Main Engine startup transient. The three parameters were the main combustion chamber pressure, 

a controlled parameter; the high pressure oxidizer turbine discharge temperature, a redlined 

parameter; and the high pressure fuel pump discharge pressure, a failure-indicating performance 

parameter. Network inputs consisted of time windows of data from engine measurements that 

correlated highly to the modeled parameter. A standard backpropagation algorithm was used to train 

the feedforward networks on two nominal firings. Each trained network was validated with four 

additional nominal firings. For all three parameters, the neural networks were able to accurately ^ 

predict the data in the validation sets as well as the training set. 

Nomenclature 

L-IDS 

DUMl 

DUM2 

e(t) 

f 

FPB 

FPOV 

HPFP 

HPFT 

HPFTP 

HPOT 

MCC 

n, 

net, 

Oi 

OP 

OPB 

OPOV 

PBP 

r 

rms 

ssc 

ssnip: 

t 

tP 

‘i 

q(t) 

wij 

y(t) 

activation function of hidden and output layer nodes 

command and data simulator 

open-/closed-loop variable for the MCC pressure model 

pre-/post-prime time and open-/closed-loop variable for the 

HPOT discharge temperature model 

additive uncorrelated noise 

nonlinear function describing relationship between system variables 

fuel preburner 

fuel preburner oxidizer valve 

high pressure fuel pump 

high pressure fuel turbine 

high pressure fuel turbopump 

high pressure oxidizer turbine 

main combustion chamber 

the window size of function input u&I 

the net input to node i 

the output of node i 

the predicted value for input pattern p 

oxidizer preburner 

oxidizer preburner oxidizer valve 

preburner boost pump 

number of model input variables 

root mean squared 

Stennis Space Center 

Space Shuttle Main Engine 

time 

the target value for input pattern p 

the bias term for node i 

a function input variable 

weight connecting nodes i and j in adjacent layers 

the function output 
The current SSME safety system employs basic redline limits and ignition confirm criteria. 

The redlines have upper and/or lower limits assigned to them. Limit monitoring commences at 

scheduled times during startup.’ In addition, ignition confirm criteria are administered to three 

parameters during startup to ensure that ignition has occurred. Failure to meet any of the criteria 

results in engine shutdown? Current post-test analysis of the start transient consists of visually 

comparing parameters to two standard deviation limits and to previous start transients? 

Recent SSME condition monitoring activities have focused on both real-time safety monitoring 

and post-test diagnostics.‘“’ These efforts have demonstrated the potential of advanced algorithms 

to provide improved failure detection capability during ground test firings, thus reducing engine and/or 

test stand damage, and to facilitate the post-test diagnostic process. Efforts in advanced safety 

monitoring systems for the SSME have emphasized mainstage failure detection.‘sJ“ Startup is difficult 

to monitor because of the highly complex and nonlinear nature of the SSME dynamics. Accurate 

models of parameters during startup would provide improved engine and sensor failure detection 

capability during the first seconds of engine operation. The models would also provide additional 

information for fault detection and isolation when used as part of an automated engine diagnostic 

system.8 In both cases, the residual between the actual and predicted values must be analyzed to 

detect an anomalous engine condition or to identify an engine or sensor failure. 

The ability of feedforward networks to model nonlinear systems has been demonstrated in the 

literature; it has been shown that neural networks with only one hidden layer can uniformly 

approximate any continuous function?‘l Neural networks are well-suited for problems in which the 

exact relationships between sensor measurements are complex or unknownl’ In this investigation, 

neural networks were used to learn the relationships among several SSME sensor measurements 

during the startup transient. A standard backpropagation algorithm was used to train the networks. 

The training set consisted of Command and Data Simulator (CADS) and facility data from the first 

six seconds of two nominal firings, B1070 and B1072. The trained networks were validated using data 

from four additional nominal firings: B1073, B1074, B1075 and B1077. The first two characters of a 

test firing designation indicate the test stand at Stennis Space Center @SC) on which the firing took 

place, and the last three numbers indicate the test number. In addition to Bl, there are two other 

SSME test stands at SSC, Al and A2. In order to improve model prediction accuracy, several issues 

related to the engine system and the neural network architecture were addressed when training the 

networks. These issues included the selection of measurements in the input vector, the number of 

nodes in the hidden layer, the transition from open loop to closed-loop control, and the prime times 

of the MCC, the Fuel Preburner (FPB) and the Oxidizer Preburner (OPB). Performance of the trained 

networks, or models, on the training and validation sets was measured by the total root mean squared 

(rms) error over all of the output patterns of a given set and by the maximum percent deviation 

between actual and predicted values. 

2 
the presence of nonpolynomial nonlinearities while neural networks can accurately model both 

polynomial and nonpolynomial nonlinearities? 

Consider the nonlinear function, f; that describes the relationship between several system 

variables: 

y(Z)=jb,(t-1) ,..., u&t-n,>,u,(t-1) ,..., I(&-nz) ,..., u&t-l) ,..., q(t-ni) ,..., u&t-l) ,..., u,(t-n,)) +e(t) (1) ‘ 

where y(t) is the function output, q(t) is a function input variable, n, is the window size for input 

variable u,(t), and e(t) is additive uncorrelated noise. ‘I One of the function inputs, u,(t), can represent 

autoregressive information. The total number of input variables is r. Neural networks are used to 

approximate the function f based on observed system variables, y(t). 

Feedforward networks with a single hidden layer were used in this investigation. Each layer 

consists of processing elements called nodes; the structure of a feedforward network is given in Fig. 

1. Each node of a given layer receives input from all of the nodes in the previous layer and sends its 

output to each node in the following layer. The connections are unidirectional and have weights 

associated with them. There are no connections between nodes within a layer and no connections 

bridging layers. The relationship between the input and the output of a node in the hidden or output 

layers is determined by the activation function, a. The commonly used sigmoid activation function was 

employed in this study:” 

1 1 a(r&q=oi=--- 

l+e-% 2 

where net, is the net input to node i 

(3) 

c 

3, is the bias term for unit i, oj is the output of node j in the previous layer, and wij is the weight 

between the two nodes i and j. A bias is similar in function to a threshold and is treated as a weight 

connected to a node that is always on. The values of the weights and biases are adjusted during the 

learning process.‘a 

The multiple-input single-output network can be described as a mapping function which 

uniformly approximates the function f given by Eq. (1). The approximation is achieved by using the 

backpropagation algorithm, a supervised learning procedure based on the Generalized Delta Rule.” 

Backpropagation computes the weights and bias terms to minimize the mean squared error between 

the values predicted by the network and the desired values. In this investigation, the weights and 

biases were updated after every complete pass through the training data. The learning rate and 

momentum determined the amount by which the weights were updated and were set to achieve rapid 

learning without significant oscillations in the error.1’ 

3 
error of a particular pattern, p, is given by: 

t -op 

percent error =P 

5 

(6) 

Application to SSME Data 

In using feedforward neural networks to model the SSME startup transient, several issues 

related to the network architecture were addressed. These included the selection of the measurements 

(including autoregressive information) in the input vector, the window size, and the number of nodes 

in the hidden layer. In addition, several engine system conditions required monitoring in order to 

improve network prediction accuracy. These were sensor failures, the initiation of closed-loop control 

during the start sequence, and the realization of full faceplate burning, or prime time, of the three 

combustion chambers (MCC, FPB, and OPB). These issues are discussed in this section. 

The engine measurements in the model input vector were determined by computing the 

correlation coefficient between the parameter to be modeled and the remainder of the measurements 

in the CADS and facility data sets. Many parameters were found to be highly correlated due to their 

strong response to changes in power level. Physically relevant, non-redundant measurements with 

high correlation coeficients were chosen; these parameters are given in Table 1. It should be noted 

that sensor failures affected the choice of measurements. The HPFP discharge temperature, for 

example, could not be included in the input vector for the HPFP discharge pressure, since the 

temperature measurement was faulty in several of the test firings used. Data from the first six 

seconds of test firings B1070 and B1072 were used to construct the training sets. Prior to training, 

all input-output pairs were normalized to fall within the range [-0.5,0.51 as dictated by the activation 

function given by Eq. (2). The normalization was achieved by selecting maximum values for the input 

and output variables baaed on the data in all of the training and validation sets. 

The impact of including autoregressive information in the network input was investigated for 

all three parameters. Autoregressive information did not improve the predictive accuracy of the MCC 

pressure and the HPFP discharge pressure models and was not used in the final models for these 

parameters. The HPOT discharge temperature model, on the other hand, exhibited a large 

improvement in prediction accuracy when autoregressive information was added; the total rms error 

decreased by a factor of 1.8. Autoregressive data increased the size of the input layer and hence was 

accompanied by increases in training and processing times. Autoregressive information was retained 

in the final HPCT discharge temperature model, however, because significant improvements in the 

quality of the predicted signal were realized. 

The window size was chosen based on behavior observed for the MCC pressure. For a given 

neural network model, the same window size was used for each input variable, u&t). Therefore, the 

4 
the MCC pressure networks. When the number of hidden nodes was increased from 10 to 20, no 

improvement in the total rms error was observed. In addition, the larger hidden layer increased the 

number of weights and hence the training time. Training times are important since it is anticipated 

that the networks will require periodic updating as new test data becomes available. Furthermore, 

test-stand specific networks may be required. Thus, three networks would be needed for each 

parameter. Excessive training times would prevent practical implementation of these models. Larger 

layers also increase the processing time when the network is being used in a failure detection or 

diagnostic mode. Ten hidden nodes were used for all subsequent simulations. 

An important system condition which was taken into account during network training was the 

closed-loop thrust and mixture ratio control of the SSME. Engine thrust is directly proportional to 

the MCC pressure. Complete closed-loop control is achieved at engine start +3.6 seconds. The error 

between actual and desired main combustion chamber pressures drives the oxidizer preburner oxidizer 

valve (OPOV) and the proper mixture ratio is maintained by adjusting the Fuel Prebulmer Oxidizer 

Valve (FPOV). All other valves are scheduled.” Closed-loop control was taken into account when 

modeling the MCC pressure and the HPOT discharge temperature, since the input vectors for these 

two parameters included the FPOV and OPOV. For the MCC pressure model, a dummy variable, 

DUMl, was added to each time slice in the input layer to indicate whether the data at that time slice 

represented partially open or completely closed-loop behavior: 

DUMl= 0 < t < 3.6 

t > 3.6 

(6) 

A slightly modified version of Eq. (6) was used for the HPOT discharge temperature and is given later 

in this section. 

, 

Each of the modeled parameters is closely associated with one of the combustors and is 

therefore strongly affected by the prime time of the relevant chamber. The MCC prime time is defined 

as the time when the MCC pressure reaches 100 psia. The OPB prime time is determined by 

monitoring the HPOT discharge temperature, and occurs when the temperature changes from a 

decreasing to an increasing trend. Although the HPFP discharge pressure is not used in determining 

the FPB prime time, it is strongly affected by the prime time of this chamber. The FPB prime time 

is defined as the point at which the High Pressure Fuel Turbopump (HPFI’P) shaft speed exhibits a 

sharp increase in slope. During a nominal firing, the FPB primes first, followed by the MCC and the 

OPB.16 The prime times for the test firings used in this investigation were obtained using the above 

criteria. The dependence of model use 0i-1 the determination of prime times is not unreasonable, even 

for a real-time safety system, since complicated calculations are not required. Typical prime times for 

the FPB, MCC and OPB are 1.37, X44, and 1.62 seconds from engine start, respectively.‘6 

The effect of prime time on model prediction accuracy was investigated for all three 

parameters. The solid curves in Figs. 2(a), 2(b), and 2(c) give mean values for the MCC pressure, the 

HPFP discharge pressure and the HPOT discharge temperature, respectively, during the first six 

5 
FPB prime time data was included in the training set. The FPB primes earlier than the MCC; 

therefore, the time interval during which a predicted value is not available is smaller for the HPFP 

discharge pressure than for the MCC pressure. Since errors approaching 100 percent of the actual 

value are not likely to provide useful information to a safety or diagnostic system, pre-prime time data 

was not included in the final models for the pressures. 

The HPOT discharge temperature was trained on pre- and post-prime time data since it is 

nonzero prior to the prime of the OPB. This was desirable since the OPB primes the latest of all three 

chambers, typically around engine start +1.62 seconds. Training on post-prime time data only would 

significantly decrease the failure coverage for this parameter. The effect of prime time on the HPOT 

discharge temperature was assessed by training networks with and without a variable to indicate the 

transition from pre-prime to post-prime time behavior. The dummy variable indicating open-/closedloop behavior given by Eq. (6) was modified for the HPOT discharge temperature to include the 

transition to full faceplate burning of the OPB: 

0.0, 0 -z t < OPB prime time 

DUMZ= -.25, 

i 

OPB prime time -c t < 3.6 (7) 

+.25, t > 3.6 

The introduction of the prime time variable was accompanied by a decrease in the total rms error. 

Results and Discussion 

Data from two nominal SSME firings were used to train feedforward networks to model three 

parameters during portions of the SSME startup transient. Several issues were presented in the 

application of the feedforward networks to the MCC pressure, the HPFP discharge pressure and the 

HPOT discharge temperature. The network which yielded the best model for each parameter when 

trained on data from test firings B1070 and B1072 was subsequently tested using data from four 

additional nominal firings: B1073, B1074, B1075 and B1077. The results are discussed below. 

The performance of the best model for each parameter is given in Tables 2,3 and 4. The total 

output rms error and maximum percent error, described by Eqs. (4) and (5), are given for each training 

and validation set. All three models used a window size of ten and a hidden layer with ten nodes. 

Table 1 summarizes the complete set of variables which comprised the input for each model. All 

models were trained for 20000 cycles. In a real-time safety or post-test diagnostic application, the 

number of training cycles should be chosen to achieve an optimum balance between model performance 

and practical implementation concerns. The MCC pressure model used to generate the values in Table 

2 was trained on post-prime time data only and included the open-/closed-loop variable given by Eq. 

(6). The HPFP model evaluated in Table 3 was trained on post-FPB prime time data. The HPOT 

discharge temperature model of Table 4 was trained on the entire first six seconds of engine operation. 

It included autoregressive information and the prime time and open-/closed-loop variable given by Eq. 

(7). In all cases, the total rms error and the maximum percent error were lower on the training test 

firings than on the validation test firings. The maximum percent error on a validation set, however, 

6 
pg

When considering the test-to-test variations shown in Fig. 2(c), it can be seen that the 

performance of the HPOT discharge temperature model represented the most dramatic improvement 

over the two standard deviation limits. The quality of the predicted signals is displayed graphically 

for the HPOT discharge temperature in Figs. 4 and 5. Figure 4(a) gives the actual and predicted 

values for a test firing in the training set, B1070. The first predicted value is at .40 seconds due to . 

the window size of ten. Figure 46) gives the difference between the two curves; the maximum error 

is less than 6 deg R. Figure 5 illustrates the performance of the same model on a validation set test 

firing, B1077. Actual and predicted values are shown in Fig. B(a) and the difference between the 

actual and predicted values is given in Fig. 5(b). The maximum error on this firing is less than 16 deg 

R. A comparison of both Fig. 4(a) and Fig. 5(a) to Fig. 2(c) indicates that the neural network is a good 

predictor of the, HPOT discharge temperature even in areas where the temperature varies widely. 

A final note is in order regarding the models generated in this investigation. Each parameter 

had an input vector which contained a large number of highly correlated, non-redundant engine 

measurements. Alternate measurements were not considered. Smaller input vectors would reduce 

training time, yet may also degrade model accuracy. The effect of reducing the input vector size on 

prediction accuracy may suggest that smaller input vectors are adequate, particularly for a real-time 

implementation. In addition, fault isolation becomes difficult when a given parameter appears in the 

input vector for a large number of parameters. The inclusion of autoregressive information in the 

model of a parameter may desensitize the model to slow drifts in that parameter and therefore impede 

the detection of soft sensor failures or engine degradations which are manifested as drifts. The ability 

of feedforward networks to accurately model critical SSME parameters during the startup transient, 

has been demonstrated; the needs and limitations of the safety or post-test diagnostic system will 

determine many of the issues involved in model construction. 

Concluding Remarks 

Feedforward neural networks were used to accurately model three critical parameters during 

portions of the SSME startup transient. The formulation of accurate models is the first step towards 

improved startup fault detection and isolation. Once the models have been established, the residuals 

between the actual and synthesized values must be analyzed for indications of engine or sensor 

anomalies. Furthermore, fault isolation logic must be applied to the residuals in order to identify the 

source of the failure; more detailed fault isolation will be possible in a post-test diagnostic system. 

The models, along with the appropriate ‘fault detection and isolation logic, can then be incorporated 

into an existing safety or diagnostic system. As part of an advanced safety system, for example, the 

neural network models could assist the ignition confirm criteria in ensuring safe engine operation 

during startup. 

In this investigation, the MCC pressure, the HPFP discharge pressure, and the HPOT 

discharge temperature were simulated using time windows of data from highly correlated engine 

7 
system conditions and by adjusting variables related to the network architecture. Dramatic 

improvements in network performance were realized when the pressures were trained only on data 

following the prime time of the relevant chamber. Although training on only post-prime time data 

reduces the failure coverage for the MCC pressure and the HPFP discharge pressure, the large percent 

errors experienced prior to MCC or FPB prime would be of little benefit to a safety or diagnostic 

system. The MCC and the FPB prime at approximately 1.44 and 1.37 seconds after engine start, 

respectively. The HPOT discharge temperature model was trained on the entire first six seconds of ^ 

SSME operation; model improvement was achieved by introducing a flag to indicate the occurrence 

of OPB prime. The HPOT discharge temperature model was further improved by adding 

autoregressive information; autoregressive data did not improve the quality of the predictions for the 

two pressures. Larger window sizes were also found to improve model performance. A larger window 

size, however, reduces the failure coverage for the modeled parameter by increasing the time until the 

first predicted value is available to the safety or diagnostic system. 

The tradeoff between model accuracy and the requirements and limitations of a safety or posttest diagnostic system was evident throughout this investigation. Improvements in model accuracy 

were often accompanied by longer training times and increased processing and memory requirements. 

This is because larger window sizes and autoregressive information increase the number of weights 

thereby increasing the number of computations per pass when the networks are being trained and 

when they are being used to model a new test firing. Although the highly parallel architecture of 

feedforward neural networks facilitates real-time implementation, the models are anticipated to be one 

component of an advanced safety system and will have limited computing and memory resources. 

Furthermore, some computations will be required to interpret the errors between the actual and 

predicted signals. Training times are important since it is anticipated that the networks will require 

periodic updating as new test data becomes available. All’of the models constructed for this 

investigation were trained and validated using test data from one test stand; test stand specific models 

may be required. Therefore, a large number of models may require maintenance. All networks were 

trained for 20000 cycles since model accuracy was the objective of this investigation. Practical 

considerations may suggest a smaller number of training cycles. 

This work was supported 

with Larry P. Cooper as monitor. 

Acknowledgment 

by the NASA Lewis Research Center under contract NAS3-25266 

References 

1. Taniguchi, M.H. Failure Control Techniques fir the SSME, Phase I Final Report. NASA CR179224,1986. 

2. Roth, P. Contpter Progrant Contract End Item, Flight 4C Configuration, Space Shuttle Main 

Engine Controller Operational Program, Part 1. CP406R0001, Revision F, Rockwell 

8 
7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

, 

17. 

Identification Techniques. AIAA Paper 90-1993, July 1990. 

Maul, W.A. Multi-sensor Analysis Techniques for SSME Safety Monitoring. AL4A Paper 90- 

1990, July 1990. 

Zakrajsek, J.F. The Development of a Post-Test Diagnostic System for Rocket Engines. AIAA 

Paper 91-2528, June 1991. 

Lapedes, A. and Farber, R. Nonlinear Signal Processing Using Neural Networks: Prediction 

and System Modelling. Los Alantos National Laboratory Technical Report LA-UR-87-2662, July 

1987. 

Weigand, A.S., Huberman, B.A., and Rumelhart, D.E. Predicting the Future: A Connectionist 

Approach. Stanfird PDP-90-01, April 1990. 

Chen, S., Billings, S.A., and Grant, P.M. Non-linear Systems Identification Using Neural 

Networks. University of Edinburgh Research Report 370, August 1989. 

A.NSint User’s Manual, Version 2.30. Science Applications International Corporation, April 

1989. 

Rumelhart, D.E. and McClelland, J.L. Parallel Distributed Processing: Explorations iu the 

Microstrzrctzrre of Cognition, I. Cambridge, MA: MIT Press, 1987. 

SSME Orientation (Part A-Engine.). Course No. ME-110(&R& Rockwell InternationaYRocketdyne Division, August 1988. 

Connell, S.C. Space Shzrttle Main Engine Contponent Level Hot-fire Testirzg Procedzrre (Green 

Run Specification). RL00461, Revision L, Rockwell InternationaVRocketdyne Division, January 

1991. 

Hooper, Taylor. Private Conmzzmication. Martin Marietta at NASA Marshall Space Flight 

Center, December 1990. 

Faust, D. Private Contntzcnicatimr - SSME Startztp Tzoo Sigma Database. Martin Marietta 

Corporation at Marshall Space Flight Center, September 1990. 

9 
PBP Discharge Pressure 

HPFT Discharge Temperature 

HPOT Discharge Temperature 

OPB Chamber Pressure 

HPFP Shaft Speed 

Engine Fuel Flowrate 

Engine Oxidizer Flowrate 

DUMl X 

DUM2 X i 

’ - autoregressive input 

Table 1. Variables that appear in the neural network input for each of the three modeled 

parameters. 

II TorV TO~‘I!I$IS %z 

T .00153 .763 

T .00129 .592 

V .00238 1.48 

V .00252 1.54 

V .00531 2.92 

V .00506 1.97 

Table 2. The performance of the MCC pressure model on Training CT) and Validation (VI test firings. The network 

was trained using post-MCC prime time data only and 

using the open/closed loop flag. 

10 
model on Training CT) and Validation 0 test firings. 

The network was trained using post-FPB prime time 

data only. 

II B1070 11 T I .00125 I .960 II 

II B1072 Ii T I .00127 I 571~--1l 

II B1073 II v I .00381 I 3.29~~~~~11 

II B1074 11 V 1 JO358 1 2.07 ~~ 11 

II B1075 II v I .00787 I 3.31 II 

II B1077 II v I .00495 I 2.49 II 

Table 4. The performance of the HPOT discharge temperature 

model on Training 0 and Validation 0 test firings. 

The network was trained using the fUgt six seconds 

of etartup and using the variable indicating transition 

from pre-OPB prime to po&OPB prime to closed-loop 

behavior. Autoregressive information was also included. 

OUTPUT LAYER, y(t) 

HIDDEN LAYER 

INPUT LAYER, u(t) 

Figure 1. An example of a fully connected feedforward neural 

network with one hidden layer. 

11 
7000 

5600 

1400 

0 

1600 

1280 

960 

640 

320 

- Meon Value 

_... f 2 Standard Deviations 

0 

I I I I I 

0 1 2 3 4 5 

TIME (SEC) 

Figure 2. Nominal mean and mean plus and minus two standard deviation values during the startup transient 

for (a.) the MCC pressure, (b.) the HPFP discharge 

pressure, and (c.) the HPOT discharge temperature. 

12 
0 1 2 3 4 5 6 

TIME (SEC) 

Figure 3. Percent error as a function of time for test firing B1070. 

The dotted vertical line indicates the MCC prime time 

for this test. 

I - ACTUAL 

0 

I I I I I 

0 1 2 3 4 5 

TIME (SEC) 

20 

15 

z- 10 

z 

2. 5 

F 

u 0 

B 

E I -5 

a 

2 -10 

2 

-15 

-20 

0 

(b). BiO70 

I I I I I 

1 2 3 4 5 6 

TIME (SEC) 

Figure 4. The performance of the HPOT discharge temperature network on a test firing in the training set, B1070: 

(a.) the actual and predicted signals as a function of time and (b.) the difference between the actual and 

predicted values. 

13 
600 

0 1 I I I I I 

0 1 2 3 4 5 

TIME (SEC) 

/ 

-5 - 

-10 - 

(b). 81077 

-15 - 

r I 

/ \J-b 

-20 / I I I I I 

il 1 2 3 4 5 6 

TIME (SEC) 

Figure 5. The performance of the HPOT discharge temperature network on a validation set test firing, B1077: 

(a.) the actual and predicted signals as a function of time, and (b,) the difference between the actual and 

predicted signals. 

14