessary 

condition for observability given the Equation (3) formulation is that there are at least as many 

measurements as health parameters (Ref. 9). To construct a reduced-order state space system of 

appropriate dimension to enable Kalman filter formulation, consider a transformation matrix, V*

, that 

maps the health parameter vector, h, to a tuning vector of lower dimension, q, such that: 

q V h

*  (4) 

An approximation for h based on q can be calculated using the pseudo inverse of V*

: 

h V qˆ ˆ *  (5) 

 
NASA/TM—2016-218925 5 

Then, substituting Equation (5) into Equation (3) produces the following reduced-order state space system: 

  

 

 

G u

q

x z F NV

D u

q

x

y C MV

u

B

q

A LV x

q

x

xq

xq

xq

xq

xq xq xq xq

x

F

x

C

x A x B

  



 









 

  



 









 





 



  



 













 





 





















 





*

*

*

0 0 0

(6) 

The choice of the transformation matrix is a design decision made prior to constructing the Kalman 

gains. In this study a technique, referred to as “optimal tuner selection,” is employed to produce a 

transformation matrix that is a linear combination of all health parameters, and constructed such that the 

mean squared estimation error in the parameters of interest are minimized (Ref. 7). In this case, the 

transformation matrix was selected to minimize the estimation error in net thrust. Given Equation (6), a 

linear Kalman filter at a given operating point can be formulated as: 

 

z F x G u

y C x D u

x A KC x B u K y

xq xq

xq xq

xq xq xq xq xq

    

    

      

ˆ ˆ

ˆ ˆ

ˆ ˆ 

(7) 

After individual linear Kalman filters are designed spanning the entire engine operating envelope, they 

are combined and scheduled applying interpolation to form the piecewise linear Kalman filter. 

2.Kalman Filter Implementation for Asymmetric Thrust Detection 

A block diagram of the piecewise linear Kalman filter implementation to estimate the thrust produced 

by an individual engine is shown in Figure 1. The Kalman filter requires engine sensed measurements (y) 

and actuator inputs (u). Parameter correction is applied to improve the interpolation between grid points 

in the piecewise linear Kalman filter. Trim and matrix information corresponding to the current operating 

point are retrieved applying a three-dimensional interpolation scheme using altitude, Mach, and corrected 

fan speed as the scheduling parameters. The Kalman filter produces estimated corrected output deltas 

from trim consisting of state variables ( xq xˆ ), sensed measurements ( c yˆ ), and net thrust ( c zˆ ). Corrected 

net thrust is produced by summing the estimated delta in net thrust, c zˆ , and net thrust at the trim 

condition, ztrim. 

The Kalman filter estimated net thrust values for each engine are compared following the asymmetric 

thrust detection and confirmation logic as shown in Figure 2. The absolute difference in estimated 

corrected net thrust between the two engines is calculated and then converted to an absolute percent of 

maximum thrust. This absolute percent error signal is then compared to a pre-established detection 

threshold. When an exceedance of this threshold is detected and then persists for an established time 

duration, the asymmetric thrust condition is confirmed and annunciated. 
NASA/TM—2016-218925 6 

Kalman

Filter

Trim

Interp

Matrix

Interp

xxq,trim

utrim

ytrim

y

u

Altitude

Mach

Altitude

Mach

ztrim

Corrected

Fan Speed

+

‐

+

‐

+

+

From Engine

yc

uc

A,B,C,D,F,

G,L,M,N,K

xq xˆ

c yˆ

c zˆ

c zˆ

(Estimated

Corrected

Net Thrust)

Correct

yc

uc

Figure 1.—Kalman filter-based thrust estimation.

Engine 1

Estimated

Corrected

Net Thrust

Engine 2

Estimated

Corrected

Net Thrust

|u|

Absolute

error

Max 

Thrust



÷

100

Absolute

Percent

error detection

threshold

exceeded?

persistency

threshold

exceeded?

yes

No thrust

asymmetry 

detected

No thrust

asymmetry 

detected

no no

Annunciate

thrust

asymmetry

yes +

-

Figure 2.—Asymmetric thrust detection and confirmation logic.

Relative to the other asymmetric thrust detection approaches considered in this study, the primary 

benefit offered by the Kalman filter is the estimation accuracy it enables. It is designed to account for 

transient engine behavior and turbomachinery deterioration induced changes in engine performance. 

However, it is a relatively complex solution in terms of processing requirements compared to the other 

approaches described below. 

B. Table Lookup Approach 

This asymmetric thrust detection approach estimates the net thrust of each engine applying a 

two-dimensional table lookup approach based on corrected fan speed and Mach number as shown in 

Figure 3. The lookup table data is created from steady state data generated using an engine model 

reflecting mid-life (i.e., 50 percent deteriorated) engine performance. The model is run at operating points 

over the entire flight envelope of the engine spanning a range of corrected fan speeds, Mach number, and 

altitude settings. Then, for each corrected fan speed and Mach number combination, corrected net thrust 

results generated over the range of altitudes considered are averaged to produce the two-dimensional 

lookup model. 

An estimated corrected net thrust value is produced for each engine, then these estimated thrust 

values are processed applying the same asymmetric thrust detection and confirmation system as shown 

previously in Figure 2. As compared to the Kalman filter approach, the table lookup method is simpler in 

design, which is a benefit for a flight software application. However, unlike the Kalman filter, the table 

lookup method does not account for engine performance deterioration or engine transient dynamics. 
NASA/TM—2016-218925 7 

Net Thrust 

Table 

Lookup

Corrected Fan Speed

Mach

Estimated Corrected

Net Thrust

Figure 3.—Table lookup thrust estimation approach. 

Power

Setpoint

Control

Logic

Altitude

Commanded 

power setting

Mach

dTamb

PLA

Sensed power

setting

detection

threshold

exceeded?

persistency

threshold

exceeded?

yes

No power

mismatch 

detected

No power

mismatch 

detected

no no

Annunciate

power

mismatch in 

individual 

engine

yes |u|

Absolute

error



÷

100

Absolute

Percent

error

+

-

Figure 4.—Sensed and commanded power comparison approach. 

C. Sensed and Commanded Power Comparison Approach 

The sensed and commanded power comparison approach is fundamentally different from the 

previously described Kalman filter and table lookup approaches. Instead of estimating and comparing the 

thrust between engines, this approach monitors for a mismatch between commanded and delivered power 

in an individual engine. It does so by monitoring the engine’s control parameter, corrected fan speed or 

EPR for most turbofan engines, which serves as a proxy for the actual thrust produced by the engine. A 

block diagram representation of the approach is shown in Figure 4. Sensed power (i.e., corrected fan 

speed or EPR) is directly read from available engine measurements. Commanded power is based on the 

engine power setpoint control logic, which is a function of operating conditions (altitude, Mach, ambient 

temperature) and throttle power lever angle (PLA) setting. The logic compares sensed and commanded 

power setting, and if a mismatch of sufficient magnitude and persistency is found, a power mismatch 

condition is annunciated. A benefit of this approach is that it guards against thrust asymmetry alerts due to 

pilot-intentional split throttle command scenarios. The goal of this research is to identify methods capable 

of detecting unintended asymmetrical thrust conditions. The two thrust estimation methods discussed 

require additional logic to suppress alerts when the asymmetric thrust is intended. Additionally, the EPR 

comparison approach is able to provide an indication of which engine is the culprit for producing the 

asymmetric thrust condition—generally there should never be a mismatch between commanded and 

delivered EPR during nominal conditions. Conversely, the previously described Kalman filter and table 

lookup approach are non-specific as they simply indicate that a thrust asymmetry exists. They do not aid 

in identifying which engine is malfunctioning. Like the previously described table lookup approach, the 

logic is relatively simple. However, unlike the Kalman filter approach, it does not account for engine 

performance deterioration. 
NASA/TM—2016-218925 8 

IV. Application and Results 

This section will present simulation results illustrating the application and comparison of the three 

asymmetric thrust detection approaches. First, results from a Monte Carlo simulation study conducted to 

assess the detection sensitivity of the three approaches is presented. Then, results from the application of 

the approaches in a pilot-in-the loop flight simulation facility are presented. 

A. Asymmetric Thrust Detection Sensitivity Study 

In order to evaluate the detection sensitivity of the three asymmetric thrust approaches, a simulation 

study is conducted to quantify the average minimum thrust asymmetry that can be detected by each 

approach in the presence of representative system uncertainty. This study is conducted using the NASAdeveloped Commercial Modular Aero-Propulsion System Simulation 40k (C-MAPSS40k), a high bypass 

turbofan engine model in the 40,000 pound thrust category (Ref. 10). C-MAPSS40k is a generic turbofan 

engine model intended for controls and diagnostics research and development purposes. It includes a 

closed-loop controller with EPR as the primary engine control parameter. C-MAPSS40k sensor 

measurement, actuators, and input parameters are shown in Table 1. C-MAPSS40k input parameters 

allow the engine to be operated over a range of operating conditions and power settings. Additional inputs 

allow the end user to specify the engine’s level of performance deterioration (ranging from a new engine 

to a fully degraded engine) and to enable the inclusion of representative sensor measurement noise in the 

engine outputs. Representative variations in these inputs are included in the sensitivity study to assess the 

accuracy of each of the three methods. Utilizing the C-MAPSS40k model, a piecewise linear Kalman 

filter and a two-dimensional table lookup model are constructed to estimate thrust over the entire engine 

operating envelope. The sensed and commanded power comparison approach is designed to compare 

sensed and commanded EPR. This is performed by comparing sensed EPR (the ratio of P5 to P2) to 

commanded EPR as specified by the C-MAPSS40k control logic. 

Given the designs of the three asymmetry detection approaches, a Monte Carlo simulation study is 

conducted to assess and compare the sensitivity of the approaches. For the purposes of conducting this 

study, two C-MAPSS40k engine simulations are run in parallel to represent a twin engine aircraft. Each 

Monte Carlo trial is defined to be 10 min in duration and applies pseudo-randomly assigned simulation 

inputs of engine operating condition, deterioration level, and sensor measurement noise. Here, actual 

flight operating condition profiles are obtained from a commercial aircraft flight operation quality 

assurance (FOQA) data set. Quasi steady-state cruise segments 10 min in duration are identified and 

extracted from the FOQA data set, and the corresponding time histories of altitude, Mach, and PLA serve 

as inputs into the C-MAPSS40k simulations. A total of 216 steady-state cruise segments were identified 

within the FOQA data set. Additionally, for each 10 min trial the deterioration level of each engine is 

randomly assigned through the C-MAPSS40k deterioration parameter and sensor noise is enabled. 

TABLE 1.—C-MAPSS40k SENSOR MEASUREMENTS, ACTUATORS, AND INPUT PARAMETERS

Sensor measurements Actuators Inputs 

Nf Fan speed Wf Fuel flow Alt Altitude 

Nc Core speed VSV Variable stator vane MN Mach number 

P2 Inlet total pressure VBV Variable bleed valve PLA Power lever angle 

T2 Inlet total temperature dTamb Ambient temperature deviation 

P25 HPC inlet total pressure relative to standard day conditions 

T25 HPC inlet total temperature Det Performance deterioration level 

Ps3 HPC exit static pressure Noise Measurement noise enabled or 

T3 HPT exit total temperature disabled (discrete input) 

P5 LPT exit total pressure 

T5 LPT exit total temperature 

 
NASA/TM—2016-218925 9 

TABLE 2.—APPLIED DETECTION THRESHOLDS FOR THE THREE 

ASYMMETRIC THRUST DETECTION APPROACHES

Method Threshold,

percent 

Persistency,

seconds 

False alarms 

Kalman filter 0.187 6.5 2 of 216 trials 

Table lookup 0.087 6.5 2 of 216 trials 

Sensed and commanded EPR comparison 0.95 6.5 2 of 216 trials 

TABLE 3.—AVERAGE MINIMUM LEVEL OF DETECTABLE THRUST ASYMMETRY

Method Average absolute percent of 

corrected thrust asymmetry at 

the time of detection, 

percent 

Standard deviation, 

percent 

Kalman filter 0.9664 2.7792 

Table lookup 0.7647 2.1976 

Sensed and commanded EPR comparison 2.7672 4.0936 

To enable a common basis of comparison between the three asymmetric thrust detection approaches, 

detection logic for each approach was defined to produce a common false alarm rate. All three methods 

applied a threshold exceedance persistency check of 6.5 sec in duration. The corresponding detection 

threshold was manually adjusted until two of the 216 steady-state cruise segments experienced a false alarm. 

For these cases, no thrust asymmetry existed beyond that caused by the different level of performance 

deterioration assigned to each engine and noise in the sensor measurements used by the closed-loop control 

system, which produce a relatively small mismatch in thrust. The thresholds applied for the three detection 

approaches are shown in Table 2. It should be emphasized that the detection thresholds applied for this 

study are much smaller than what would be reasonable to implement in practice as a false alarm rate of 

0.93 percent (2 of 216) vastly exceeds what would be considered acceptable. However, establishment of a 

common false alarm rate does provide a common basis in order to enable comparison of the methods. 

Given the defined detection thresholds for each method, the approaches were then evaluated and 

compared to determine their sensitivity in detecting asymmetric thrust events. For this assessment, two 

C-MAPSS40k simulations were once again run in parallel to produce 10 min time histories for a twin 

engine aircraft. As before, sensor measurement noise was enabled and inputs consisting of FOQA operating 

condition data and randomly assigned deterioration levels were applied. To simulate a thrust mismatch 

between the engines, engine #1 was setup to experience an uncommanded slow linear bias increase in PLA 

above its actual true PLA setting. This resulted in an overthrust condition for engine #1, where it produced 

more thrust than commanded. A Monte Carlo simulation study was conducted, and the average absolute 

percent thrust mismatch between the engines at the time of detection was quantified. This average is based 

on results from the same 216 steady-state cruise cases used to establish the detection thresholds. The results 

are summarized in Table 3 and show the average and standard deviation of the absolute percent corrected 

thrust asymmetry at the time of detection. It is observed that the table lookup approach is able to detect the 

smallest levels of thrust asymmetry, followed by the Kalman filter approach, and then the EPR comparison 

approach. The table lookup approach relies on corrected fan speed to estimate thrust, because they are 

highly correlated variables. For C-MAPSS40k, the relationship between corrected fan speed and thrust is 

not significantly impacted by engine performance deterioration. Additionally, the corrected fan speed 

measurement noise is relatively small. As such, the table lookup method performs well in estimating and 

comparing engine produced thrust at the quasi-steady-state cruise conditions considered. The Kalman filter 

provides comparable performance to the table lookup model. The slight increase in average detectable thrust 

asymmetry is attributed to the sensor noise, which is more prominent in the additional C-MAPSS40k 

sensors used in the Kalman filter implementation. The sensed and commanded EPR comparison approach 

utilizes P2 and P5 sensor measurements to calculate sensed EPR. These sensors exhibit more noise than the 

fan speed sensor does. Additionally, there is a lag between commanded and delivered EPR which comes 

into play due to oscillations in the PLA command and operating conditions within the FOQA data. As such, 

the sensed versus commanded EPR comparison approach exhibits a larger magnitude and standard deviation 

in its average minimum detectable thrust asymmetry. 
NASA/TM—2016-218925 10 

Figure 5.—NASA GRC flight simulation testbed. 

B. Piloted Flight Simulation Evaluation 

In order to further assess the capabilities of the asymmetric thrust detection approaches, a 

pilot-in-the-loop flight simulation evaluation is conducted where simulated failure scenarios causing 

asymmetric thrust conditions are introduced. This evaluation allow the techniques to be evaluated under 

more realistic operating conditions including transient operating conditions and pilot interactions with the 

aircraft. The subsections below will describe the test setup and example results of asymmetric thrust 

detection in the flight simulator environment. 

1.NASA GRC Flight Simulation Testbed 

The NASA GRC flight simulation testbed is capable of real-time piloted evaluation of the asymmetric 

thrust detection methods and provides a unique opportunity for this purpose. This demonstration vehicle 

generally meets FAA guidelines; so, it provides a valid test environment (Ref. 11). In this study, the flight 

simulation testbed utilized the two-engine transport class Model (TCM) aircraft simulation developed by 

NASA LaRC (Ref. 12) and the C-MAPPS40k model developed by NASA GRC for each engine. The 

integration of the TCM aircraft simulation and the C-MAPSS40k engine simulation is referred to as the 

TCM with enhanced engine control (EEC). The TCM EEC has been used for NASA GRC aeropropulsion projects, and it serves as a realistic demonstration vehicle. Shown in Figure 5 is a picture of 

the cockpit from the flight simulation testbed. 

2. Integration of the Asymmetric Thrust Failure Scenarios and Detection Methods 

Modifications to the TCM EEC flight simulation were completed for including the asymmetric thrust 

failure scenarios, which included stuck throttle failures as well as EPR-type failures. For the stuck throttle 

failures, the ability to fail either throttle was implemented in the two-engine TCM EEC simulation. From 

the reported incidents and accidents, the typical asymmetric thrust failure scenario usually involves one 

engine that is not responsive to throttle movement. The EPR failure scenarios were implemented as 

failures in the EPR sensor or in the fuel meter valve (FMV) system. 

The three asymmetric thrust detection methods were integrated into the TCM EEC for subsequent 

evaluation. The two detection methods based on comparing estimated thrust, the Kalman filter and table 

lookup approaches, were implemented as previously shown in Figure 2 and the EPR comparison 

approach was implemented as shown in Figure 4. For asymmetric thrust detection and confirmation all 

three methods applied a persistency check of 6.5 sec. The estimated thrust mismatch threshold for the 

Kalman filter and the table lookup model was set to 10 percent, and the EPR mismatch threshold was set 

to 5 percent. The 10 percent estimated thrust mismatch threshold was selected to be consistent with 

current engine failure indication logic activation levels (Ref. 4). The 10 percent thrust mismatch was 

selected as a practical threshold already implemented in the industry, whereas the thrust mismatch values 

identified in section IV provided a common ground for comparison between methods. The threshold 

values obtained in section IV are not practical for implementation in real world settings due to the 

considerable high false positive rate. The 5 percent threshold applied for the EPR comparison approach 

was selected to provide the capability to detect comparable thrust imbalance levels of approximately 

10 percent. 
NASA/TM—2016-218925 11 

C. Examples Asymmetric Thrust Failures 

From previous pilot-in-the-loop testing and the available accident reports and documentation, the 

stuck throttle failure provides realistic emergency conditions for the pilot to handle; so, it was used for 

this preliminary evaluation of the asymmetric thrust detection methods. The modeled stuck throttle 

failures were evaluated in the GRC flight simulation testbed. These pilot-in-the-loop tests were used to 

demonstrate the capabilities of the stuck throttle subsystems that were implemented in the TCM EEC. The 

failure where the throttle is stuck at its last position at a user-defined time was selected as the failure 

scenario. For this specific example, the pilot has finished the cruise portion of the flight and is starting to 

make the approach to land. Without the pilot’s knowledge, the stuck throttle failure was inserted into the 

real-time flight simulation. The pilot recognized that there was a throttle failure, but a comparison 

between the pilot’s reaction time and when the asymmetric thrust condition was detected was not 

evaluated. Since, the primary purpose for this demonstration was to show the integration of the failure 

scenario and asymmetric thrust detection methods with the real-time flight simulation. 

Figure 6 shows an example of the correct detection and annunciation of an asymmetric thrust event 

based on the Kalman filter thrust estimation approach. The top plot shows the estimated net thrust for 

engine one and engine two. At time equal to 15 sec, engine one experiences a stuck throttle failure. The 

middle plot shows the absolute net thrust difference between engines one and two along with the 

10 percent target detection threshold. The bottom plot shows the asymmetric thrust detection logic output. 

Asymmetric thrust is correctly detected and confirmed after the event persists for greater than 6.5 sec. The 

other approaches were also found to be able to successfully detect simulated asymmetric thrust scenarios. 

An analysis similar to the one that was performed for the sensitivity study was not repeated again due to 

the many pilot-in-the-loop simulations that would have to be performed. Although, more than one 

pilot-in-the-loop test was performed, the results from those tests are similar to the one presented here. 

Figure 6.—Detection and confirmation of asymmetric thrust based on 

the Kalman Filter thrust estimation approach. 
NASA/TM—2016-218925 12 

D. Discussion 

The three asymmetric thrust detection methods presented in this paper all performed as expected in 

detecting thrust asymmetry between engines of 10 percent or more, as demonstrated in a pilot-in-the-loop 

test. As such, all are potential candidates for detecting large asymmetric thrust events of the magnitude 

that might pose a safety concern. The two methods that monitored for a mismatch in the estimated thrust 

produced between engines (i.e., the Kalman filter and table lookup approach) were both found to be 

effective in detecting the simulated asymmetric thrust events. However, the Kalman filter is more 

complex, and was not found to yield a significant detection benefit over the simpler table lookup 

approach when applied to C-MAPSS40k. Additionally, some practical implementation challenges 

associated with the two thrust comparison methods are acknowledged. First, they can produce alarms in 

the event that an intentional split throttle setting exists. Additional logic would have to be added for the 

methods to suppress alerts when intentional asymmetric thrust is commanded. For example, the detection 

logic could be designed to only be engaged when the automatic controls are activated and disengaged 

during all other times. Another limitation of the estimated thrust comparison approaches is that the 

detection of a thrust asymmetry is nonspecific and does not aid the crew in determining which engine is 

malfunctioning or why the engine is malfunctioning (Ref. 4). Additional diagnostic logic, or manual 

troubleshooting would be necessary to determine the problem and the appropriate mitigating actions 

necessary to address the thrust asymmetry. The sensed and commanded power setting comparison 

approach was also found to be an effective and simple design. Furthermore, it is able to identify the 

specific engine that is the culprit for producing either overthrust or a thrust shortfall. One issue with the 

sensed versus commanded approach is that it is limited to detecting only those events that result in a 

mismatch between commanded and sensed power output. If there is an issue upstream such as a throttle 

linkage issue resulting in the wrong PLA command being provided to the detection logic, this approach 

will not be able to detect such a scenario. For any of the three detection methods considered, additional 

development and maturation would be necessary to enable practical implementation. For additional 

information on recommendations and challenges associated with providing aircraft indications of thrust 

asymmetry and other propulsion malfunctions, readers are referred to Reference 4. 

V. Summary and Conclusions 

The flight crew is responsible for recognizing and responding to unintended asymmetric thrust 

conditions. However, asymmetric thrust is often not recognized because of an increasing reliance on 

automated flight controls (i.e., autopilot). Therefore, an asymmetric thrust condition can be masked from 

the flight crew until a flight control limit is reached when recovery is difficult or not possible. Simulation 

studies conducted under this effort have shown that reliable automated real-time detection of asymmetric 

thrust conditions is feasible. Three asymmetric thrust detection approaches were developed and evaluated 

including two approaches designed to estimate and compare the thrust between engines (a Kalman filter 

thrust estimation technique and a corrected fan speed table lookup model) and a third approach designed 

to detect a mismatch between commanded and delivered Engine Pressure Ratio (EPR) in an individual 

engine. The approaches were evaluated in the NASA GRC flight simulation testbed under a variety of 

failure scenarios. All approaches were found to be successful in detecting asymmetric conditions. In 

particular, for the stuck throttle failure, the asymmetric thrust detection and confirmation was shown to be 

successful. 

 
NASA/TM—2016-218925 13 

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