Robust Strategyfor

Rocket Engine

Health Monitoring

Institution:

Principal Investigator:

Christian Brothers University

650 East Parkway South

Memphis, TN 38104

L. Michael Santi

Report Type:

Performance Period:

Grant Number:

Summary of Research

June 1, 2000 - May 31, 2001

NAG3-2454

NAG3-2454 supplement

Executive Summary

The inference phase of rocket engine health monitoring involves analysis of results from the

acquisition phase, comparison of analysis results to establish health measures, and assessment of

health indications. A particular model based procedure developed for the inference phase of

engine health monitoring and referred to as Generalized Data Reduction (GDR) was the subjectof this effort. The GDR method can be considered a strategy for solving the inverse performance

analysis problem often referred to as data reduction. The primary objective of this research

effort was to investigate methods of enhancing the GDR strategy in order to make it a flight

capable real-time diagnostic platform for the engine system of choice.

A brief conceptual description of the basic GDR strategy punctuated by significant

mathematical results and a description of major components is presented. The MC-1 engine

system was specified as the test platform for evaluating GDR capabilities and assessing

candidate enhancement procedures. Data from the R2 and R3 series of MC-1 engine tests

conducted at Rocketdyne's Santa Susanna Field Laboratory in California were utilized to seed

the data reduction process. A ROCETS performance model of the MC-1 engine was used to

generate influence matrices used by GDR and a modified ROCETS data reduction model

provided conventional data reduction results used to assess the accuracy potential of GDR

predictions.The basic GDR procedure was shown to provide consistent approximation of hardware

function that agreed well with the recognized standard for MC-1 engine data reduction.

Modifications to the basic procedure were explored to increase the effective solution range as

well as improve computational speed, accuracy, and stability of the solution procedure. An

efficient procedure based on singular value decomposition (SVD) of the hardware influence

matrix was implemented and tested as was a partial second order extension of the basic GDR

procedure. Computational efficiency was improved using the SVD technique. No improvement

was observed using the partial second order extension.

The original MC-lhardware parameter set used for data reduction was functionally

regrouped and GDR analyses were performed with the revised hardware set. Agreement of

predictions with accepted standards was excellent. Single source anomaly resolution capability

was found to be excellent using the revised parameter set. A study was performed to determine

the effects of single sensor failure on reduction predictions. Degradation of reduction results in

the presence of sensor failure was characterized. GDR analyses were also performed using a

highly restricted flight measurement suite. Loss of hardware discrimination capability using

only flight available measurements was characterized and results were evaluated as reasonable

for real-time monitoring applications.

Two automated subset selection procedures were developed in order to identify compatible

sets of measurements and hardware parameters for data reduction applications. Results of

preliminary testing are reported and the shortcomings of sequential subset selection procedures

are identified.

Summary evaluation of GDR performance for MC- 1 data reduction is provided and

recommendations for future development are presented.

Table of Contents

Executive Summary .................................................................................... iTable of Contents ....................................................................................... ii

List of Tables and Figures in Appendices ........................................................... iii

1.0

2.0

3.0

4.0

4.1

4.2

4.3

5.0

5.1

5.2

6.0

7.0

7.1

7.2

7.3

7.4

8.0

9.0

10.0

Introduction ..................................................................................... 1

Objectives ....................................................................................... 2

The GDR Strategy ............................................................................. 3

Study Components ............................................................................ 5

Engine System ............................................................................. 5Test Data Source ........................................................................... 6

Parent Performance ........................................................................ 7

GDR Pre-analysis .............................................................................. 9

GDR Preprocessing Tasks ............................................................... 10

MC-1 Engine Test Data .................................................................. 11

Initial GDR Analysis Results ................................................................ 12

GDR Modifications ............................................................................ 15

Solution Procedure Using Singular Value Decomposition ........................... 18Partial Second Order Formulation and Solution Procedure .......................... 20

Formulation with Hardware Parameter Functions ..................................... 21

7.3.1 GDRA and ROCETS DR Comparisons ......................................... 22

7.3.2 Single Source Anomaly Resolution Capability ................................. 23

7.3.3 Sensor Failure Response ........................................................... 24

7.3.4 Results with Flight Measurement Suite .......................................... 25Subset Selection Procedures ............................................................. 26

Summary of Research Effort ................................................................ 27Assessments and Recommendations ........................................................ 28

References ...................................................................................... 30

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Appendix G

Appendix H

Appendix I

MC-1 engine propellant flow schematics ................................

MC-1 engine - temporal plots of R2 and R3 test series --one

second averaged data .......................................................

MC-1 engine - temporal plots of R2 and R3 test series - one

second averaged data adjusted to standard inlet conditions ............

MC-1 engine - temporal plots for test R2-1 - hardware parametervariation with the standard reduction variable set ......................

MC-1 engine - allocation of single source anomaly effects byData reduction ................................................................

MC-1 engane - comparison of standard ROCETS DR with GDRA

using only flight measurements ...........................................

MC-1 engine- R2 and R3 test series information for data reduction

MC-1 engine- R2 and R3 test series data ................................

MC-1 engine - GDR prediction comparisons ...........................

A1-A5

B1-B25

C1-C21

D1-D17

El-E20

F1-F18

G1-G6

H1-H9

II-I6

List of Tables and Figures in Appendices

Appendix A. MC-1

FigureA1

A2A3

A4

A5

Appendix B. MC-1

FigureB1

B2

B3B4

B5

B6B7

B8

B9B10

Bll

B12B13

B14

B15B16

B17

B18B19

B20B21

B22

B23B24

B25

Appendix C.

FigureC1C2

C3

C4C5

engine propellant flow schematics

DescriptionMC-1 Engine Conceptual Schematic

MC-1 Engine Oxygen System

MC-1 Engine Fuel System

MC-1 Engine GG/Turbine SystemMC-1 Engine MCC/Nozzle System

engine - temporal plots of R2 and R3 test series - one second averaged data

DescriptionPSVL10 one second average test data

TTVL10 one second average test data

PSRPFV one second average test dataTTRPFV one second average test data

PSOXDS one second average test data

PSVL13 one second average test dataPTVL14 one second average test data

PSVL15 one second average test data

PTVL18 one second average test data

TTVL14 one second average test dataTTVL18 one second average test data

WOXTOTL one second average test data

PSVL00 one second average test dataPSVL01 one second average test data

PTVL05 one second average test dataPTVL09 one second average test data

TTVL05 one second average test dataWRPTOTL one second average test data

PTHTGI one second average test data

PTVL22 one second average test dataTTHTGI one second average test data

TTHTGD one second average test data

PTMCHY one second average test dataSNSHFT one second average test data

FT15A one second average test data

MC-1 engine - temporal plots of R2 and R3 test series - one second averaged

data adjusted to standard inlet conditions

DescriptionPSOXDS test data adjusted to standard inlet conditionsPSVL 13 test data adjusted to standard inlet conditions

PTVL 14 test data adjusted to standard inlet conditions

PSVL 15 test data adjusted to standard inlet conditionsPTVL18 test data adjusted to standard inlet conditions

iii

Appendix C.

FigureC6C7

C8

C9

C10

CllC12

C13

C14C15

C16

C17C18

C19

C20C21

Appendix D.

FigureD1

D2

D3D4

D5

D6

D7D8

D9D10

DllD12

D13D14

D15

D16D17

Appendix E.

FigureE1E2

E3E4

E5

MC-1 engine - temporal plots of R2 and R3 test series - one second averaged

data adjusted to standard inlet conditions (continued)

DescriptionTTVL14 test data adjusted to standard inlet conditionsTTVL18 test data adjusted to standard inlet conditions

WOXTOTL test data adjusted to standard inlet conditions

PSVL00 test data adjusted to standard inlet conditions

PSVL01 test data adjusted to

PTVL05 test data adjusted toPTVL09 test data adjusted to

standard inlet conditions

standard inlet conditions

standard inlet conditions

TTVL05 test data adjusted to standard inlet conditions

WRPTOTL test data adjusted to standard inlet conditionsPTHTGI test data adjusted to standard inlet conditions

PTVL22 test data adjusted to standard inlet conditions

TTHTGI test data adjusted to standard inlet conditionsTTHTGD test data adjusted to standard inlet conditions

PTMCHY test data adjusted to standard inlet conditions

SNSHFT test data adjusted to standard inlet conditionsFT15A test data adjusted to standard inlet conditions

MC-1 engine - temporal plots for test R2-1 - hardware parameter variationwith the standard reduction variable set

Description

Comparison of GDR and ROCETS/DR resultsComparison of GDR and ROCETS/DR results

Comparison of GDR and ROCETS/DR results

Comparison

ComparisonComparison

Comparison

ComparisonComparison

ComparisonComparison

ComparisonComparison

of GDR and ROCETS/DR

of GDR and ROCETS/DR

of GDR and ROCETS/DRof GDR and ROCETS/DR

of GDR and ROCETS/DRof GDR and ROCETS/DR

- RCALMF- RCALMO

- RKFL1

results - ROLN1results - XMGGKO

results - XMGGOO

results - CDGGKIresults - CDGGOI

results - CDKINJ

of GDR and ROCETS/DR results - CDOINJ

of GDR and ROCETS/DR results - PSIMKPMPof GDR and ROCETS/DR results - PSIMOPMP

of GDR and ROCETS/DR results - CDGGNZ

Comparison of GDR and ROCETS/DR results - FRICFACTComparison of GDR and ROCETS/DR results - CDNOZL

Comparison of GDR and ROCETS/DR results - ECSMMCHB

Comparison of GDR and ROCETS/DR results - QDOTVL 18

MC-1 engine - allocation of single source anomaly effects by data reduction

DescriptionRMMCRP single source anomaly allocation

RMMCOX single source anomaly allocation

RKFL1 single source anomaly allocationROLN1 single source anomaly allocation

RMGGRP single source anomaly allocation

iv

Appendix E.

FigureE6E7

E8

E9

El0Ell

El2El3

El4

El5El6

El7

El8

El9E20

Appendix F.

FigureF1

F2

F3F4

F5

F6

F7F8

F9F10

Fll

F12

F13

F14

F15

F16

F17

F18

MC-1 engine - allocation of single source anomaly effects by data reduction

(continued)

DescriptionRMGGOX single source anomaly allocation

RGGKI single source anomaly allocationRGGOI single source anomaly allocation

RKINJ single source anomaly allocation

ROINJ single source anomaly allocationPSIMKPMP single source anomaly allocation

PSIMOPMP single source anomaly allocation

TRQMKPMP single source anomaly allocationTRQMOPMP single source anomaly allocation

CDGGNZ single source anomaly allocation

ETAMHTGT single source anomaly allocationPWRFACT single source anomaly allocation

CDNOZL single source anomaly allocation

ECSMMCHB single source anomaly allocationQDOTVL18 single source anomaly allocation

MC-1 engine - comparison of standard ROCETS DR and GDRA

using only flight measurements

DescriptionReduction results

Reduction results

Reduction resultsReduction results

Reduction results

Reduction resultsReduction results

with flight measurement set - R3MCRPwith flight measurement set - R3MCOX

with flight measurement set - R3GGRPwith flight measurement set - R3GGOX

with flight measurement set - PSIMKPMP

with flight measurement set - PSIMOPMP

with flight measurement set - PWRFACTReduction results with

Reduction results withReduction results with

R3MCRPReduction results with

R3MCOXReduction results with

R3GGRP

Reduction results withR3GGOX

Reduction results with

PSIMKPMPReduction results with

PSIMOPMP

flightflight

flight

flight

flight

measurement set - ECSMMCHB

measurement set - QDOTVL18measurement set and 20-23 second avg flows -

measurement set and 20-23 second avg flows -

measurement set and 20-23 second avg flows -

flight measurement set and 20-23 second avg flows -

flight measurement set and 20-23 second avg flows -

flight measurement set and 20-23 second avg flows -

Reduction results with flight measurement set and 20-23 second avg flows -PWRFACT

Reduction results with flight measurement set and 20-23 second avg flows -ECSMMCHB

Reduction results with flight measurement set and 20-23 second avg flows -

QDOTVL 18

Appendix G. MC-1 engine - R2 and R3 test series - information for data reduction

Table

G1G2

G3

G4

G5

G6

Appendix H.

Table

H1H2

H3

H4

H5H6

H7H8

H9

Appendix I.

Table

1112

I3

I4I5

16

Description

Description of MC-1 engine test sequence used as study data sourceParameters for MC-1 engine reduction study

Baseline values for MC-1 engine measurement variables

Baseline values for MC-1 engine hardware parameters

Revised hardware parameter list for MC- 1 engine reduction study

Flight parameter list for MC- 1 engine reduction study

MC-1 engine - R2 and R3 test series data

Description

MC-1 engine - test R2-1 one second average dataMC-1

MC-1

MC-1MC-1

MC-1

MC-1MC-1

MC-1

engine - test R2-2 one second average dataengine - test R2-3a one second average data

engine - test R2-3b one second average data

engine - test R2-4 one second average dataengine - test R3-la one second average data

engine - test R3-2b one second average data

engine - R2 series tests - general observationsengine - R2 series tests - observations adjusted to std input

MC-1 engine - GDR prediction comparisons

DescriptionComparison of GDRA and ROCETS/DR resultsComparison of GDRA (linear) and GDRC (2nd order) results

Comparison of GDRA and ROCETS/DR results using modified hardware set

Sensor elimination study results

Comparison of standard ROCETS/DR and GDRA using flight measurementsonly

Subset selection examples with MC-1 engine parameters

vi

1.0 Introduction

Monitoring the health of rocket engine systems is essentially a two-phase process. The

acquisition phase involves sensing physical conditions at selected locations, converting physical

inputs to electrical signals, conditioning the signals as appropriate to establish scale or filter

interference, and recording results in a form that is easy to interpret. The inference phase

involves analysis of results from the acquisition phase, comparison of analysis results to

established health measures, and assessment of health indications.

A variety of analytical tools may be employed in the inference phase of health monitoring.

These tools can be separated into three broad categories: statistical, rule based, and model based.

Statistical methods can provide excellent comparative measures of engine operating health.

They require well-characterized data from an ensemble of "typical" engines, or "golden" data

from a specific test assumed to define the operating norm, in order to establish reliable

comparative measures. Statistical methods are generally suitable for real-time health monitoring

because they do not deal with the physical complexities of engine operation. The utility of

statistical methods in rocket engine health monitoring is hindered by practical limits on the

quantity and quality of available data. This is due to the difficulty and high cost of data

acquisition, the limited number of available test engines, and the problem of simulating flight

conditions in ground test facilities. In addition, statistical methods incur a penalty for

disregarding flow complexity and are therefore limited in their ability to define performance shift

causality.

Rule based methods infer the health state of the engine system based on comparison of

individual measurements or combinations of measurements with defined health norms or rules.

This does not mean that rule based methods are necessarily simple. Although binary yes-no

health assessment can sometimes be established by relatively simple rules, the causality

assignment needed for refined health monitoring often requires an exceptionally complex rule

base involving complicated logical maps. Structuring the rule system to be clear and

unambiguous can be difficult, and the expert input required to maintain a large logic network and

associated rule base can be prohibitive.

Model based methods incorporate physical relations and empiricisms in the inference phase

of health monitoring. Such methods are typically more involved because the flow physics of

rocket engines is generally described by complex and interdependent, nonlinear relations. The

attending computational complexity presents a significant impediment to the use of model based

methods in real-time health monitoring. However, the addition of physical detail does provide a

basis for determining performance shift causality at the component level. Recent surveys of

model based inference procedures applicable to propulsion systems are available [ 1, 2].

A particular model based procedure referred to as Generalized Data Reduction (GDR) [3, 4]

was the subject of this effort. GDR was initially developed at Marshall Space Flight Center

(MSFC). Mathematically, GDR can be considered a strategy for solving the inverse performance

analysis problem often referred to as data reduction. More specifically, the GDR method inverts

a canonical representation of the engine system performance model to estimate parameters that

characterize the operation of hardware components such as pumps, turbines, injectors, nozzles,

orifices, valves, etc., consistent with test data. As a propulsion system analysis procedure, the

basic form of GDR is similar to gas path analysis techniques [see e.g. 5] commonly used for fault

detection and isolation in air-breathing systems. GDR has been applied to mainstage data

reduction of both the Space Shuttle Main Engine (SSME) [3] and the MC-1 engine system [4].

In theseapplicationsGDRdemonstratedcomputationalspeedsconsistentwith real-timemonitoringrequirements.

2.0 Objectives

The primary objective of the subject research effort was to investigate methods of enhancing

the Generalized Data Reduction strategy in order to make it a flight capable real-time diagnostic

platform for the engine system of choice. The principal areas targeted for enhancement were asfollows:

1. Basic algorithm refinement to improve computational efficiency and reduction

cycle speed

2. Extensions to incorporate additional engine system knowledge, especially

uncertainty estimates

3. Subset selection refinement to improve stability and sensitivity of hardware-

measurement compatibility assessment and selection process

4. Range extension methods to expand the engine operating range of application

5. Techniques for responding to sensor degradation/failure

6. Methods of incorporating creep scale transients within main stage engine

diagnostics.

Secondary topics of study that depended on the GDR development path were identified in the

grant supplement as described below:

7. Methods for improving the gateway for input of statistical parameters to the

data reduction process

8. Methods for improving data reduction stability with expanded measurementand/or hardware sets

9. Methods for improving performance model feedback from data reduction

predictions

10. Methods for improving test data/model accuracy assessment

11. Methods for improving reduction model capability with limited measurement

sets.

A brief description of the basic GDR method is presented in the next section of this

report in order to introduce terminology and define the development baseline.

3.0 The GDR Strategy

A detailed development of the basic GDR strategy can be found in two recent papers [3, 4 ].

A brief conceptual description punctuated by significant mathematical results and a description

of major component procedures is provided below.

The mainstage performance model of a rocket engine system can be thought of as a set of

functional relations F between the following parameter sets.

1. known/measuredsystemcontrolsettingsand/orinput/outputconditionsC; e.g.,valvepositions,inlet/outlettemperatures,pressures,etc.

2. nominally fixed parametersH describingcomponenthardwarefunction;e.g.,efficiencies,dischargecoefficients,headcoefficients,line resistances,etc.,and

3. internalengineconditionsP at variouslocations;e.g.,temperatures,pressures,flows,heattransferrates,thrust,etc.

Theobjectiveof performanceanalysisis to predicttheinternalengineconditionsP,givenknownor assumedvaluesfor themembersof H andC.

If the performance model relations between P, H and C are assumed to be linear near some

known base state designated by the subscript "o", then they can be approximated in the following

form.

Linearized Performance Model Relations

whereAP = JHo AH + Jco AC

JHo = L_HjJo _ L Z_r-IjJo Jco = [_c3C_o _ o

(1)

(2)

AH = H-Ho AC = C-Co AP = P-Po (3)

H = [ H1 H2 • • • Hn l T C = [ C1 C2 • . • CL IT P = [ P1 P2 • • • Pm ]T (4)

JHo

Jco

mxn Jacobian matrix of P with respect to H at base state o

mxL Jacobian matrix of P with respect to C at base state o

The Jacobian matrices defined in relations (2) above are commonly referred to as first

order influence matrices. Elements can be approximated using a standard finite difference

scheme and results of performance model simulation runs at incremented values of each

hardware and control component about its defined base state value.

The problem of determining values of the hardware shifts All so that equation system (1)

is satisfied, given measurement indicated values for AP and AC, is the linear data reduction

problem. Unfortunately determination of the hardware parameter solution All is complicated by

several factors. In general, the number of hardware parameters Hj is greater than the number of

available measurements Pi, i.e. n>m. This prevents straightforward inversion of the hardware

Jacobian to obtain a unique solution to equation system (1). It also presents the problem of

selecting the correct hardware operating state from an infinite set of candidate hardware states

for the given observation set. Added to the discrimination problem is another related to

computational stability. If the hardware Jacobian is ill conditioned, the data reduction solution

AH may be unstable. Little confidence can be placed in the solution to an ill conditioned system

even with low levels of measurement noise.

The basic GDR strategy attempts to address these problems using a two-stage solution

process. Terminology pertinent to the solution procedure is given below.

a$

P$

Jltso

WQR-Pi

vector subset ofns hardware parameters selected for adjustment in reduction analysis

vector subset of ms measured internal conditions selected for reduction analysis matching

msxns submatrix of hardware Jacobian Jno corresponding to selected hardware, H$, and

measured internal conditions, P$

L2 condition number of the indicated matrix A

nsxns diagonal matrix of weighting factors associated with selected hardware H_

column pivoted QR factorization of selected mxn matrix A, i.e., APi = QR where Q is an

orthogonal mxm matrix, R is a mxn upper triangular matrix, and Pi is a nxr permutationmatrix

Using the above terminology, the basic GDR strategy can be described as follows.

Basic GDR Strategy

Process 1. Subset Selection

Select H$ c H and P$ _c P

using QR-Pi factorization of Jno

QR-Pi factorization of Jno T

such that K2(Jnso) < l(2-threshold

to select H$c_H

to select P$ _c P

Process 2. Optimized Reduction

Select AH$ to

minimize AH$ T W AH$

subject to APs = JHso AHs + Jcso AC$

The subset selection process provides a method of identifying appropriate combinations of

hardware parameters and internal measurement variables that limit the solution error bound. The

L2 condition number of the hardware Jacobian, K:/(Jn$o), affords a measure of the computational

limits of solution accuracy separate from model and measurement uncertainty effects. This is

reflected in a general guideline for underdetermined linear systems which estimates the number

of significant digits lost in the solution process to be equal log(K2).

The pivoted QR factorization process [see, e.g. 6, 7] sequentially arranges hardware

parameter columns and internal measurement rows of the influence matrix Jno in descending

order of independence up to the rank of the matrix. After pivoting, elimination of parametersassociated with later colunms and measurements associated with later rows tends to reduce the

resulting submatrix condition number, thereby reducing the computational error bound. The

penalty associated with column elimination is artificial reduction in the hardware parameter state

space range. The penalty associated with row elimination is loss of state space discrimination.

Theaccuracytrade-offs for underdetermined systems are clearly indicated in a perturbation

result presented by Golub, et al [6, page 273].

The optimized reduction process requires solution of a weighted least squares problem

with equality constraints. Orthogonalization methods based on QR factorization or singular

value decomposition (SVD) are effective and dependable solution procedures for problems of

this type [6 7 8 9 10 ]. However, the basic GDR strategy utilizes Powell's implementation of the

Goldfarb and ldnani dual quadratic programming algorithm [I ! ] as the solution procedure. This

method, although less efficient, provides the flexibility to include inequality constraints as well

as linear and covariant terms in the optimization merit measure.

A conceptual view of the GDR strategy is presented in the figure below.

Figure 1 GDR Conceptual Strategy

I PlannedTest/Flight Profile

Influence

MatricesI Baseline

Definition

GDR Preprocess ]

4.0 Study Components

To define the study basis, a description of three specific components is needed: the engine

system that served as the test platform for evaluation of GDR, the test data source for the

specified engine system, and the parent engine performance model that was used to derive

engine system influences. Definition of these components is provided below.

4.1 Engine System

The MC-1 engine system was specified as the test platform for evaluating GDR

capabilities and assessing candidate enhancement procedures. The MC-1 engine is a 60,000 lb

thrust, pump-fed liquid fuel rocket engine that was developed by the Marshall Space Flight

Center (MSFC) [12]. It bums a mixture of RP-1 hydrocarbon fuel and liquid oxygen. Hot gas

produced by a gas generator is used to power a turbine that rotates an inline turbopump

assembly. The engine uses five orifices to control engine thrust and mixture ratio. These are the

gas generator liquid oxidizer orifice, the gas generator RP-1 orifice, the main liquid oxidizer

orifice, the main RP-1 orifice, and the gas generator nozzle orifice. The MC-1 engine is intended

to be reusable with the exception of the ablative nozzle. A conceptual schematic displaying

major components of the engine system is presented in Appendix A, Figure A1.

4.2 Test Data Source

Three series of MC-1 tests were recently conducted on the Alfa-1 test stand at

Rocketdyne's Santa Susanna Field Laboratory in California. The R1 series was focused on

resolving any issues associated with the new test stand. The R2 and R3 series consisted of

several tests of Engine 3 and Engine 5, respectively. Engines 1 and 2 had previously been tested

in the horizontal test facility at NASA Stennis Space Center (SSC), and Engine 3 had previously

been tested at the Propulsion Test Article Facility at SSC. The R2 series used a 15:1 area rationozzle and the R3 series used a 30:1 area ratio nozzle. Both series were conducted at test stand

altitude.

Both R2 and R3 series data sets were utilized in this study. The R2 series consisted of five

tests: the first four - R2-1, R2-2, R2-3a and R2-3b - were 24 seconds in duration, and the final

test - R2-4 - was a full duration test of 159 seconds. The R3 series consisted of two tests:

R3-1a and R3-2b, each 24 seconds in duration.

The tests had varying objectives [13]. R2-1 established an Engine 3 calibration baseline.

The effects of LOX inlet pressure variations on pump run characteristics were investigated in

R2-2. R2-3a was intended to evaluate engine calibration in response to an orifice change;

however, due to a leak in the oxidizer bleed valve, this was not accomplished until test R2-3b.

Finally, R2-4 was intended to assess engine calibration during a full duration test of 159 seconds.

The main liquid oxidizer orifice and gas generator nozzle orifice were not changed during

the R2 series. All other orifices were changed after tests R2-2 and R2-3b. Therefore, tests R2-1

and R2-2 contained identical orifice configurations, as did tests R2-3a and R2-3b. The Engine 5

calibration baseline was established in test R3-1a. Data from this test was used to guide

selection of an appropriate orifice configuration for use with the high area ratio nozzle. Test

R3-2b used the same orifice configuration as R2-4 and was used to evaluate Engine 5 calibration

in response to an orifice change. A summary of engine configuration and test definition

information for the R2 and R3 test series is provided in Appendix G, Table G1.

4.3 Parent Performance Model

A ROCETS [14] performance model of the MC-1 engine was developed at MSFC to

support engine design and testing. Fluid conditions in all of the major engine components and

flow ductsweremodeledusingone-dimensionalflow physicsandempiricisms.Thismodelwasthenonlinearsimulationplatformusedto generateenginesysteminfluencematricesfor GDRanalyses.TheROCETS/MC-1mainstagemodelwasalsomodifiedto run in datareduction(DR)mode.This fully nonlinearreductionmodel,hereindesignatedROCETSDR,providedtheconventionaldatareductionresultsusedto assesstheaccuracypotentialof GDRpredictions.

For computationaltestingof theGDRstrategy,25enginesystemmeasurements,correspondingto performancemodelvariables,wererecordedat samplingratesfrom 25Hz to250Hz. Thesemeasurementsandtheir associatedvariablenamesin theROCETS/MC-1enginemodelareprovidedin AppendixG, TableG2. Theyincludefour inlet conditionmeasurementsand21 internalenginemeasurements.Fourteenpressures,seventemperatures,two flows, oneturbopumpshaftspeed,andtheenginethrustcomprisethemeasurementlist.

A totalof 22candidatehardwareparameterswasoriginally selectedfor reductionanalysisconsideration.These are also listed in Table G2 and include four duct/line resistances, four

valve area ratios, four injector discharge coefficients, two pump head coefficient multipliers, two

pump torque coefficient multipliers, and one each turbine efficiency multiplier, gas generator

(GG) exhaust duct orifice coefficient, turbopump friction factor, nozzle discharge coefficient,

main combustion chamber (MCC) C* efficiency multiplier, and GG liquid oxygen (LOX) inlet

duct heat transfer rate.

Only 17 of the 22 candidate hardware parameters were employed in standard data

reduction analyses performed with the ROCETS DR model. The five parameters not used in

conventional reductions included the two pump torque multipliers, two main flow valve area

ratios, and one turbine efficiency. In addition, only 17 of the 21 available internal measurements

were targeted for matching in conventional reduction analyses. The four measurements not used

in standard data reduction analyses included the gas generator oxidizer valve (GGOV) inlet

pressure, the LOX dome temperature, the fuel manifold temperature, and the turbine discharge

temperature. Hardware parameters and measurements not used in standard data reduction

analyses are identified in Table G2. Subsystem schematics depicting the approximate flow path

location of all measurements relative to major hardware components are presented in Appendix

A, Figures A2 through A5.

5.0 GDR Pre-analvsis

In order to evaluate both the capabilities and limitations of the basic GDR strategy, it is

necessary to understand the analysis set-up procedure and characteristics of the reduction study

test data. The next two subsections provide the following information: an outline of the GDR

analysis setup procedure and a summary of characteristics of the R2 and R3 test series data used

in reduction analyses.

5.1 GDR Preprocessing Tasks

Once candidate measurements and hardware parameters were identified for the MC-1

engine system, five off-line preprocessing tasks were performed to prepare for a basic GDR

analysis sequence. These tasks are identified below.

Preprocessing Tasks

1. Identify an appropriate baseline state, Ho Co and Po

2. Normalize all measurement variables and hardware parameters

3. Compute elements of the normalized influence matrices at the base state

4. Assign weighting factors W for the least squares terms

5. Assimilate information into appropriately formatted input files.

Baseline values were selected to closely approximate expected operating conditions of the

engine system. Baseline values of performance model variables corresponding to internal

measurements are also required to be an achievable solution of the parent performance model

with specified baseline values of the hardware parameters and model variables corresponding to

control/input measurements. The parent performance model for this GDR study was the

ROCETS/MC-1 mainstage engine model.

For purposes of this study, baseline values were defined for each MC-1 engine test by the

following procedure.

Baseline Definition Procedure

1.1 The average of data sampled at rates from 25 Hz to 250 Hz (depending on the

specific measurement) was computed over the time interval from 22 to 23

seconds for each of the 17 internal measurements and 4 input measurements

used in standard data reduction.

1.2 The averages obtained in the previous step were used as inputs to the ROCETS

DR model to obtain test specific baseline values for the hardware parameters

Ho.

1.3 Input variables were assigned the baseline values Co indicated below.

PSVL 10 - LOX inlet pressure 47 psia

TTVL10 - LOX inlet temperature 164.5 R

PSRPFV - Fuel inlet pressure 43 psia

TTRPFV - Fuel inlet temperature 505 R

1.4 Baseline values P. for variables associated with the internal measurements were

then obtained by running the ROCETS/MC-1 performance model with

hardware parameters assigned baseline values Ito from step 2 and input

variables assigned the baseline values Co indicated in step 3.

This four-step procedure was adopted to provide a baseline state indicative of the best

available information regarding engine operation with standard inputs. It was also meant to

approximate an operational procedure that uses information available from engine acceptance

tests. Baseline information derived using the above procedure for each MC-1 test is presented in

Appendix G, Tables G3 and G4.

The second preprocessing procedure involving normalization of variables is essential for

robust reduction analysis. The normalization procedure generally affects the parameter selection

process, the reduction solution Hs, and the confidence bounds associated with the solution. The

preferred scaling procedure involves uncertainty measure normalization. In the absence of

reliable uncertainty estimates, one approach is to normalize the shift from baseline value for each

variable by the baseline value for that variable. This is equivalent to uncertainty normalization

under the assumption that the uncertainty as a percentage of baseline value is the same for all

variables. Variable and Jacobian normalizations using this assumption are specified below.

Normalization Groups

(5)

JHo _ Jco* =0 o

(6)

The mathematical forms of both the normalized selection process and the normalized

reduction process in the basic GDR strategy are unchanged using the above groups despite the

fact that both the selection and solution results may be significantly altered by the rescaling.

A central difference scheme utilizing ROCETS/MC-1 engine simulation results was

employed to approximate all Jacobian components. The standard mathematical form of this

approximation is indicated below.

Pi(Hoi+,SHi) - Pi(I-Ioi-SHi)

JHo-ij _ 2*SHj(7)

In this expression, Pi(Hoj---rHj) is the ROCETS/MC-1 output value for dependent variable Pi

corresponding to an internal measurement with all hardware parameters and input conditions at

base state conditions except Hj. Baseline incremented values of the hardware parameter, Hj =

Hoj+rHj, are used in the simulation runs that determine values of Pi for the numerator difference.

A similar central differencing procedure was used to obtain the control Jacobian elements Jco-ik.

The diagonal weighting matrix W provides a means of incorporating information that

augments the physical and empirical basis of the parent model. If reliable hardware parameter

uncertainty estimates are available, the diagonal components of the weighting matrix afford an

effective means of incorporating this information. In this study, the weighting matrix was set

equal to the identity matrix for all basic GDR analyses. This is consistent with the parameter

normalizations described in equation (5) and effectively assumes the same level of confidence

for estimates of all hardware parameters.

The GDR input file accumulates information required for a reduction run including:

parameter names and baseline values, parameter normalizing factors, weighting matrix

components, normalized hardware and control influences, and other parameter designations that

identify the dimension of the reduction problem. In this study, test data was embedded in the

GDR input file and processed sequentially, one time slice at a time, to simulate an actual data

input stream. For real time processing of test or flight data, preloading of data within the input

file would be replaced by an appropriate interface to the data stream.

5.2 MC-1 Engine Test Data

MC-1 engine R2 and R3 test series data for each of the 25 measured quantities identified in

Table G2 were used. Data gathered during the first five seconds of operation after engine

ignition were not considered in this study in order to reduce the influence of start up transients.

One second averaged data over the operating interval from 6 to 23 seconds were used for all tests

except R2-4. Test R2-4 was a full duration test of 159 seconds, and one second averaged data

overtheoperatinginterval from 6to 158secondswereusedfor this test. Datafor eachmeasuredvariableovertheoperatinginterval from 6to 23 secondsfor all testsaredisplayedin AppendixB, FiguresB1 throughB25. Onesecondaverageddatafor all seventestsareprovidedinAppendixH, TablesH1 throughH7.

Generalinformationdescribingcharacteristicsof theR2 seriestestdataarepresentedinAppendixH, TableHS. For aspecifictest,thecharacteristicincrease(or decrease)in ameasuredparameterthatoccurredduringthe 17secondtestintervalfrom 6 to 23secondswascomputedby determiningtheslopeof thebestfit linerelatingthemeasuredparameterto time;multiplying thisresultby the 17secondintervallength;andthendividing by thetestbaselinevalueof theparameter.Theresultis acharacteristicincreaseexpressedasapercentageof thebaselinevalue. Thefive-testaverageincrease(or decrease)computedin this fashionis presentedin TableH8. Thesevaluesindicatethemagnitudeanddirectionof datatrendsoverthe 17secondinterval from 6 to 23seconds.Theabsolutevaluesof thesetrendsgenerallyfell in theinterval fromoneto threepercent.A significantexceptionwastheinlet LOX pressurewhichexhibitedanaverageincreaseof morethan6%.

As mentionedearlier,thesameorifice set- number5 - wasusedin testsR2-1 andR2-2. Foreachmeasuredparameter,theabsolutevalueof thedifferencebetweenthetestR2-1observedvalueatagiventime slice,andthetestR2-2observedvalueatthesametime slice,averagedoverall time slices,providesan indicationof thenormaldispersionof themeasuredparameterfor aconstantconfigurationenginesystem.Similardispersioninformationfor a constantconfigurationenginesystemusingorifice set6 wasobtainedby examiningdatafrom tests R2-3a

and R2-3b. These test-to-test dispersion measures are presented in Table H8 for each measured

parameter. The observed differences are caused by inlet condition, hardware function, and

measurement system variation. For example, the effects of engine fuel inlet pressure (PSRPFV)

variation are clearly mirrored by the fuel pump inlet pressure (PSVL00) difference in the orifice

set 5 test sequence R2-1 R2-2. The large difference in turbine discharge temperature

(TTHTGD) for the orifice set 5 test sequence was caused by a temperature sensor failure duringtest R2-1.

The effects of inlet condition variation can be removed by adjusting values of all measured

internal parameters for standard conditions, i.e., expected values given baseline inlet conditions

and baseline hardware conditions. Using the linearized performance model relations from

equation (1), expected values of the measured internal parameters adjusted for standard baseline

inlet conditions can be estimated by the relation below.

Pstd = Pmeas - Jco (Cmeas - Co) (8)

Plots of R2 series test data adjusted for standard inlet conditions are shown in Appendix C,

Figures C1 through C21. Examination of these plots indicates a significant reduction in the rates

of increase (decrease) of most measured intemal parameters over the sampled range from 6 to 23

seconds. These rate reductions are confirmed by the average R2 series rise (drop) values for

standard inputs shown in Appendix H, Table H9. This suggests that much of the time dependent

variation in measured parameters was due to inlet condition variation over the course of the test.

Orifice set 5 average absolute differences for the test sequence R2-1 R2-2 were reduced for

all internal measurements adjusted for standard inlet conditions as shown in Table H9. However,

orifice set 6 differences, associated with the test sequence R2-3a R2-3b, were generally greater

after correction to a standard input state. For each internal measurement parameter, the observed

10

test-to-test average absolute difference after adjustment for standard inlet conditions was caused

primarily by hardware function and measurement system variation. The oxygen bleed valve leak

that occurred in test R2-3a represents an additional unknown boundary condition variation that

impacted orifice set 6 differences.

6.0 Initial GDR Analysis Results

In order to facilitate comparison with accepted reduction results obtained from the parent

ROCETS DR model, the same 17 hardware parameters used in the parent reduction process were

used in GDR analyses of the MC-1 engine. These 17 parameters have been identified previously

and correspond to the unshaded hardware parameters shown in Appendix G, Table G2.

After preprocessing operations were completed, the automated subset selection process was

performed to eliminate redundant or ill-scaled measurements, thereby reducing the L2 condition

number of the hardware Jacobian matrix to an acceptable value. In all cases the first four

measurements eliminated by the automated selection process were as indicated below.

TTVL05

TTVL14

TTHTGD

PSVL15

Fuel manifold temperature

LOX dome temperature

Turbine discharge temperature

Gas generator oxidizer valve (GGOV) inlet pressure

These were precisely the four measurements eliminated by expert selection prior to ROCETS

DR analyses. After elimination of these four measurement variables, the resulting Jacobian

condition number was not small enough to guarantee stability. However, basic GDR analyses

were run using the 17 remaining internal measurements and 4 inlet measurements to facilitate

direct comparison to the accepted ROCETS DR standard.

Typical GDR and ROCETS data reduction results for test R2-1 are displayed in Appendix

D, Figures D1-D17. These figures contain both GDR and ROCETS time history data reduction

results for each of the 17 selected hardware parameters. Differences between GDR and

ROCETS DR results are generally observed to be small over the entire test time interval. The

largest differences are associated with the fuel pump inlet line resistance RKFL1 and the gas

generator fuel valve area ration XMGGKO.

The difference between GDR and ROCETS DR predictions was computed for each

hardware parameter at each one second time slice. Absolute values of these differences were

averaged over all time slices in the test interval for each hardware parameter. This information is

displayed in Appendix I, Table I1. Average absolute deviations greater than 0.5% of baseline

were confined to test R2-1 and test R2-2. This indicates that the basic GDR procedure was

capable of providing a consistent approximation of hardware behavior that agrees well with the

recognized standard for MC-1 engine data reduction. However, average absolute deviations in

excess of one percent for two parameters in each of tests R2-1 and R2-1 plus the large Jacobiancondition number were concerns.

It should be noted that the primary motivation for constructing a simplified representation of

the performance model is to improve analysis speed to support health monitoring. The basic

GDR results for the MC-1 engine were processed at a rate greater than 200 time slice reductions

per second on an 800 MHz Pentium III processor. This qualifies the procedure as a real-time

analysis tool. There are other advantages to the simplified GDR representation of the engine

11

relatedto stability andaccuracycharacterizationthat areaddressedlaterin thisreport. Thenextsectiondocumentsenhancementsconsideredfor thebasicGDRprocedure,which will henceforthbeidentifiedasGDRA, in orderto improvecomputationalspeed,accuracy,andstability.

7.0 GDR Modifications

Three types of modifications to the basic GDR strategy were explored in efforts to improve

the effective solution range of the method as well as the computational speed, accuracy, and

stability of the solution process.

Types of GDR modifications1. Modifications of the subset selection scheme

2. Modifications of the solution procedure

3. Modifications of the problem formulation

Specific changes investigated during the course of this effort are described in the followingsubsections.

7.1 Solution Procedure Using Singular Value Decomposition

A very efficient procedure for determining the minimum 2-norm solution to a linear system

is based on the singular value decomposition (SVD) of the coefficient matrix. This procedure,

applied to the balance relations described in equation (1), requires computation of the SVD of thehardware Jacobian matrix. The form of the decomposition is described below [see, e.g. 6].

where

U T Jno V = Z (9)

U is a mxm orthogonal matrix with column partitioning U = [ ul • • •Um ]

V is a nxn orthogonal matrix with column partitioning V = [ Vl. • • vn ]

= diag(_l... Crp) is the diagonal matrix of singular values cri arranged in

descending order of magnitude

p = min(m,n)

Using information from the decomposition, the minimum 2 norm solution to the system

JnnAH = b = AP-JcoAC (10)

can be computed directly using the relation

r

An = __ uiT----_b •o'i vi

i=1

where r _<p is the estimated rank of Jao.

Equation (11) is obtained using a generalized inverse of the hardware influence matrix toisolate the hardware solution. Once the SVD of the Jacobian Jno is computed, hardware

(11)

12

solutionsmaybeobtainedveryquickly fromthedirectcomputationof AH prescribedbyequation(11). A versionof GDRbasedon theSVD decompositionproceduredescribedinequations(9) through(11)wasimplementedandwill bereferredto asGDRB.

Computationalexperimentswereperformedwith GDRBto determineefficiencyandtoassesspotentialfor reducingsubsetselectionoverhead.For nearrankdeficientJacobians,reductionin therankestimater, whichcorrespondsto eliminationof nearsingulardirections,canbeusedinsteadof parametereliminationto reduceredundancyandscalingproblems. This

effectively reduces the need for a separate subset selection process. Unfortunately, rank

reduction has two significant drawbacks that disqualified it as a subset selection substitute.

1. Ifa rank estimate r < p is used in equation (11), hardware shifts are no longer a

continuous function of the data

2. Realistic single parameter shifts may not be recoverable upon elimination of singular

direction(s) implicit with rank reduction.

Because of the computational overhead added to complete the initial SVD, improvements in

GDRB reduction cycle speed were negligible for short duration test runs. The average reduction

cycle rate for test R2-4 - the full duration test of 159 seconds - was increased by approximately

30%. Coupled with the QR-Pi subset selection routine, GDRB reduction solutions were

essentially the same as those returned by the basic GDR procedure.

7.2 Partial Second Order Formulation and Solution Procedure

The primary range and accuracy restrictions of the GDR procedure are imposed by the

model linearization leading to equation (1). There are many paths available to relax the linear

approximation. Perhaps the most direct approach is to incorporate higher order effects in a

sequence beginning with second order terms. For a system with 17 defining hardware

parameters, there are 153 distinct second order terms - 136 covariant terms and 17 second order

terms of the form (AHj) 2. If component hardware performance parameters are defined such that

there is little interaction between the parameters, i.e., the performance parameters are

independent, then the covariant terms are negligible.

Although the hardware parameters used for MC-1 engine reduction analyses were not

strictly independent, a second order extension of GDR adding only terms of the form (AHj) 2 was

implemented and tested. This extension, designated GDRC, used the approximate second orderbalance relations below to define the reduction solution.

where

AP _ Jno All1 1

+ Jco AC + ] Drlo diag(AH) AH + _- D¢o diag(AC) AC (12)

bno = aHj2 j Dco = c3Ck2 j (13)

A five point central difference scheme was employed to compute elements of the second

order influence matrices Dn, and Dco. The measurement selection process was assumed static -

utilizing only the first order hardware Jacobian at the base state in the QR-Pi factorization that

13

identifiedmeasurementsto eliminate. A Newtontypeiterativemethod[15 ] wasusedto solvebalancerelations(12) reorganizedin theformbelow.

[ 1 ] 1Jno + ] DHo diag(AH) AH = AP - Jco AC - ] Dco diag(AC) AC (14)

Because deviations from standard DR results returned by GDRA were larger for tests R2-1

and R2-2 (see Appendix I, Table I1), nonlinear GDRC analyses were performed using only R2-1

and R2-2 test data. Comparisons to GDRA results are given in Appendix I, Table I2.

It is obvious from Table I2 that predicted deviations from standard DR results were not

consistently improved using the nonlinear GDRC formulation. In addition, the deviation of

GDRC predictions from standard DR results for the GG fuel valve area multiplier XMGGKO

were significantly greater than those returned by GDRA. Further testing was not performed

given the greater computational overhead and lack of significant improvement in solution

accuracy.

7.3 Formulation with Hardware Parameter Functions

Modification of the original hardware parameter set was indicated based on the following

observations.

1. Influences of the main fuel line calibrating resistance RCALMF were large

relative to hardware specific resistances along the main fuel line.

2. Influences of the main oxidizer line calibrating resistance RCALMO were large

relative to hardware specific resistances along the main oxidizer line.

3. Shaft friction factor FRICFACT shifts were very large as a percent of baselineat the reduction solution. This indicated that FRICFACT was not well scaled

and could artificially dominate a linear systems solution process.

4. All valve area multipliers and injector discharge coefficients were proportional

to one over a driving pressure difference squared (i.e., valve XM's and injector

CD's oc 1/AP2). Therefore, pressure dependence on XM's and Cd's is

inherently nonlinear.

These observations motivated a revision of the set of hardware parameters used for MC-1

engine reduction analyses as indicated in Table 1 below. The complete set of hardware

parameters used in data reduction analyses after incorporating the revisions below is

given in Appendix G, Table G5.

14

Table 1 MC-1 engine revised hardware parameters

Original Hdwe

parameterCDGGKI

CDGGOI

CDKINJ

CDOINJ

XMMCKO and[

RCALMF

KMMCO0 and

RCALMO

XMGGKO

XMGGO0

FRICFACT

Modified hdwe

parameter Modified hdwe description

RGGK1

RGGOI

RKINJ

ROINJ

RMMCRP

RMMCOX

RMGGRP

RMGGOX

PWRFACT

GG fuel injector equivalent resistance

GG oxidizer injector equivalent resistance

VlCC fuel injector equivalent resistance

MCC LOX injector equivalent resistance

Main fuel line equivalent resistance

Main LOX line equivalent resistance

GG fuel line equivalent resistance

GG LOX line equivalent resistance

Turbopump power factor

Spanning PressuresPSVLO9 - PTHTGI

PSVL18 - PTHTGI

PTVL05 - PTMCHY

PTVL14 - PTMCHY

PSVL01 - PTVL05

PSOXDS - PSVL13

PSVL01 - PTVL09

PSVL15 - PSVL18

PWRFACT in the above list can be thought of as the ratio of actual pump shaft delivered

power to actual turbine shaft supplied power. It combines the effects of turbine efficiency

multiplier, pump torque multipliers, and shaft friction factor such that the following

proportionality applies

1-FRICFACT

PWRFACT oc ETAMHTGT * (2 pump equivalent torque multiplier)(15)

The switch to equivalent resistances is a way of converting the original hardware parameter

set to a more natural parameter set composed of linearly independent nonlinear functions of the

original parameters. Since resistance is by definition proportional to spanning pressure drop,

measured pressures are more naturally represented as linear functions of the equivalent

resistances.

In general terms, the data reduction problem with the modified hardware parameters can

be represented as follows.

Find Af(H) such that

AP _ Jf(Ho)Af(H) + Jco AC (16)

where

f(H) = [ fl(H). • • fn(H) Ir Af(H) = [ fl(H)-fl(Ho) • • fn(H)-fn(no) l r (17)

[eP 7Jf.,o)= l Jo (18)

For the MC-1 engine, the functions fOt) represent the modified hardware parameter setidentified in Table G5.

7.3.1 GDRA and ROCETS DR Comparisons

15

GDRA analyses of the MC-1 engine were performed using the revised hardware parameter

set listed in Table G5. The deviation of GDR predicted values from standard ROCETS DR

results, converted to display values of the revised hardware parameters, is provided in Appendix

I, Table I3. The agreement is observed to be excellent. Over the seven test R2 and R3 series,

only the inlet fuel resistance RKFL1 in test R2-1 exhibited an average deviation greater than one

percent. Time slice reduction cycles were performed at a rate greater than 200 per second on a

system equipped with an 800 MHz Pentium III processor. The accuracy of these reduction

results coupled with high cycle speed qualifies the process as a real time monitoring candidate

for nominal MC-1 engine operation.

7.3.2 Single Source Anomaly Resolution Capability

In order to assess GDR capability to identify single source anomalies, a series of simulations

were performed with single source hardware anomaly input. Simulated test data for each single

source anomaly was obtained as output of ROCETS/MC-1 runs with one hardware parameter

modified from its baseline value. This data was provided for GDRA reduction analyses to

determine if the anomaly would be identified. Results are presented in Appendix E, Figures E 1

through E20. Each figure identifies the magnitude of the input anomaly and the distribution of

causation allocated by each of ROCETS data reduction and GDRA using simulated test data.

Two GDRA results are presented, one that employed the standard 17 measurement set also used

to derive ROCETS DR results, and one using only 16 measurements as an example of lost

measurement effect on anomaly resolution capability. The additional measurement eliminated

for the 16 measurement case was the LOX GG inlet temperature TTVL 18.

High fidelity anomaly recovery is generally observed. The following comments address

specific characteristics of the simulation results.

1. Figure El3. A fuel pump torque multiplier (TRQMKPMP) anomaly reduction is

recovered as a clearly identifiable power factor (PWRFACT) increase by all reduction

procedures. This is consistent with the definition of power factor.

2. Figure El6. Same comments as number 1 for a turbine efficiency multiplier

(ETAMHTGT) reduction.

3. Figure E20. LOX inlet duct heat transfer (QDOTVL18) shift was not recovered by

GDRA using 16 measurements. This is because the GG LOX inlet duct temperatureTTVL18 is a direct indicator of duct heat transfer. When this measurement is lost, the

ability to identify heat transfer rate is also lost. This is an example of a very specific lossof discrimination effect. Other effects of TTVL18 measurement loss on anomaly

resolution capability are negligible.

4. Figure E14. An oxygen pump torque multiplier (TRQMOPMP) reduction was allocated

as various effects: a main oxygen line equivalent resistance (RMMCOX) increase, a gas

generator oxygen line equivalent resistance increase (RMGGOX), and a power factor

(PWRFACT) increase by all reduction methods, and a LOX duct heat transfer

(QDOTVL18) reduction by both ROCETS DR and GDR using 17 measurements. This

was the only case in which no reduction procedure, including the parent ROCETS DR

procedure, could allocate a single source anomaly to a single predominant reduction

16

parameter. This indicates a need to modify the measurement suite and/or the parent

performance model to allow clear identification of anomaly operation.

It should be noted that shifts in both the fuel pump torque multiplier (TRQMKPMP) and the

turbine efficiency multiplier (ETAMHTGT) have a clear power factor (PWRFACT) signature.

This suggests that shifts in these parameters can be detected but not discriminated using the

revised reduction parameter set. The oxygen pump torque multiplier (TRQMOPMP) is the only

parameter that did not have a clear anomaly signature.

7.3.3 Sensor Failure Response

A study was performed to determine the effects of single sensor failures on reduction

analysis predictions using the revised set of hardware parameters. GDRA solutions with

individual sensors eliminated were obtained and compared to standard ROCETS DR results

using all 17 measurements. Results using test R2-4 data are reported in Appendix I, Table 14, in

the form of average absolute deviations from ROCETS DR results as a percentage of baseline

hardware parameter value.In each column of Table I4, measurements eliminated by subset selection are identified in

addition to the measurement eliminated to simulate sensor failure. Hardware parameters with

deviations in excess of 2% are identified as unreliable with the indicated sensor failure.

Parameters with deviations between 1% and 2% are identified as only marginally reliable with

the indicated sensor failure. Results indicate that the total LOX flow (WOXTOTL) and the

turbine inlet temperature (TTHTGI) are the most critical for reduction accuracy.

7.3.4 Results with Flight Measurement Suite

Only five intemal measurements in addition to the four inlet measurements were planned

for MC-1 flight engines. The flight measurement set is identified in Appendix G, Table G6, and

includes one temperature at the turbine inlet (TTHTGI), and four pressures: two pump discharge

pressures (PSOXDS and PSVL01), the gas generator pressure (PTHTGI), and the main chamber

pressure (PTMCHY). No flow measurements were anticipated for the flight engine.

The candidate hardware parameter set was reduced to 12 by combining resistances between

pressure measurements and by eliminating the nozzle discharge coefficient characterized

primarily by thrust. The set of candidate hardware parameters for flight data reductions isdefined in Table G6.

Three of the flight candidate hardware parameters were further eliminated because relevant

temperature measures were not available. These included the two pump torque multipliers

(TRQMKPMP and TRQMOPMP) and the turbine efficiency multiplier (ETAMHTGT). GDRA

analyses were performed using data from test R2-4 for five internal measurements and four inletcondition measurements to estimate the nine remaining hardware parameters. Results of these

analyses are compared to ROCETS DR results with a full suite of 17 measurements in Appendix

F, Figures 1 through 9. Summary observations are provided below.

1. Loss of detail discrimination is evident for main fuel line series resistance R3MCRP in

Figure F 1.

17

2. Somelossof detailandtrendingis observedfor mainoxidizer line seriesresistanceR3MCOXin FigureF2.

3. Little orno resolutionlossis observedfor GGinlet seriesresistancesR3GGRPin FigureF3andR3GGOXin FigureF4.

4. Little discriminationlossandonly slighttail endtrendinglossis observedfor thefuelpumpheadcoefficientmultiplier in FigureF5.

5. Sometrendinglossis observedfor theLOX pumpheadcoefficientmultiplier in FigureF6.

6. Very slighttrendinglossis observedfor thepowerfactortermPWRFACTin FigureF7.7. Sometrendinglossis observedfor theMCC efficiencymultiplier in FigureF8.8. HeattransfereffectsQDOTVL18werenot recoveredat all asindicatedin FigureF9.

Averageandmaximumabsolutedeviationsof GDRA results,obtainedusingonly flightmeasurements,from standardROCETSDR predictions,obtainedusinga full suiteof 17measurements,areprovidedin AppendixI, TableI5. Consideringthelimited measurementinput,resultswerejudgedto bequitegoodwith only oneparameter(QDOTVL18) deviatingover2%from its standardvalue.

In anattemptto correctsomeof thedetailandtrendinglossesapparentin FiguresF1throughF9, fixedLOX andfuel flow ratesobtainedby averagingflow dataover thetime intervalfrom 20 to 23secondswereaddedto theflight datafor reductionanalysis.Thiswasintendedtosimulatetheuseof bestavailableflow informationfrom acceptancetesting. Reductionresultsobtainedusingthefixed flow ratesarepresentedin AppendixF, FiguresF10throughF18.Summaryobservationsareprovidedbelow.

1. Most of thediscriminationlossreportedfor R3MCRPwasrecoveredasshownin FigureF10.

2. Most of thetrendinglossreportedfor R3MCOXwasrecoveredasshownin FigureF11.3. Most of thetrendinglossreportedfor PSIMOPMPwasrecoveredasshownin Figure

F15.4. Trendinglosseswereexacerbatedfor PWRFACTasshownin FigureF16.5. Mostof thetrendinglossreportedfor ECSMMCHBwasrecoveredasshownin Figure

F17. Detaildiscriminationwasreducedhowever.6. No improvementin QDOTVL18recoverywasobservedasshownin FigureF18.

Averageandmaximumabsolutedeviationsof GDRAresults,obtainedusingflightmeasurementswith 20-23secondaverageflows, from standardROCETSDR predictions,obtainedusinga full suiteof 17measurements,arealsogivenin AppendixI, TableI5. With theexceptionof QDOTVL18,someimprovementis evidentespeciallyin thestandarddeviationoftheabsolutedifferences.GDRAreductionresultusingflight measurementsaugmentedwithfixed averageflows indicativeof actualengineoperation,suchasavailablefrom acceptancetests,wereevaluatedasreasonablefor real-timemonitoringapplications.

7.4 Subset Selection Procedures

One of the key components of the GDR strategy is a parameter selection strategy.

Automated parameter subset selection is applied primarily to eliminate measurements and

18

stabilize ill-conditioned underdetermined systems. In the basic GDR method, this is

accomplished using a QR-Pi factorization of the transpose of the hardware Jacobian matrix.

Although heuristic, this method appears to effectively isolate and eliminate measurement

redundancy and scaling problems.

Automated hardware parameter selection is inherently more difficult. For robust engine

health monitoring, hardware parameters should be selected based primarily on

failure/degradation risk and impact. Failure/degradation potential can only be established by

examining the experience base of like components and engine systems. Lacking effective

estimates, hardware parameter elimination is difficult to justify and can be detrimental if

components with significant failure risk are eliminated.

Despite the above observations, two automated procedures for selecting both hardware andmeasurement variable eliminations were constructed and implemented. One was based on

sequential QR-Pi factorization of the hardware Jacobian and its transpose. The second was

based on sequential condition number reduction. In both cases, the order of hardware and

measurement eliminations is user specified.

Computational experience with the dual selection strategies is still limited. Typical results,

obtained using the QR-Pi dual elimination algorithm to select 5 measurements from the

available suite of measurements for the MC-1 engine, are presented in Appendix I, Table 16.

The leftmost shaded section of the table displays the flight internal measurement set specified for

the MC-1 engine. The remainder of the table presents results of four automated subset selection

sequences differing by user specified front-end eliminations and measurement-hardware

elimination sequence. Candidate measurement variables, before any elimination, were the 21

MC-1 internal measurements identified in Appendix G, Table G2. Candidate hardware

parameters, before any elimination, included only members of the revised hardware set defined

in Table G5.

The procedure designated "Auto-Selection 1" in Table I6 was a measurement only

elimination sequence beginning with four user defined hardware eliminations and one

measurement parameter - engine thrust - elimination. The automated procedure eliminated 15additional measurements. The five remaining measurements variables were the LOX pump

discharge pressure (PSOXDS), the turbine inlet temperature (TTHTGI), both the fuel and LOX

total flows (WRPTOTL and WOXTOTL), and the turbine discharge pressure (PTVL22). Onlytwo of the five selected measurements is included in the flight list. There are many possible

reasons for this difference that have nothing to do with the mathematical characteristics of the

hardware Jacobian. These include a host of practical consideration including cost, ease of

installation and maintenance, reliability, life, uncertainty, etc.

"Auto-Selection 2" is another measurement only elimination sequence, but beginning with

three user defined eliminations including both propellant flow rates. The selection process

identified five measurements from a list that does not include the propellant flows. The five

selected measurements include three on the flight list.

"Auto-Selection 3" is a repeated measurement-hardware elimination sequence that selects

five measurements and five compatible hardware parameters. The selected measurements arethe same as identified in auto-selection 2. The selected hardware parameters include critical

turbopump (PSIMKPMP, PSIMOPMP, and PWRFACT), chamber (ECSMMCHB), and gas

generator nozzle (CDGGNZ) characteristics.

"Auto-selection 4" is another repeated measurement-hardware elimination sequence that,

because of user eliminations, begins with a smaller set of hardware parameters. The parameters

19

selectionsaresimilarto thoseof"Auto-Selection3" andthereaderisreferredto TableI6 fordetailedinformation.

It is importantto understandthatsequentialselectionproceduresdonot identify globallyoptimumsubsetsin general.This is amajordrawbackandsuggeststheneedfor computationaltestingto validatethesuitabilityof parameterselections.

The mathematical and statistical literature dealing with subset selection is extensive [see

e.g., 6, 15, 16, 17, 18]. A robust selection strategy must incorporate risk and uncertainty

information that goes beyond classical analytical considerations of stability. Uncertainty scaling

is one natural method of incorporating uncertainty information within the selection procedure;

however, the assignment of risk and uncertainty estimates appropriate for MC-1 engine operation

was beyond the scope of this effort.

8.0 Summary of Research Effort

The following procedures were developed and implemented during the course of this

research effort.

1. An efficient generalized inverse solution procedure based on singular value

decomposition of the hardware Jacobian. This solution procedure was incorporated in

the code version identified as GDRB.

2. A version of GDR that incorporates a restricted second order approximation model of

engine performance and a Newton type solution scheme. This approximation model and

solution procedure was incorporated in the code version designated GDRC.

3. A redefined hardware parameter formulation for the MC-1 engine that improves the

linear system approximation and a general formulation that characterizes hardwarecombination schemes

4. Two dual sequential subset selection schemes that identify computationally compatible

combinations of hardware parameters and measurement variables for data reduction.

The following GDR performance measures for MC- 1 engine system reduction analysis wereobtained.

1. GDRA reduction analysis cycle rate >200 cycles per second, GDRB > 250 cycles per

second, GDRC > 50 cycles per second

2. Average hardware parameter deviation from full nonlinear parent model data reduction

results using full measurement suite and revised hardware list, < 0.5% except for isolated

cases (Table I3)

3. Single source anomaly recapture capability with full measurement suite and revised

hardware list (based on simulations), >90% of parent model signature with one possible

exception (Figures E1 through E20)

4. Qualified integrity of reduction hardware parameter recovery for single sensor losses and

identified loss of discrimination parameters for each sensor loss (Table 14)

5. Average deviation of GDRA hardware predictions, using only the flight measurement set,

from full nonlinear parent model DR results using full measurement suite, <1% with two

exceptions, <2% with one exception (Table I5)

20

9.0 Assessments and Recommendations

The following assessments are specific for the MC-1 engine system instrumented with the

standard measurement suite (Table G2) and GDRA using the revised hardware parameter set

(Table G5).1. Assuming sensor integrity, GDR would be an effective real time monitoring tool for the

MC-1 engine system.

2. GDR is capable of detecting and isolating most single source hardware anomalies and

should be capable of resolving many multiple source anomalies. GDR cannot identify

oxygen pump efficiency anomalies and cannot discriminate between efficiency losses in

the turbine or fuel pump.

3. GDR can reliably track the behavior of most hardware parameters in the presence of a

single sensor failure if the failure is recognized.

4. GDR can predict nominal trends of flight revised hardware parameters (Table G6) given

the five specific internal flight measurements identified in Table G6 and good estimates

of engine component propellant flows. Reliable anomaly resolution capability using only

the designated flight measurements is unlikely.

The following are general assessments and recommendations based on results of this study.

1. The QR-Pi dual subset selection routine developed during this effort provides an

effective sequential method of specifying compatible measurement and hardware sets for

reduction analyses. It is limited to considerations of scale and redundancy based on

information from the best available system model.

2. Significant improvement in selection of appropriate measurements for robust health

monitoring will require reliable estimates of both measurement and model uncertainty.

3. If reasonable uncertainty estimates of measurement and model uncertainty are available,

GDR should be modified to incorporate uncertainty scaling. This would improve both

the subset selection process and the solution procedure.

4. A globally optimum measurement and hardware selection procedure should be

developed.

5. The GDR development path is incremental. Reliable extensions will require application

to an engine system with a larger controlled operating range.

6. GDR predictions are susceptible to data bias. GDR should be used in conjunction with a

reliable sensor qualification algorithm, or a qualification procedure should be

incorporated in GDR.7. A simulation platform to study the effects of noise and measurement uncertainty on

prediction reliability should be developed.

21

10.0 References

. Aguilar, R., Garcia, R., Luu, C., Panossian, H., and Ruhkala, D., "Propulsion System Model BasedAssessment," draft report, NASA Contract NAS3-99135, Boeing-Canoga Park, Canoga Park,California.

, Grodent, M. and Navez, A., "Engine Physical Diagnosis Using a Robust Parameter Estimation

Method," AIAA 2001-3768, 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Salt Lake

City, LIT, July, 2001.

. Santi, L. and Butas, J., "Generalized Data Reduction Strategy for Rocket Engine Applications,"AIAA 2000-3306, 36 thAIAA/ASME/SAE/ASEE Joint Propulsion Conference, Huntsville, AL, July,

2000.

. Butas, J. P., Meyer, C. M., Santi, L. M., and Sowers, T. S., "Rocket Engine Health Monitoring Usinga Model-Based Approach," AIAA 2001-3764, 37 thAIAA/ASME/SAE/ASEE Joint Propulsion

Conference, Salt Lake City, UT, July, 2001.

5. Doel, D. L., "An assessment of weighted-least-squares based gas path analysis," J. of Engineering for

Gas Turbines andPower, Vol. 116, 1994, pp. 366-373.

6. Golub, G. H. and Van Loan, C. F., Matrix Computations, 3rd ed., The Johns Hopkins University

Press, Baltimore, MD, 1996.

7. Bjrrck, A., Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA, 1996.

8. Gulliksson, M. and Wedin, P- A., "Modifying the QR-Decomposition to Constrained and Weighted

Linear Least Squares," SIAMJ. Matrix Anal. Appl., Vol. 13, 1992, pp. 1298-1313.

9. Bj6rck, A. and Paige, C. C., "Solution of Augmented Linear Systems Using Orthogonal

Factorizations," BIT, Vol. 34, 1994, pp. 1-24.

10. Hubert, L., Meulman, J., and Heiser, Willem, "Two Purposes for Matrix Factorization: A Historical

Appraisal," SIAM Review, Vol. 42, No. 1, 2000, pp. 68-82.

11. Goldfarb, D. and Idnani, A., "A Numerically Stable Dual Method for Solving Strictly Convex

Quadratic Programs," Mathematical Programming, Vol. 27, 1983, pp. 1-33.

12. Ballard, R. O. and Olive, T., "Development Status of the NASA MC-1 (Fastrac) Engine," AIAA

2000-3898, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Huntsville, A1, July, 2000.

13. "MC-1 ALFA-1 R2 Test Series Data Review, Engine Systems Section," NASA Marshall Space

Flight Center, September, 2000.

14. "System Design Specification for the ROCETS (Rocket Engine Transient Simulation) System," Pratt

& Whitney FR-20284, prepared for NASA MSFC, August 24, 1990.

15. Bjrrck, A., Park, H., and Elden, L., "Accurate downdating of least squares solutions," SIAMJ. Matrix

Anal Appl., Vol. 15, No. 2, 1994, pp. 549-568.

22

16.Feiveson, A. H., "Finding the Best Regression Subset by Reduction in Nonfull-Rank Cases," SIAMJ.

MatrixAnaL AppL, Vol. 15, No. 1, 1994, pp. 194-204.

17. Kanjilal, P.P., Saha, G., and Koickal, T. J., "On Robust Nonlinear Modeling of a Complex Processwith Large Number of Inputs Using m-QRcp Factorization and Cp Statistic," IEEE Transactions on

Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 29, No.l, 1999, pp. 1-12.

18. Couvreur, C. and Bresler, Y., "On the Optimality of the Backward Greedy Algorithm for the SubsetSelection Problem," SIAMJ. Matrix Anal AppL, Vol. 21, No. 3, 2000, pp. 797-808.

23

Appendix A

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