Statement A: Approved for Release. Distribution is unlimited.
Presented In Partial Fulfillment of the Requirements of a Master of Science Degree
Penn State Department of Mechanical Engineering
February 29, 2016

APPLYING ARTIFICIAL NEURAL NETWORKS TO PREDICT NOMINAL VEHICLE
PERFORMANCE
Adam J. Last
Applied Research Laboratory
P.O. Box 30
State College, PA 16804
e-mail: ajl5263@arl.psu.edu

ABSTRACT
This paper investigates the use of artificial neural
networks (ANNs) to replace traditional algorithms and manual
review for identifying anomalies in vehicle run data. The
specific data used for this study is from undersea vehicle
qualification tests. Such data is highly non-linear, therefore
traditional algorithms are not adequate and manual review is
time consuming. By using ANNs to predict nominal vehicle
performance based solely on information available pre-run,
vehicle deviation from expected performance can be
automatically identified in the post-run data. Such capability is
only now becoming available due to the rapid increase in
understanding of ANN framework and available computing
power in the past decade. The ANN trained for the purpose of
this investigation is relatively simple, to keep the computing
requirements within the parameters of a modern desktop PC.
This ANN showed potential in predicting vehicle performance,
particularly during transient events within the run data.
However, there were also several performance cases, such as
steady state operation and cases which did not have sufficient
training data, where the ANN showed deficiencies. It is
expected that as computational power becomes more readily
available, ANN understanding matures, and more training data
is acquired from real world tests, the performance predictions
of the ANN will surpass traditional algorithms and manual
human review.

Timothy F. Miller
Applied Research Laboratory
P.O. Box 30
State College, PA 16804
e-mail: nfn@arl.psu.edu

service lives to ensure proper functionality. Results from these
qualification runs can include hundreds of channels of data,
including speeds, pressures, temperatures, flow rates,
vibrations, and many others. Further, each qualification run
usually has a unique mission profile, which is the progression
of commanded speeds throughout the run. This makes direct
comparison between qualification runs difficult.
Therefore, identifying anomalous behavior from the
post-run data requires many highly trained and experienced
engineers manually reviewing each data channel. Even then,
due to human error, subtle anomalies can be overlooked or,
conversely, normal behavior can be flagged as anomalous. To
counter this, creating an algorithm or method to predict results
based solely on the mission profile is highly desirable. The
current best method is to average the measured values for a
given data channel at a given speed from all previous runs, and
assume that is the “normal” operating condition for that speed.
However, the response of each data channel is highly nonlinear, as not only the current speed command but also the
cumulative effect of all prior operation determines current
performance. As a result, traditional algorithms become
unwieldy and unreliable for this application.

PROBLEM
Undersea vehicles, like any high performance systems,
require many qualification runs prior to and throughout their

INTRODUCTION
Overcoming the breakdown of traditional algorithms
on large non-linear data sets has been a focus for many
industries in recent years. Data center optimization [1],
handwriting recognition [2], language translation [3], and
image classification [4] are examples of problems that
traditional algorithms cannot effectively solve. Decades of

Statement A: Approved for Release.
Distribution is unlimited.

1

exponential growth in available computing power, along with
recent developments in mathematical methods, has enabled a
new approach to handling large data sets- artificial neural
networks (ANNs). ANNs have been deployed in the last few
years to enable everything from real time language translation
[5] to instant handwriting recognition [6] to financial market
analysis [7].
This paper outlines the approach to using the existing
undersea vehicle qualification run data to train an ANN to
predict future hypothetical run results, with the only input being
the mission profile. Then, when the hypothetical qualification
run is actually performed in the real world, the results can be
fed back to the computer. The ANN can then identify where
differences exist between its predicted result and the actual
results to automatically flag anomalous behavior.
TECHNICAL BACKGROUND
The first work on artificial neural networks began in
the mid-20th century with the concept of perceptrons. The
perceptron is essentially a logic gate, where multiple inputs are
taken in, individually weighted, and summed. If the sum of the
weighted inputs are greater than a threshold value, then the
output of the perceptron is “1”, otherwise the output is “0”.
This is shown graphically in Figure 1 (graphic adapted from
Nielson [8]).

0 𝑖𝑓 ∑ 𝑤𝑗 𝑥𝑗 ≤ 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
𝑜𝑢𝑡𝑝𝑢𝑡 = {
1 𝑖𝑓 ∑ 𝑤𝑗 𝑥𝑗 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
Figure 1. Perceptron logic

The perceptron was later refined to allow for nonbinary output (i.e. output other than just 1 and 0). This is
accomplished by replacing the step function logic with a
sigmoid function. For this reason, the new model for the
perceptron was named the “sigmoid neuron”. The “neuron”
portion of the name derives from the sigmoid neuron’s
similarity in operation to a biological neuron, which on a very
basic level activates an output given a sufficient input [8].
Sigmoid neurons become useful when linked together
to perform complex logic, and were renamed “hidden neurons”
in the scope of neural networks. Figure 2 (graphic adapted
from Nielson [8]) shows an artificial neural network containing
3 inputs, 4 hidden neurons, and one output.

Statement A: Approved for Release.
Distribution is unlimited.

Figure 2. Simple ANN

To orient Figure 2 to the current problem at hand, the
input layer would be known values (such as the commanded
speed). The output layer would be whatever data channel you
are trying to simulate, the most intuitive being actual vehicle
speed. There will obviously need to be far more than 4 hidden
neurons for any meaningful results.
For a neural network to be useful, the weighting
factors for each input to each hidden layer sigmoid neuron must
be defined. To do so, a training process must be undertaken.
The training process requires a large set of already known
input/output pairings. In this case, this known set is the
available previous vehicle qualification runs, which have
known inputs (such as commanded speed) and measured output
(such as actual speed). Initially in the training process, a
random set of weights is defined. The output is then calculated
and compared to the actual output. This is the error in the
neural network for the current “evolution”. The weights are
then adjusted (shown as Δw in Figure 2) and the ANN resolved.
This process is repeated until the error is below an acceptable
value or a preset number of evolutions has been achieved [9].
There are several methods for determining the
amounts by which to adjust each individual weight. One of the
easiest to implement and most computationally efficient is the
optimization method of stochastic gradient decent. Gradient
descent is a well-known mathematical model for finding
minima and maxima. Stochastic methods are employed to
introduce an element of randomness into the optimization
routine. This allows for the optimization to escape local
minima and maxima during the solution and continue
improving on the solution through many evolutions [10].
While stochastic gradient decent is efficient, it is still
very computationally intensive when solving the weights for
many (hundreds or more) hidden layer sigmoid neurons. That
is why the recent sustained exponential growth in available
computing power has been critical to making ANNs practical.
Once the ANN weights are solved, it takes very little
computational resources to run new inputs through the ANN to
find the output.
There have been several advances in mathematical
methods in recent years that have made ANNs much more
powerful and extensible to more applications. However, for the
purpose of this paper, using the methods already outlined is
sufficient.

2

ANN SETUP
A simple ANN was set up that was capable of being
run on a single desktop computer with 4 GB RAM. This ANN
was built using the Netlab MATLAB toolbox developed by
Nabney [11]. The training data was taken from 20 qualification
runs of an undersea vehicle. This gave 64,779 unique “time
steps”. Each “time step” represents a discrete amount of
runtime. Time and speeds have been non-dimensionalized.
For each “time step”, input values must be provided to
the ANN. For the engine of this vehicle, like many other
vehicles, the only true control input is commanded speed. All
other engine parameters are adjusted internally for the goal of
matching that commanded speed as closely as possible.
Though not strictly a “control” parameter, the other engine
input is the amount of energy reserves remaining (and, by
extension, the amount of reserves that has already been used).
For various systems, this could take the form of percentage of
combustible fuel remaining in a tank, remaining battery power,
etc. For many systems, such as the one under study, this energy
reserves input also functions as a “state of health” parameter
(i.e. for electric systems, motors may not perform optimally
once the batteries drop below a threshold voltage).
From these general “inputs”, the specific input data
that was deemed pertinent to be provided to the ANN is as
follows…

1.

2.

Speed Command Information…
a. Current Commanded Speed
b. Time at Current Commanded Speed
c. Previous Commanded Speed
% of Energy Reserves Depleted (termed “Utilization”
for the purposes of this paper)

Also provided for training the ANN was the actual measured
vehicle speed for each data point. The “success” of the ANN
training would be determined by comparing the actual vehicle
measured speed to the ANNs predicted vehicle speed.
The ANN was initialized to have 750 hidden sigmoid
neurons. The training was set to terminate after 750,000
evolutions. This is about 48 hours of computation time on a PC
with an Intel Core i5-2400 CPU running at 3.1 GHz.
To assist with visualization of the training process of
this specific ANN, the notation from Figure 2 is used in Figure
3 below, depicting the ANN setup. The routine of Figure 3
would be run once for each time step each evolution (64,779
times every evolution for this data set).

Figure 3. ANN setup and training visualization

Statement A: Approved for Release.
Distribution is unlimited.

3

1

Nondimensionalized Speed

0.9

0.8

0.7

0.6

0.5

0.4

0

0.1

0.2

0.3

0.4
0.5
0.6
Nondimensionalized Time

0.7

0.8

0.9

1

Figure 4. Full ANN results

Statement A: Approved for Release.
Distribution is unlimited.

Consistently low prediction of high speed command
performance
0.9
0.8

Nondimensionalized Speed

ANN RESULTS
Figure 4 above shows the commanded speed (dark
blue line) and the ANN’s prediction for actual speed (red line).
Also given is the true actual speed as measured in the
qualification tests (light blue line).Quick inspection of Figure 4
shows that the ANN has largely succeeded in matching the
general speed response. However, there are several spans of
time where the ANN fails to predict any more accurately than
simply guessing that the actual speed is equal to the
commanded speed. The most obvious example is during long
periods of constant speed, known as steady state. Conversely,
there are several spans where the ANN prediction is much more
accurate than any traditional algorithm could be, such as during
speed changes (transients)
It is critical to attempt to understand the reasons why
the ANN is very accurate or not accurate in various situations.
If these reasons can be well understood, then adjustments can
be made to the ANN training routine to address deficiencies
and promote strengths.
Examples would be providing
additional input information, working to obtain test data for
situations where the ANN shows deficiencies, changing the
number of hidden neurons, or adjusting the evolutions to
simulation completion. To that end, the remainder of this
section of the paper examines three specific performance cases
where the ANN shows interesting prediction behavior. The
upcoming Figures 5, 6, and 7 all show magnified subsets of
data from Figure 4, to allow for in-depth analysis.

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.42

0.44

0.46

0.48
0.5
Nondimensionalized Time

0.52

0.54

0.56

Figure 5. ANN results, low predictions of high speed operation

Figure 5 shows a magnified portion of the ANN data
of Figure 4, from 0.42 to 0.56 of the nondimensional time.
Added to the plot, that was not present in Figure 4, is the nondimensionalized utilization (% of energetics used), shown in
magenta. Note that there are three separate “runs” shown, as the
utilization resetting to zero is indicative of a new run. In this
timeframe there are three instances of the vehicle being
commanded to its highest speed. In all three instances, the
ANN predicts the actual speed will only achieve about 80% of
the full speed value. However, this is only true for one of the
three occurrences; in the other two the vehicle does achieve

4

high speed operation. It is probable that the ANN is chronically
under predicting the actual high speed operation as a “safe”
prediction. This is because the speed sometimes undershoots,
but almost never overshoots, a high speed command. The
likelihood that the vehicle will undershoot the high speed
command is increased at high vehicle utilization (near the end
of an individual run- because effective control is more
difficult), as it was in the one instance of undershooting in
Figure 5. The ANN shows slight sensitivity to this as the high
speed command in Figure 5 furthest to the right occurs at the
lowest utilization; the ANN displays the highest predicted
speed. However, the prediction is still too low, and the ANN
clearly does not fully incorporate the link between utilization
and the potential for undershooting. More run data which
contains more high speed command operation at various
utilizations would likely remedy this issue.

Data overfitting during “staircase” speed increase

Accurate prediction of transient performance

Figure 7 shows a brief speed command of 0.8 nondimensionalized speed. The ANN predicted speed appears to
match the actual speed of the vehicle closely over this time.
However, the predicted speed is slowly increasing the entire
time, as if “anticipating” the next speed command. The reason
is that this speed change is part of a “staircase” pattern of speed
changes, where the speed goes from the minimum to the
maximum over a series of small changes in speed in rapid
succession. These “staircase” patterns are very common in the
training run data. Therefore, the ANN learned that when the
speed changes from a moderate speed to just a slightly higher
speed, in all likelihood it was in the middle of a “staircase”
speed profile and should anticipate another small speed step up.
However, it is obviously not always true that these small speed
steps must be part of a “staircase” sequence. Therefore, the
“anticipation” of the ANN for another immediate speed change
is unwarranted and indicative of overfitting of the data [12].
This would be remedied by additional run data which showed
small speed steps which are not part of a “staircase” pattern.

Nondimensionalized Speed

0.65

0.6

0.55

0.5

0.45

0.4

0.45

0.452

0.454
0.456
0.458
Nondimensionalized Time

0.46

0.462

0.464

Figure 6. ANN results, transient performance

Figure 6 shows one of the speed command changes in
the data. During the transient, the ANN predicted speed
showed a sharp drop then gradual step down to the final steady
state speed, consistent with actual vehicle operation. This is a
feature that a traditional algorithm would have trouble
matching, particularly once data other than speed
(temperatures, pressures, etc.), which may take a much longer
time than speed to reach steady state, are considered.

Statement A: Approved for Release.
Distribution is unlimited.

Nondimensionalized Speed

0.86
0.84
0.82
0.8
0.78
0.76
0.74
0.72
0.144

0.146

0.148
0.15
Nondimensionalized Time

0.152

0.154

Figure 7. ANN results, overfit solution

CONCLUSIONS
The results show that even simple ANNs show
promise of outperforming traditional prediction methods for
times in the data which are highly non-linear (such as speed
transients). However, the simple ANN does not have adequate
performance for all times, most notably during steady state
operation. It is highly probably that the ANN would meet or
exceed the performance of traditional algorithms if a more
complex ANN were solved on a more powerful computer.
A more fundamental limitation of the ANN
performance may be the potential for overfitting of data. This
is a result of not having a sufficiently large set of training data.
Specifically, if the same sequence of speed steps is present in
most data sets, the ANN will be highly accurate in predicting
results for that exact sequence, but not when the sequence is
altered slightly. Therefore, it is possible that even with an
advanced ANN solved on a powerful computer, the size of the
training data set could prove a limitation to ANN effectiveness.
The mitigation for this problem is the inclusion of additional

5

data sets in the training data, especially those with a diverse
mission profiles.
FUTURE WORK
The size of the training data set continues to increase,
as qualification runs of the vehicle are ongoing. Additionally,
computational power continues to become more and more
readily available. Therefore, it is prudent to develop an
advanced ANN framework now and run it with the existing
data set with the understanding that the results may not yet
outperform traditional algorithms or manual data analysis.
However, with that framework in place, retraining the ANN
with new data becomes a trivial exercise. As more data and
computational power becomes available it can be expected that
at some point the ANN will be provide the best predictive
capability. At that point additional data channels (temperatures,
pressures, etc.) can all be predicted using the same ANN
framework.
Once ANNs have been proven to reliably identify
anomalies from post run data, it will be possible to extend their
use into identifying anomalies during a run itself. For instance,
if a vehicle behaves off-prediction by some margin, the ANN
can alert the vehicle control which can then evaluate whether to
issue an early termination of the run. Even further in the future,
ANNs should be capable of assuming control for adjusting
vehicle run parameters (flow rates, pressures, etc.) in real time
to optimize vehicle performance.
CLOSING REMARKS
The conclusions of this paper (requiring more
computational power and better mathematical techniques, but
more importantly additional training data) are consistent with
the needs of nearly all ANN projects currently in development.
On the computational side, chipmakers are rushing to
provide hardware designed specifically for ANN training and
deployment [13].
This hardware leverages architecture
traditionally used for intensive graphics processing. Brand new
architecture is under development which will be even further
optimized for machine learning and neural networks [14].
On the training data side, companies have been using
devices owned and used by individuals to collect data to
improve their algorithms. The most relevant of these to this
paper might be Tesla Motors, which receives data from every
one of its cars on the road to improve its “autopilot”
(autonomous driving) feature [15]. Interestingly, this type of
training data collection is a driving force in the recent public
debate about the privacy of personal electronic devices. For
instance, Google’s efforts to track cell phone activity stems
from their desire to expand the training sets for the algorithms
that control search result prioritization, traffic congestion
prediction, language translation, and more [16].
NOMENCLATURE
x = ANN training data input
w = ANN sigmoid neuron weight

Statement A: Approved for Release.
Distribution is unlimited.

ACKNOWLEDGMENTS
The data for this paper was provided by ARL PSU from
experiments performed under NAVSEA contract. We thank the
entirety of ARL’s Energy Science and Power Systems division
for the support and resources. The Netlab MATLAB toolbox
which was utilized to perform the ANN training was developed
at Aston University by Ian Nabney and Christopher Bishop.

REFERENCES
[1] Gao, Jim. Machine Learning Applications for Data Center Optimization.
Rep.
Mountain
View:
Google,
2013.
Web.
<https://docs.google.com/a/google.com/viewer?url=www.google.com/about/dat
acenters/efficiency/internal/assets/machine-learning-applicationsfor-datacenteroptimization-finalv2.pdf>.
[2] Le Cun, Y. "Handwritten Character Recognition Using Neural Network
Architectures." 4th USPS Advanced Technology Conference (1990): n. pag.
AT&T
Bell
Laboratories.
Web.
20
Oct.
2015.
<http://yann.lecun.com/exdb/publis/pdf/matan-90.pdf>.
[3] Auli, Michael. "Joint Language and Translation Modeling with Recurrent
Neural Networks." Microsoft Research (n.d.): n. pag. Microsoft. Web. 20 Oct.
2015.
<http://research-srv.microsoft.com/enus/um/people/gzweig/Pubs/EMNLP2013RNNMT.pdf>.
[4] Szegedy, Christian. "Building a Deeper Understanding of Images."
Research
Blog.
Google,
n.d.
Web.
20
Oct.
2015.
<http://googleresearch.blogspot.com/2014/09/building-deeper-understandingof-images.html#uds-search-results>.
[5] Bergen, Mark. "Google's Neural Nets Can Now Translate Text Instantly,
Practically Everywhere." Recode. Recode, 29 July 2015. Web. 20 Oct. 2015.
<http://recode.net/2015/07/29/googles-neural-nets-can-now-translate-textinstantly-practically-everywhere/>.
[6] Martendale, Jon. "Now Our Computers Can Forge Our Letters and Checks."
Digital Trends. Digital Trends, 22 July 2015. Web. 20 Oct. 2015.
<http://www.digitaltrends.com/computing/researcher-computer-handwriting/>.
[7] "Neural Networks - Applications." Neural Networks - Applications. N.p.,
n.d.
Web.
20
Oct.
2015.
<http://cs.stanford.edu/people/eroberts/courses/soco/projects/neuralnetworks/Applications/stocks.html>.
[8] Nielson, Michael A. Neural Networks and Deep Learning. N.p.:
Determination, 2015. Determination Press. Web. 20 Oct. 2015.
<http://neuralnetworksanddeeplearning.com/chap1.html>.
[9] Bishop, Christopher M. Neural Networks for Pattern Recognition. Oxford:
Clarendon, 1995. Print.
[10] Bottou, Leon. "Stochastic Gradient Descent Tricks." Microsoft Esearch
(n.d.):
n.
pag.
Web.
20
Oct.
2015.
<http://research.microsoft.com/pubs/192769/tricks-2012.pdf>.
[11] Nabney, Ian T. NETLAB: Algorithms for Pattern Recognition. London:
Springer, 2003. Print.
[12] "Documentation." Improve Neural Network Generalization and Avoid
Overfitting.
Mathworks,
n.d.
Web.
20
Oct.
2015.
<http://www.mathworks.com/help/nnet/ug/improve-neural-networkgeneralization-and-avoid-overfitting.html>.
[13] Ferrucci, David. "AI MAGAZINE." Building Watson: An Overview of the
DeepQA Project. AAAI, Aug. 2007. Web. 03 Feb. 2016.
<http://www.aaai.org/ojs/index.php/aimagazine/article/view/2303/2165>.
[14] Colaner, Seth. "Movidius, Google Team Up To Leverage Deep Learning
On Mobile Devices." Tom's Hardware. Tom's Hardware, 27 Jan. 2016. Web. 3
Feb.
2016.
<http://www.tomshardware.com/news/movidius-google-deeplearning-mobile-devices,31078.html>.
[15] Fehrenbacher, Katie. "How Tesla Is Ushering in the Age of the Learning
Car." How Tesla Is Ushering in the Age of the Learning Car Comments.
Fortune,
16
Oct.
2015.
Web.
03
Feb.
2016.
<http://fortune.com/2015/10/16/how-tesla-autopilot-learns/>.
[16] Lafrance, Adrienne. "The Convenience-Surveillance Tradeoff." The
Atlantic. Atlantic Media Company, 14 Jan. 2016. Web. 03 Feb. 2016.
<http://www.theatlantic.com/technology/archive/2016/01/the-conveniencesurveillance-tradeoff/423891/>.

6

ANNEX A
INPUT FILE TO NETLAB TOOLBOX (MATLAB CODE)
% Running this script requires installation of Netlab 3.3 MATLAB toolbox
% Netlab toolbox available at
http://www.aston.ac.uk/eas/research/groups/ncrg/resources/netlab/downloads/
% Script derived from standard Netlab input file, demmlp1.m, by Ian T Nabney
clear all;
clc
% Input arrays must be initialized to variable 'x' as follows...
%
First Column = Current Commanded Speed
%
Second Column = Previous Commanded Speed (0 if run just started)
%
Third Column = Time Since Last Speed Command Change
%
Fourth Column = Current Utilization
% Set up network parameters.
nin = 4; % Number of inputs. (see input array comment above)
nhidden = 750; % Number of hidden sigmoid neurons.
nout = 1; % Number of outputs.
alpha = .1; % Coefficient of weight-decay prior.
% Create and initialize network weight vector.
net = mlp(nin, nhidden, nout, 'linear', alpha);
% Set up vector of options for the optimiser.
options = zeros(1,18);
options(1) = 1; % This provides display of error values.
options(14) = 75000; % Number of training cycles.
% Run Netlab to train neural network
[net, options] = netopt(net, options, x, t, 'scg');
% Use neural network to generate predicted speeds
y = mlpfwd(net, x);

Statement A: Approved for Release.
Distribution is unlimited.

7

ANNEX B
VALIDATION SET
Several months after the ANN described in this paper had been trained, new field test data became available.
This new data was used as a “validation set”, in order to test the efficacy of the ANN without re-training. The
results are shown in Figure B-1 below.

1
0.9
0.8

Nondimensionalized Speed

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

0.1

0.2

0.3

0.4
0.5
0.6
Nondimensionalized Time

0.7

0.8

0.9

1

Figure B-1. Validation Set Results

A few observations from the ANN results are given below.

Non-dimensionalized time = 0. The ANN is unable to capture the speed change at “startup”. This
is likely because there are relatively few “startups” in the training data (there is only 1 startup per field test,
with 20 field tests used in the training data).

Non-dimensionalized time = 0.25. Through this speed step, the ANN predicts a near-constant
speed that is the average of the speed transient. This is likely due to an insufficiently advance algorithm, as
the ANN “settled” into minimizing error by picking a mid-point speed, rather than accurately modeling the
transient.

Non-dimensionalized time = 0.3. The ANN anticipated a speed “overshoot” during this transient,
which did not occur. Analysis of the training data shows that, on several occasions, an “overshoot” did
happen at this speed. Therefore, this ANN error is the results of an insufficient number of training sets that
do not have an overshoot during a similar speed step.

Non-dimensionalized time = 0.55. The ANN correctly predicts a speed “undershoot” during this
transient.

Non-dimensionalized time = 0.6 through end of run. The ANN predicts that the speed will be
much less than the actual speed through the end of the run. This is likely due to previous runs in the
training set that have failed to maintain speed late in run. Therefore, more training data is necessary for the
ANN to be able to distinguish the characteristics of runs that will and will not be able to maintain speed.
From the results, we can calculate the accumulated error using two speed prediction methods. The first method
is simply presuming the actual speed is equal to the setpoint (this will be referred to as the “Non-ANN Method”). It
should be noted that this method could be improved by simple algorithms, such as assuming a time constant for
speed changes, but that is not the focus of this analysis. The second method is the prediction of the ANN. The error
Statement A: Approved for Release.
Distribution is unlimited.

8

of each of these methods can be calculated as the absolute value of prediction minus the actual speed. A graph of
accumulated error is shown in Figure B-2 below.

Accumulated Error (|Prediction Speed - Actual Speed|)

300

250

200

150

100

50

0
0

0.1

0.2

0.3

0.4
0.5
0.6
Nondimensionalized Time

0.7

0.8

0.9

1

Figure B-2. Accumulated Error from Non-ANN and ANN Speed Prediction Methods on Validation Set

Figure B-2 shows that the Non-ANN and ANN methods for speed prediction have nearly the same error
accumulation rate until late in the data set (second to last speed change). This is an encouraging sign that with
additional training-set data and more advanced ANN methods, neural networks will be practical tools for predicting
vehicle performance in the near future. In summary, the results of this validation set reinforce the assertions made in
the conclusion of this paper that ANN performance can be improved with more advanced methods and more
computing power, but more training data will be needed as well.

Statement A: Approved for Release.
Distribution is unlimited.

9

