L. Michael Santi

Glenn Research Center, Cleveland, Ohio

T. Shane Sowers

Analex Corporation, Brook Park, Ohio

Robert B. Aguilar

Boeing Rocketdyne Propulsion and Power, Canoga Park, California

Optimal Sensor Selection

for Health Monitoring Systems

NASA/TM—2005-213955

September 2005

AIAA–2005–4485
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L. Michael Santi

Glenn Research Center, Cleveland, Ohio

T. Shane Sowers

Analex Corporation, Brook Park, Ohio

Robert B. Aguilar

Boeing Rocketdyne Propulsion and Power, Canoga Park, California

Optimal Sensor Selection

for Health Monitoring Systems

NASA/TM—2005-213955

September 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

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cosponsored by the AIAA, ASME, SAE, and ASEE

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AIAA–2005–4485
Acknowledgments

The authors would like to acknowledge the contributions of several persons and groups to the concepts and information

presented within this paper; the Rocketdyne RS-84 Engine Control and Health Management System development

team for its many inputs related to HMS system design, data, and models; the engine component design teams at

Rocketdyne for their input in the furtherance of fault mode understanding, modeling, and risk allocation; Charles L.

Nola, Marshall Space Flight Center, for providing consistent focus on RS-84 system requirements impacting high

level S4 development activity; and Claudia M. Meyer for motivating sensor selection studies and consistently providing

valuable health management system perspectives.

Available from

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Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2005-213955 1

Optimal Sensor Selection for Health Monitoring Systems 

L. Michael Santi 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

T. Shane Sowers 

Analex Corporation 

Cleveland, Ohio 44135 

Robert B. Aguilar 

Boeing Rocketdyne Propulsion and Power 

Canoga Park, California 91304 

Abstract 

Sensor data are the basis for performance and health assessment of most complex systems. Careful selection and 

implementation of sensors is critical to enable high fidelity system health assessment. A model-based procedure that 

systematically selects an optimal sensor suite for overall health assessment of a designated host system is described. 

This procedure, termed the Systematic Sensor Selection Strategy (S4), was developed at NASA John H. Glenn 

Research Center in order to enhance design phase planning and preparations for in-space propulsion health 

management systems (HMS). Information and capabilities required to utilize the S4 approach in support of design 

phase development of robust health diagnostics are outlined. A merit metric that quantifies diagnostic performance 

and overall risk reduction potential of individual sensor suites is introduced. The conceptual foundation for this 

merit metric is presented and the algorithmic organization of the S4 optimization process is described. 

Representative results from S4 analyses of a boost stage rocket engine previously under development as part of 

NASA’s Next Generation Launch Technology (NGLT) program are presented. 

Nomenclature 

DM Diagnostic Model 

DT Detection Threshold 

FMEA Failure Modes and Effects Analysis 

FT Appropriate Fault Response Family 

FM Diagnostic Model Indicated Fault Response Family 

GA Genetic Algorithm 

HMS Health Management System(s) 

LOX Liquid Oxygen 

LT Failure Threshold 

MMSE Minimum Mean Square Error 

NGLT Next Generation Launch Technology 

NP Nonlinear Polynomial Time 

RTM Real Time Model 

RP1 Type of hydrocarbon fuel 

SLI Space Launch Initiative 

S4 Systematic Sensor Selection Strategy

A State space model state matrix 

B State space model input matrix 

C State space model output matrix 

D State space model influence or direct transmission matrix 

F Matrix of hardware influence functions 

O Observability matrix 

Q Observability Gramian matrix 
NASA/TM—2005-213955 2

h Vector of health parameters 

sh Hardware parameter summation vector 

x Vector of state parameters 

y Vector of sensor derived measurements 

u Vector of independent inputs 

δc Diagnostic model solution convergence criterion 

δdet Measurement shift from normal indicating anomaly conditions 

δp Distance to equal likelihood boundary 

nh Number of hardware parameters 

Nm Number of fault modes 

NT Number of characteristic fault trajectories 

P Minimum probability most likely diagnosis is correct over all pairwise fault mode comparisons 

Prb Probability most likely diagnosis is correct for pairwise fault mode comparison 

R Risk reduction potential for timely diagnosis 

T Time to reach diagnostic threshold 

Tmin Minimum time to reach diagnostic threshold 

I. Introduction 

Health management systems (HMS) monitor and control the function of critical systems and components in 

order to ensure safe and efficient operation. The need for autonomous health management capability depends on the 

risk associated with system failure and the potential benefit of timely response to faulted or degraded operations. 

The criticality of the system and the intensity and/or hostility of the operating environment are important factors in 

assessing the need for HMS. Space systems in general, and especially man-rated systems, present an ideal 

application for realizing the benefits of health management technologies. 

 Sensor data provide the foundation for performance and health assessment of most complex systems. Although 

opportunities for remote sensing of system function exist, the primary input for health diagnostics is generally 

provided by a network of sensors integrated within or in close proximity to the system of interest. Robust HMS 

require effective specification and placement of these sensors in order to support reliable and timely diagnoses over 

the range of potentially critical failure modes. Therefore effective sensor selection is an HMS enabling technology 

that supports agile control and planning for safe, productive, and cost effective system function. 

 There is a substantial body of literature that treats the many, often competing, criteria that impact selection of 

sensors for system monitoring. This paper focuses on sensor selection for effective health diagnostics. It is organized 

in five parts. Background information on current selection strategies is presented in this section. While not an 

exhaustive review, the survey provides perspective of representative methods for diagnostic sensor selection. 

Subsequent sections present a conceptual foundation for sensor selection that facilitates health diagnostics and the 

logic structure of a new sensor selection process termed the Systematic Sensor Selection Strategy (S4). 

Representative results from an application of the S4 process to select diagnostic sensors for a large boost stage 

rocket engine system are then reported. The final section contains recommendations based on early experience with 

the S4 process. 

A. Traditional Approach 

There are many considerations that impact sensor selection for space propulsion health management applications 

(see ref. 1 for a list of typical criteria). Traditional approaches to measurement and sensor selection for space 

propulsion applications are generally heuristic and support performance measures, but may not produce an optimal 

suite for health diagnostics/prognostics. A typical first step in the selection process is to have the various engine 

component teams submit lists of desired measurements. These measurements are used to support engine 

development, model verification, and/or detection of physical limit (redline) violations. As the system design 

matures, the component teams supply more detailed specifications such as measurement ranges, response 

requirements, etc. This information along with reliability requirements is used to determine the type and number of 

sensors needed at each engine location. The compiled list is then separated into categories associated with 

measurement use, e.g. ground test, flight, etc. Measurements are assigned a priority, with the highest priority given 

to measurements required for engine control. The list is often condensed as the design matures due to factors such as 

accessibility, cable routing, or reduced need. A maximum number of sensors is then determined based on 

storage/transmission capability, cost, and other considerations, which may include arbitrary limits. The component 

teams and chief engineer then negotiate until the final suite is selected. 
NASA/TM—2005-213955 3

Traditional approaches to sensor selection draw heavily upon domain expertise. They do not generally utilize a 

consistent quantitative method to assess the implications of choices on the diagnostic capability that enables 

effective health management. The absence of an accepted quantitative assessment methodology is a technology gap 

that must be closed to achieve the ambitious objectives of future space missions. Methods for assessing diagnostic 

capability are available, and specific procedures are discussed in the sections that follow. 

B. Linear System Measures 

 A well-developed theory and an extensive array of computational tools are available for solution of linear system 

problems and estimation of solution error bounds (see ref. 2). If health diagnostics for the system of interest can be 

effectively modeled in terms of a linear algebraic system, mature error estimation tools are available to guide sensor 

selection. A number of linear algebraic influence models (see refs. 3 to 8) have been developed for estimation of 

propulsion system health parameters. These models generally take the matrix form 

[ ] ⎥

⎦

⎤ ⎢

⎣

⎡ =

c

h

h c u

u

y D D (1) 

where Dh is the hardware parameter influence matrix, Dc is the matrix of control input influences, uh is the vector of 

hardware parameter deviations from a nominal baseline, uc is the vector of control input changes from a baseline 

command state, and y is the vector of measurement deviations from normal operating conditions. Knowledge of the 

control state uc and full column rank of the influence matrix Dh are the criteria for detectability of any fault state that 

can be represented as a linear combination of hardware parameter deviations. Fault discrimination can be 

characterized by the condition number of the influence matrix Dh. The condition number provides an indication of 

potential hardware state estimation error and its relation to measurement uncertainty. Large values increase state 

estimation uncertainty and impede clear and timely response to faults. Systematic selection of sensors to improve the 

condition estimate is a natural row partitioning process that provides quantitative metrics of diagnostic capability in 

terms of solution error bounds. Mathioudakis and Kamboukos (ref. 9) describe a sensor selection process based on 

minimization of the influence Jacobian condition number. Butas et al. (ref. 8) use a heuristic procedure for row 

partitioning of equation (1) to achieve influence matrix condition estimates consistent with accurate diagnostics. 

Although useful in many applications, sensor selection based on influence model condition estimates has several 

limitations. A linear influence model is inherently range limited for systems with appreciable nonlinear response 

characteristics. It does not explicitly consider sensor/system response dynamics nor does it discriminate hardware 

parameter solutions based on probability of occurrence over the range of combinations representing potential fault 

states. Good discrimination of hardware state solutions in regions with low probability of occurrence obviously 

contributes little to diagnostic effectiveness. 

 State space models are a natural extension of influence methods commonly used to represent the behavior of 

physical systems. State space models can be represented by the general matrix relation 

( )

( )⎥

⎦

⎤ ⎢

⎣

⎡ ⎥ =

⎦

⎤ ⎢

⎣

⎡

g x,u

f x,u

y

x& (2) 

where x(t) is the state vector composed of variables needed to describe system behavior, x& is the time derivative of 

x, and f and g are vector functions of the state and input variables (see ref. 10). Linear state space models are a 

simplified first order approximation of the general relations in equation (2) often used to approximate the behavior 

of systems (see refs. 11 and 12). Linear state space models can be expressed in the matrix form 

⎥

⎦

⎤ ⎢

⎣

⎡

⎥

⎦

⎤ ⎢

⎣

⎡ ⎥ =

⎦

⎤ ⎢

⎣

⎡

u

x

C D

A B

y

x& (3) 

where A, B, C, and D are the state, input, output, and direct transmission matrices respectively. A system described 

by equation (3) is said to be state observable if, for any time t1>0, the initial state x0 = x(t = 0) can be determined 

from the time history of the input u(t), and the output y(t) in the interval [0,t1]. A linear time invariant system is said 

to be state detectable if all unstable modes are state observable (ref. 10). For such a system, state detectability is 

assured if and only if the observability matrix O given by the relation 

 
NASA/TM—2005-213955 4

[ ]

T n 1 O C CA ... CA − = (4) 

has full column rank. 

 Fault detectability is of course necessary for effective health diagnostics; however, it does not characterize the 

timeliness of detection or the quality of fault discrimination. A number of scalar functions of the observability 

Gramian have been proposed to characterize the degree or quality of observability (refs. 13 to 15). The Gramian 

matrix Q is defined by the relation 

∫

∞

≡

0

t t e e dt A T A Q C C T

 (5) 

A clear description of the Gramian matrix and its role in state vector determination is provided by van den Berg 

(ref. 15). Dochain et al. (ref. 14) use the condition number of the Gramian to determine the most observable system 

model, and van den Berg describes several related Gramian metrics. Selection of the measurement variables y,

together with the associated output matrix C, to optimize a Gramian fault discrimination metric provides a 

quantitative basis for systematic sensor selection. 

Although state space models are an effective means of characterizing system dynamics, they retain the range 

restrictions inherent with linear approximation of nonlinear system response. In addition, sensor selection strategies 

based on Gramian metrics do not explicitly consider the distribution of fault occurrences or severity over the range 

of potential state solutions x. For example, preferred fault directionality is an implicit fault distribution constraint 

that is not considered in Gramian metrics. As previously noted, good fault discrimination in state space regions with 

low probability of occurrence contributes little to diagnostic value. 

In practical applications, measurements are corrupted by random noise, and the system itself may be subjected to 

random disturbances. Therefore, individual state variables of a dynamic system can seldom be determined exactly 

from direct measurements. They must be estimated from noisy observations. The basic Kalman filter is a linear 

system estimator used when processes and measurements contain significant random components. Kalman filtering 

has been the subject of extensive research and application. If all random components are Gaussian, the Kalman filter 

estimator can be shown to be optimal in the minimum-mean-square-error (MMSE) sense (refs. 19 to 21). Extended 

Kalman filter strategies that approximate nonlinear system dynamics, albeit with additional complexity, are also 

available (refs. 19 to 21). Kalman filtering is especially useful for off-line diagnostics and error analysis studies. 

With continuing improvement in computational speed, Kalman filtering has increased potential for real-time 

diagnostics depending on response time requirements. 

Sensor selection based on minimizing the variance of health parameter estimation error from a state estimation 

Kalman filter has been considered in a number of studies (see refs. 16 to 20). However use of error variance 

measures alone to guide sensor selection has certain shortcomings. Selection of measurement type and location can 

affect system dynamic response, potentially impacting timeliness of diagnosis as well as health parameter estimation 

error. In addition, models that describe fault propagation dynamics are generally immature in the early phases of 

system design. As a consequence, measurement distributions during fault sequences may be difficult to characterize 

with sufficient confidence for effective Kalman filtering. 

C. Targeted Fault Strategies 

 System health diagnostics based on physical models associate fault conditions with the deviation of model health 

parameters from normal values. Sensor suites admitting reliable determination of fault states over the full continuum 

of potential health parameter values are most desirable. However realistic fault scenarios will in general occupy only 

a fraction of the full parameter space range. This observation suggests the use of strategies that target regions of 

highest fault probability and severity. Targeted fault selection strategies often utilize specialized criteria to identify 

the optimal sensor suite for health diagnostics. In a series of papers, Bhushan and Rengaswamy (refs. 22 to 24) 

investigate the problem of sensor location based on various fault observability and resolution criteria. Narasimhan et 

al. (ref. 25) present four measurement selection algorithms using a qualitative reasoning framework to assess fault 

detection and isolation for dynamic systems. A method for designing a cost optimal sensor system for a designated 

diagnosability level is presented by Spanache et al. (ref. 26). In this latter study, a system is said to be fully 

diagnosable with a given set of sensors if and only if (i) for any relevant combination of sensor readings, there is 

only one minimal diagnosis candidate, and (ii) all faults of the system belong to a candidate diagnosis for some 

sensor readings. For most physical systems, only partial diagnosability can be realistically achieved because 
NASA/TM—2005-213955 5

multiple faults may share the same approximate signature and/or some faults are not detectable before failure occurs. 

In a recent study, Yan (ref. 27) considers sensor placement based on discriminability analysis where two faults may 

be discriminated if they generate different measurement output signatures over some subset of the available sensors. 

D. Complexity Analysis 

 The complexity of various sensor selection problems has been investigated. Problems associated with 

determination of sensor sets of minimum cardinality guaranteeing diagnosability, normality, or observability for 

discrete event systems are considered by Yoo and Lafortune (ref. 28). Each is shown to be a member of the class of 

problems termed NP-complete (ref. 29). Problems in this class are notoriously difficult to solve, suggesting that 

optimal diagnostic sensor selection for complex systems can be a formidable task. This result motivates 

consideration of special problem structures and heuristic strategies leading to efficient selection algorithms. To be 

useful, however, the specified sensor suite must optimize diagnostic performance regardless of selection process 

complexity. The absence of a universally accepted diagnostic performance measure presents a significant 

impediment to robust sensor selection. 

II. Conceptual Basis 

There are a variety of pertinent criteria for selection of sensors supporting system health diagnostics. The 

focused objective of this effort was to develop a sensor selection strategy supporting high fidelity, real-time, targeted 

fault diagnostics that maximizes operational risk reduction. More specifically, we wish to select sensors to minimize 

fault detection time and maximize fault source discrimination in order to maximize targeted fault risk reduction for 

the system of interest. 

 To facilitate overall system design assuring safety and reliability, and to minimize potentially expensive system 

retrofits, selection of sensors for effective health diagnostics is properly a design phase function. This limits the 

availability of test data as a selection guide, especially for prototype systems, and suggests that selection of sensors 

must be supported by fault simulations and diagnostic models. Limited system experience does not support fault 

diagnostics based on changes in measurement data variances, spectral properties, and/or complex pattern 

characteristics. Because of design evolution and limited test data availability, use of mean shifted performance data 

for fault detection and discrimination is indicated. 

 To establish foundation and motivation for the S4 process, it is useful to have a conceptual understanding of 

propagating fault manifestations, and to characterize the impact of sensor selection on fault detection and isolation. 

The following subsections provide a pertinent conceptual framework. 

A. Trajectories 

 For fault conditions to be diagnosable, they must induce sufficiently large measurement deviations from normal. 

A representation of the states traversed during a specific fault development history will be referred to as a fault 

signature or trajectory. The fault trajectory refers to both the measurement space sequence and the causal hardware 

parameter sequence associated with fault development. The function of the diagnostic model (DM) is to predict the 

hardware parameter sequence consistent with the observed measurement space trajectory. An approximation to the 

observed measurement sequence may be recovered by inserting the hardware parameter trajectory predicted by the 

DM into the system performance model and generating a measurement trajectory consistent with the DM solution. 

Differences between the observed measurement trajectory and the measurement trajectory recovered using the DM 

solution are a measure of the fidelity of the diagnostic model. Regenerated measurement trajectories based on DM 

results for faults designated A and B together with the actual fault B trajectory are identified in the notional twodimensional measurement space depicted in figure 1. 

 An accurate DM is essential for reliable fault isolation. Inaccuracies can also delay fault detection or lead to false 

alarms. Trajectory implications for fault diagnostics are treated more fully in the subsections that follow. 

B. Fault Detection 

 Fault detection requires sufficient measurement deviation to discriminate an anomaly condition from normal 

state variation. A plant hardware fault cannot be reliably discriminated from a sensor fault if measurements from 

only a single sensor source exhibit an anomaly excursion. Therefore, measurements from multiple sensor sources 

must exceed a prescribed threshold limit for reliable plant hardware fault detection. The minimum measurement 

deviation level for reliable fault detection within defined false alarm limits is designated δdet. This is termed the 

detection threshold limit. In figure 1, the detectable fault zone is simply the measurement space region in which the 

output from both displayed measurement space sensors has exceeded the detection threshold limit. The boundary of 
NASA/TM—2005-213955 6

the detectable fault zone is termed the fault detection threshold. A fault is initially detectable when its level is 

sufficient to reach a measurement trajectory location that intersects the detection threshold.

C. Fault Isolation 

 Once a fault condition has been detected, the DM attempts to isolate the fault source and provide a measure of 

fault severity. A fault is deemed to be isolated when the recovered DM solution trajectory point closest to the 

observed measurement data point is within a defined convergence threshold limit δc for one and only one fault. A 

fault is correctly diagnosed if the isolated DM solution corresponds to the true input fault type. 

 The selection of sensors affects the proximity of the individual fault trajectories and hence the fidelity of fault 

discrimination. Closer measurement space trajectories are associated with less effective fault discrimination. For 

faults that may induce measurement shifts in opposed directions from the normal operating state (faults with linear 

bi-directional measurement trajectories), orthogonal trajectories are ideal for reliable fault discrimination. For a fast 

response system well represented by an influence model of the form given in equation (1), orthogonal trajectories 

correspond to minimal hardware influence matrix condition number and lower hardware parameter solution error 

bounds in the traditional sense (ref. 2). However, component degradation and fault induced measurement trajectories 

are generally nonlinear and/or unidirectional (induce measurement shifts in only one direction). In such cases, 

orthogonal trajectories may not be optimal and a more general measure of fault discrimination is needed. 

 During a realistic fault progression, measurement data exhibit random scatter due to system/sensor noise and 

uncharacterized fault dynamics as depicted conceptually in figure 2. This scatter obscures the fault induced 

measurement trajectory and complicates the detection process. If the selected sensor suite admits closely aligned 

measurement trajectories for distinct faults, reliable fault discrimination may be delayed well beyond the detection 

point. This is clearly seen in figure 2 by examining the fault A data for sensor suite 1 and the fault B measurement 

data. An effective sensor suite separates fault induced measurement trajectories and provides good fault 

discrimination capability. This is clearly depicted in figure 2 by the large separation of the fault A data using sensor 

suite 2 and the fault B data near their respective detection points. 

δdet

δdet

δdet δdet

Sensor 1 δ (σ S1 )

Detectable Sensor 2 δ (σ S2 )

Fault Zone

Detectable 

Fault Zone

Detectable 

Fault Zone

Detectable 

Fault Zone

True Fault 

Trajectory

DM Fault B 

Solution

Fault Detected

δ c

δ p

Thresholds

δ det - Detection

δ c - Convergence

δ p - Equal Likelihood

 Boundary

DM - Diagnostic Model

Equal Liklihood Boundary

Nominal Sensor Values

DM Fault B DM Fault A

 Figure 1.—Notional measurement space with well-defined fault trajectories. 
NASA/TM—2005-213955 7

DM predicted fault trajectories are also displayed figure 2. For diagnostic systems utilizing measurement data 

with significant random fluctuation, a natural measure of fault discrimination is the probability that the most likely 

solution fault mode is the true fault mode. Since the objective is to select sensors that support reliable real-time fault 

diagnosis, it is important to achieve good fault discrimination immediately upon fault detection. Therefore the 

probability that the most likely DM solution fault mode corresponds to the true fault mode at the detection threshold 

is an appropriate measure of real-time fault discrimination potential. One method of estimating this probability is to 

determine the equal likelihood threshold limit δp depicted in figure 1. This threshold parameter is defined as a 

measure of the proximity of the initial fault detection state to the equal likelihood boundary between the DM fault 

signature of the true fault and the most proximate DM signature of another targeted fault mode.

D. Fault Families 

 Sensor selection that is narrowly focused to optimize health diagnostics for a small group of well defined faults 

is unlikely to support robust health management for systems with a wide range of potential fault manifestations. 

Fault families defined by combinations of hardware parameters describe large arrays of potential fault trajectories. 

Conceptual measurement space representations of a pair of two parameter fault family ranges are depicted in figure 

3. A specific fault occurrence generates an individual trajectory within the appropriate fault family measurement 

space range. The distribution of realistic fault trajectories within a given family is generally unknown. However, a 

conservative estimate of DM fault family discrimination can be determined by examining the most proximate family 

trajectories. In figure 3, the single parameter fault A1 trajectory is the most proximate family A member to fault 

family B. Data scatter about the mean fault A1 detection point defines the probability that a family A fault will be 

determined as most likely. The previously described equal likelihood threshold distance δp can be used to generate 

an estimate of this probability. 

δdet

δdet

δdet δdet

Sensor 1 δ (σ S1 )

Sensor 2 δ (σ S2 )

Sensor Suite 1

DM Fault A - DM Fault B 

Equal Liklihood Boundary

Simulation or Test Data

Pre / Post Detection

 / Fault A Suite 1

 / Fault A Suite 2

 / Fault B

Detection Test

k of n Consecutive 

Measurements > δ det

For at Least m Distinct 

Sensors 

A - Suite 1

A - Suite 2

B

Sensor Suite 2

DM Fault A - DM Fault B 

Equal Liklihood 

Boundary

Figure 2.—Notional measurement space with fault trajectories from diagnostic 

model solutions, and actual data from propagating faults for 

two distinct sensor suites. 
NASA/TM—2005-213955 8

III. Selection Process 

 The Systematic Sensor Selection Strategy, referred to as S4, is described in this section. S4 is intended primarily 

for system design phase utilization. It is a model-based, targeted-fault process for selection of sensors supporting 

health diagnostics. S4 can be logically partitioned into the three major subdivisions displayed in figure 4: the 

knowledge base, the down-select iteration, and the final selection analysis. Each of these subdivisions is described 

below. 

A. Knowledge Base 

 The inputs required for productive use of S4 consist of evolving system design information together with a 

condensed form of related systems experience focused on components with health implications. This information 

provides a foundation for construction of effective system models, and together with these models constitutes the 

knowledge base needed to support use of S4. Pertinent knowledge base components are listed below. 

1. Failure modes and effects analysis (FMEA) identifying system critical faults and providing initial 

indications of sensible fault signatures 

2. Risk assessments associated with critical fault modes targeted for health diagnosis 

3. Candidate sensors listed by location and type, including associated response characteristics 

4. Estimates of measurement output variances due to sensor noise and system effects for candidate sensors 

5. Remediation response families correlated to targeted fault modes and severity levels 

6. False alarm constraints 

7. Model(s) of normal system operation based on the experience base of related systems and the appropriate 

physics governing as designed system function 

8. Fault simulation model(s) correlating targeted fault modes to the system model hardware parameters whose 

deviations can be used to describe these modes and their severity 

It is important to note that knowledge base components evolve during the system design phase and hence diagnostic 

sensor selection should be considered an integral component of the overall system design iteration sequence. 

δdet

δdet

Faults States in Families 

 A and B

Defined by Parameters

 A1 A2 B1 B2 

One Parameter δ Trajectories

 A1 A2 B1 B2

Data Scatter About Det Mean 

Actual A1 Mean at Det - 

Equal Liklihood Boundary 

DM Fault A1 - DM Family B

 - - - - - - - - - -

DM Fault A Most Likely -

DM Fault B Most Likely - 

A2

B1

A1

B2

Fault Family A Region

Bounded by Trajectories

A1 and A2

Sensor 2 δ (σS2)

Sensor 1 δ (σS1)

Fault Family B Region 

Bounded by Trajectories

B1 and B2

Figure 3.—Notional measurement space with distinct fault families 

defined in terms of hardware parameter combinations. 
NASA/TM—2005-213955 9

Figure 4.—Systematic Sensor Selection Process Diagram. 

B. Down-Select Iteration 

 The sensor suite down-selection is an iterative process for identifying a group of sensor suites that provide good 

fault detection and isolation for targeted fault trajectories. It is composed of three basic components: a system health 

diagnostic model, a sensor suite merit algorithm, and a sensor suite down-select algorithm. The function and 

interactions of each component are described below. 

1. Sensor Suite Merit Algorithm 

 The merit algorithm assigns a diagnostic merit value to each candidate sensor suite based on detection speed, 

probability of correct fault remediation family identification at the fault detection threshold, and risk reduction 

measures. The hardware parameter groups that describe each fault mode and the remediation response family 

associated with each fault mode are knowledge base inputs. An individual measurement trajectory for a given fault 

mode is an output sequence that may be approximated by the system simulation model. It is generated by causal 

hardware parameter time evolution input to the system simulation model. The number of discrete fault trajectories 

considered in characterizing diagnostic capability for a targeted fault mode is dictated by the range and distribution 

of mode faults. System domain expertise and knowledge base information guide definition of mode characteristic 

hardware fault trajectories. At a minimum, a single parameter trajectory for each hardware parameter pertinent to the 

fault mode as well as the highest likelihood multiple hardware parameter trajectories associated with the fault mode 

should be considered. Using characteristic fault mode trajectories, the merit value associated with a specific sensor 

suite is constructed using the component definitions below. 

DTij detection threshold state for true fault mode i trajectory j 

LTij failure threshold state for true fault mode i trajectory j 

DMiij diagnostic model mode i solution state for DTij using measurements available with current sensor suite 

DMkij diagnostic model mode k solution state for DTij using measurements available with current sensor suite 

FTij appropriate fault response family for DTij

FMiij fault response family associated with best mode i DM solution state for DTij using measurements 

available with current sensor suite 

FMkij fault response family associated with best mode k DM solution state for DTij using measurements 

available with current sensor suite 

Nm number of fault modes considered 

NTi number of characteristic trajectories considered for fault mode i 

System 

Diagnostic 

Model 

Sensor Suite 

Merit 

Algorithm 

Statistical 

Evaluation 

Algorithm 

Down-Select 

Algorithm 

Optimal 

Sensor 

Suite 

Health Related 

Information

System 

Simulation 

Model 

Knowledge Base 

Test Sensor Suites Good Sensor Suites

Candidate Selection Complete

Yes

Down-Select Iteration

No

 Final Selection 
NASA/TM—2005-213955 10

Rij risk reduction potential allocated to timely diagnosis of fault mode i trajectory j 

RT total risk reduction potential = ∑ ∑= =

Nm Ti

i 1

N

j 1

Rij

Tij time to reach DTij using a given sensor suite 

Tminij minimum time to reach DTij using any sensor suite 

Prbkij 

⎪

⎪

⎩

⎪⎪

⎨

⎧

< = = ≠

= =

≠

ij

B 1 if DT reached before LT ,B probability FM FT more likely than FM FT

1 if DT reached before LT using the given sensor suite,FM FT , and FM FT

0 if LT reached before DT using the given sensor suite or FM FT .

ij ij iij ij kij

ij ij iij ij kij ij

ij ij iij ij

 

Pij ( ) kij modes k i

min Prb ≠

 The overall merit value of a specific sensor suite is defined in terms of the parameters above. 

 

Merit = ∑ ∑

= = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

m Ti⎛ N

i 1

N

j 1 ij

ij

ij ij

T Tmin

T

R P

R

1 (6) 

The merit function identifies, i) the overall timeliness of fault condition detection as a fraction of the fastest possible 

detection time using any set of candidate sensors (terms Tij/Tminij), and ii) the quality of fault discrimination in 

terms of the minimum probability of correct remediation response family identification near the detection threshold 

(terms Pij). The discrimination quality metric is based on pairwise fault mode likelihood comparisons. The product 

of these two terms is used to estimate the fraction of risk reduction potential that can be ideally realized at the fault 

detection threshold with a specific sensor suite. This is a useful metric for assessing real-time health monitoring 

potential of candidate sensor suites. The ideal merit value is 1.0, indicating greatest potential real-time risk reduction 

for targeted fault modes using available sensors. 

 The merit evaluation algorithm accepts a variety of one-time inputs from the knowledge base including true 

trajectory characteristics for all targeted fault modes. It also receives diagnostic model solutions for targeted fault 

trajectories and proximate mode trajectories for each sensor suite under consideration. The merit algorithm supplies 

diagnostic merit values for each current sensor suite to the down-select algorithm described below. 

2. Down-Select Algorithm 

The combinatorial nature of the down-select iteration 

lends itself to the use of a genetic algorithm (GA), hence a 

GA was developed to perform down-selection of candidate 

sensor suites. At each GA iteration stage or generation, 

candidate sensor suites in the current (input) population 

compete to evolve suites with improved diagnostic 

capability, and to pass desirable properties to subsequent 

stages of iteration or generations. A detailed description of 

typical GA operations is given in Goldberg (ref. 30). 

Encoding the sensor selection problem in a GA format 

is a simple process. Each individual member of a 

population is referred to as a chromosome and represents a 

single candidate sensor suite. Each chromosome is 

composed of bits called genes associated with individual candidate sensors. Binary encoding of the gene indicates if 

the particular sensor associated with the gene is in the sensor suite represented by the chromosome. A chromosome 

mask may be employed to force either selection or omission of particular sensors as desired. 

Each chromosome in the input population has an assigned merit value received as input from the merit 

algorithm. To choose output sensor suites passed to the next generation, roulette-wheel selection was employed (ref. 

30). With roulette-wheel selection, sensor suites with higher relative merit values have an increased probability of 

being selected as parents. Once parent suites are selected, single point crossover is employed to construct offspring 

suites for the next generation. The crossover point is selected randomly and genes are copied from the parents as 

depicted in figure 5. Elitism is used to advance the best sensor suites to the next generation without modification. 

Mutation or random bit-flipping, is employed during parent-to-child gene copying for its diversifying effects. As 

the generations progress, the population will increasingly converge to a group of similar sensor suites providing 

Parent1 = 

Crossover Point

G11 G12 G13 G14 G15 G16

G21 G22 G23 G24 G25 G26 Parent2 =

Child1 = G11 G12

G13 G14 G15 G1 G21 G22 6

G23 G24 G25 G26

Child2 =

Parent1 = 

Crossover Point

G11 G12 G13 G14 G15 G16

G21 G22 G23 G24 G25 G26 Parent2 =

Child1 = G11 G12

G13 G14 G15 G1 G21 G22 6

G23 G24 G25 G26

Child2 =

Figure 5.—Single point crossover example. 
NASA/TM—2005-213955 11

good diagnostic capability. Increasing the probability of mutation with each generation aids in increasing the 

diversity of the population. Preserving diversity assists the population in evolving away from local optima in the 

solution space. 

The basic steps of the GA employed in this study are given below. 

Step 1 Initialize—Input the initial population of sensors from the knowledge base and make it the current 

generation. The initial population is randomly generated. 

Step 2 Merit Function—Input the merit algorithm assigned value for each sensor suite in the current generation. 

Step 3 Elitism—Automatically advance 2 sensor suites with the highest merit value to the next generation. 

Step 4 Selection—Select two sensor suites using roulette-wheel selection. 

Step 5 Crossover—Determine if crossover occurs. 

 Step 5a No Crossover—Both parents advance to the next generation without modification. 

 Step 5b Crossover—Apply single point crossover with the possibility of mutation as each gene is copied. 

Step 6 Repeat—Return to Step 4 until next generation is populated. 

Step 7 Repeat—Set the current generation equal to the newly formed next generation. 

Step 8 Output—Send current generation of sensor suites to the DM to reinitiate the merit assignment process. 

Return to Step 2 until target number of generations is reached. 

3. System Diagnostic Model 

 Any procedure that is capable of assigning time indexed hardware health parameter values based on current and 

past measurement states is a candidate system diagnostic model. Since diagnostic speed is a critical issue for realtime applications, an inverse model was employed to estimate hardware state conditions at each time increment. The 

most straightforward type of inverse model determines hardware parameter deviations uh from normal by solving a 

set of system approximating relations of the form 

y = g(uh, uc) (7) 

where y is the vector of diagnostic system measurements available for a given sensor suite. The control state vector 

uc and diagnostic measurement state vector y are treated as inputs and some type of general nonlinear equation 

solver is used to determine hardware state conditions uh at each sampled time slice. For S4 purposes, a modified 

Levinberg-Marquardt procedure (ref. 31) was used as the DM solver 

 If the output measurement variation from normal is assumed to be a summation of control effects and 

independent single parameter fault effects, a considerable simplification of equation (7) may be achieved. 

 

y = F(uh) sh + g(uc) (8) 

In this expression, the function matrix F(uh) is composed of elements fij(uhj) that provide the contribution of each 

hardware parameter uhj to each individual measurement yi. The nh×1 summation vector sh = [1 1 . . . 1]T

 effects 

superposition of the individual hardware parameter contributions. A planned sequence of system fault simulations is 

required to support development of the functional relations in either of equations (7) or (8). Of course the support 

sequence is much simplified if the summation form of equation (8) provides an adequate representation of targeted 

fault manifestations. This would be the case if for instance targeted fault modes are primarily single parameter 

modes. 

 The standard inverse model approach trades increased fidelity available from more detailed dynamic response 

models for improved diagnostic speed afforded by assuming instantaneous or matched propagation characteristics. 

For systems with well-matched measurement time constants or slow fault propagation rates, this trade is most 

favorable for effective real-time diagnostics. 

C. Statistical Evaluation Algorithm 

 Because effective real-time diagnostic models must address the trade between diagnostic fidelity and speed, it is 

important to challenge both criteria in selecting an optimal sensor suite. The down-select iteration provides a set of 

“good” sensor suites based on approximate risk coverage, and speed. However, diagnostic model simplifications, 

sensor/system noise characteristics, and variations in fault manifestation dynamics from the assumed form for 

targeted fault trajectories provide sources of diagnostic performance uncertainty. The statistical evaluation algorithm 

is intended to provide a final robustness test for each down-selected sensor suite. The fault test case protocol may 
NASA/TM—2005-213955 12

include best estimates of measurement fluctuation due to i) sensor/system noise, ii) systematic variation in fault 

mode manifestation dynamics, and/or iii) random variations in fault manifestation. Once the test protocol is 

established, fault simulations are run to provide near detection point data for each test case. The ability of the 

diagnostic model to identify the correct response family using this data is assessed using the evaluation metric 

described in equation (6). The sensor suite that maximizes the merit metric is identified as the optimal sensor suite 

for health diagnostics. 

IV. Representative Results 

The S4 process described above was applied to identify optimal suites of flow path sensors for health diagnostics 

of rocket engine systems. Two systems developed through conceptual design by Boeing Rocketdyne as part of 

NASA’s Space Launch Initiative (SLI) and Next Generation Launch Technology (NGLT) programs served as test 

platforms for the S4 process. S4 analysis information and representative results for the RS-84 engine system are 

presented below. The RS-84 engine system was a large liquid fueled LOX-RP1 staged combustion engine originally 

intended for boost stage use in support of payload/vehicle orbital insertion. Its design vacuum thrust was in excess of 

one million pounds. 

The knowledge base for this application was obtained primarily from Space Shuttle Main Engine (SSME) data 

archives and Rocketdyne engine system component teams. A Real Time Model (RTM) of the RS-84 engine 

provided the basis of engine performance predictions and fault simulation cases used to support the S4 process, 

including construction of the RS-84 inverse model that served as the DM basis. General characteristics of Real Time 

Models for related system applications can be found in references 32 and 33. Only single parameter hardware faults 

and single source leaks were considered, hence equation (8) was used as the basic DM relation. System faults and 

risks defined by component teams were allocated to single parameter fault modes using a heuristic but logical 

procedure. The population of each generation considered in the GA was composed of 100 sensor suites. 

Information defining the scope of the S4 analysis for the RS-84 engine system is presented in table 1 below. The 

30 hardware faults included i) turbomachinery parameter faults, ii) duct, valve, and injector resistance or blockage 

faults, and iii) combustion chamber and nozzle performance faults. The 42 single source leak faults were specified 

by device and location. A total of 58 sensors was defined as the pool of candidates for health diagnostics. 

Summary results of the S4 analysis are presented in table 2. Leak faults were generally undetected prior to 

reaching a system failure point using the inverse model with candidate flow path sensors, typical system/sensor 

noise levels, and detection thresholds consistent with a low allowable false alarm rate. One way to address this 

problem is to invoke data filters that reduce noise levels and hence the detection threshold value. This is a viable 

option only if leak rate propagation is long relative to the filter interval. Data filtering experimentation was 

performed with considerable success relative to reduction in detection thresholds to facilitate leak detectability. 

However, no knowledge base information was available to characterize leak rate propagation rates and timeframes 

relative to failure onset or filtering intervals. Therefore sensor selection was performed targeting only the 30 single 

parameter hardware faults in the list of targeted faults. A complete inverse model diagnostic cycle, including 

inversions for all 30 hardware parameter faults, could be performed at a frequency greater than 20 Hz using a 

standard 800 megahertz Pentium processor. 

Control responses for various fault modes had not been formalized as of initial S4 analyses. Therefore control 

and maintenance response families had not been finalized and the DM discrimination requirement was not well 

defined. For initial S4 testing, individual hardware parameter response families were assumed and single parameter 

faults initiated only during steady-state operation were considered. Use of individual parameter specific response 

families is an extremely ambitious fault discrimination requirement, certainly more stringent than is likely to be 

required for effective health diagnostics. Using individual hardware parameter response families, an optimal merit 

index value of 0.62 was achieved as displayed in table 2. Most of the merit losses from the ideal value of 1.0 were, 

not surprisingly, due to fault discrimination issues rather than fault detection. The merit index value of 0.62 for the 

optimal sensor suite was considered reasonable considering the level of design definition as of the initial S4 analysis 

sequence. 

The general configuration of the optimal sensor suite is also identified in table 2. It is composed of 31 sensors 

used for health diagnostics, 6 of which are used to establish control and boundary conditions defining the normal 

engine operating state. 
NASA/TM—2005-213955 13

 TABLE 2.—S4 OPTIMAL SENSOR 

TABLE 1.—RS-84 S4 ANALYSIS BASIS. SUITE FOR RS-84. 

Targeted Faults Optimal Diagnostic Sensor Suite

Hardware Faults (single param) 30 Merit Evaluation (Hdwe Faults Only) 

Leak Faults (single source) 42 

Total Faults 72 Merit Index 0.62 

 

Candidate Sensors (type+location) Optimal Diagnostic Sensor Suite 

(Hardware Faults Only)

Flow Rate 17 Flow Rate 3 

Pressure 22 Pressure 12 

Shaft Speed 4 Shaft Speed 4 

Temperature 11 Temperature 10 

Valve Position 3 Valve Position 2 

Composite 1 Total Sensors 31 

Total Sensors 58 (Total includes 6 boundary and control state input 

defining sensors) 

 

V. Summary and Recommendations 

The Systematic Sensor Selection Strategy described herein provides a logical procedure for quantifying the value of 

candidate sensor suites for targeted fault diagnostics based on criteria pertinent to real-time health management. 

These criteria include speed of detection, probability of correct fault source isolation, and overall risk reduction 

potential. The S4 process also provides a framework for organizing and utilizing an evolving system knowledge 

base, including system performance and simulation models, in the selection process. The sensor suite identified by 

the S4 process as optimal for health diagnostics is closely associated with the diagnostic model employed for fault 

identification. The diagnostic model must reflect the desired compromise of diagnostic fidelity and speed consistent 

with false alarm limits and potential remediation responses that maximize overall operational risk reduction. 

 Based on experience with S4 development and general consideration of the role of sensor selection in effective 

system health management, the following recommendations are offered. 

1. Effective health management is enabled by the availability of sensor data that facilitates health diagnosis. 

Therefore systematic sensor selection for improved diagnostics should be an integral component of health 

management system development. 

2. To maximize potential risk reduction benefit, sensor selection for health diagnostics should be an integral 

system design phase activity that both evolves with and impacts host system design. 

3. The linkage between physical fault modes, the parameter based simulation of these modes, and the model 

based use of hardware parameter shifts for fault isolation should be strengthened to support more robust 

health diagnostics. 

4. Sensor faults are not explicitly considered by the current S4 process. Methods of expanding the process to 

support sensor selection for health management system data qualification/validation should be explored. 

5. Extensions of the standard inverse model to better consider system nonlinearity and fault dynamics are 

accessible. These extensions and other diagnostic models should be examined within the S4 framework to 

determine the best compromise of diagnostic fidelity and speed for specific applications. 

6. The S4 process may be used to quantitatively assess the impact of specific sensor losses during operation and 

potential sensor additions on diagnostic capability. This capability should be refined and systematically 

applied for long-term health management system development and maintenance. 

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Prevention Group, Gaithersburg, MD, 1982. 
NASA/TM—2005-213955 14

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Approach,” AIAA–2001–3764, 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 

2001. 

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Proceedings of ASME Turbo Expo 2004 – Power for Land, Sea, and Air, Vienna, Austria, June 2004. 

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West Sussex, England, 1996. 

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This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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21

Optimal Sensor Selection for Health Monitoring Systems

L. Michael Santi, T. Shane Sowers, and Robert B. Aguilar

Systems health monitoring; Qualification; Diagnosis; Program verification; Propulsion;

False alarms; Error analysis; Performance tests; Simulation

Unclassified -Unlimited

Subject Categories: 20, 61, and 65

Prepared for the 41st Joint Propulsion Conference and Exhibit cosponsored by the AIAA, ASME, SAE, and ASEE, Tucson Arizona,

July 10–13, 2005. L. Michael Santi, Glenn Research Center (currently at Christian Brothers University, 650 E. Parkway S.,

Memphis, Tennessee 38104); T. Shane Sowers, Analex Corporation, 1100 Apollo Drive, Brook Park, Ohio 44142; and Robert B.

Aguilar, Boeing Rocketdyne Propulsion and Power, 6633 Canoga Avenue, Canoga Park, California 91309. Responsible person, T.

Shane Sowers, organization code RIC, 216–433–3405.

Sensor data are the basis for performance and health assessment of most complex systems. Careful selection and

implementation of sensors is critical to enable high fidelity system health assessment. A model-based procedure that

systematically selects an optimal sensor suite for overall health assessment of a designated host system is described. This

procedure, termed the Systematic Sensor Selection Strategy (S4), was developed at NASA John H. Glenn Research

Center in order to enhance design phase planning and preparations for in-space propulsion health management systems

(HMS). Information and capabilities required to utilize the S4 approach in support of design phase development of

robust health diagnostics are outlined. A merit metric that quantifies diagnostic performance and overall risk reduction

potential of individual sensor suites is introduced. The conceptual foundation for this merit metric is presented and the

algorithmic organization of the S4 optimization process is described. Representative results from S4 analyses of a boost

stage rocket engine previously under development as part of NASA’s Next Generation Launch Technology (NGLT)

program are presented.