Design Optimization of a Parallel
Hybrid Electric Vehicle
Uncertainty Analysis
Mahmoud Al-Zahrani, Andrew Carlile, Nikhil Ramaswamy and Hao Chen
1
Contents
0. Modeling Risk Preferences ....................................................................................................................... 3
1. Identify and Model the Uncertainty in your Design Analysis Model ....................................................... 4
2. Elicit a Detailed CDF for the Most Significant Uncertain Variables ...................................................... 12
2.1 Driver Mass....................................................................................................................................... 12
2.2 Glider Mass ....................................................................................................................................... 13
2.3 Battery Initial SOC ........................................................................................................................... 15
2.4 Throttle Deviation ............................................................................................................................. 16
2.5 Wheel Radius .................................................................................................................................... 17
3. Determining the Distribution of the Output of our Model ...................................................................... 19
4. Exploring the design space ..................................................................................................................... 30
5. Updating Project Web-page .................................................................................................................... 34
References ............................................................................................................................................... 36
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0. Modeling Risk Preferences
The commonly used expression for calculating utility is given by Eq 1.
−𝑥
𝑢(𝑥) = 1 − 𝑒 ( 𝑅 )
(1)
We assume that the risk tolerance(R) is a constant. To obtain R we first elicit the maximum
profit. To do this we consider the sales of Honda Civic 2012 Hybrid for year 2012 this is 7512
cars. Using the demand spreadsheet we then calculate the maximum profit for this to be
$37802189. To determine our certainty equivalent we play a 50/50 gamble from $0 profit to
$37802189(maximum profit) and ask ourselves at which value are we indifferent. We obtain this
value to be $12000000. This is our certainty equivalent xm = 12000000. Thus
𝑢(𝑥𝑚 ) = 0.5(𝑢(0) + 𝑢(37802189))
(2)
Using Eq 1 we obtain the value of R to be $ 23495322.
Figure 1 Utility as a function of the profit for a risk tolerance R=$25,956,628
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Figure 1 shows the Utility as a function of the profit for a risk tolerance R=$25,956,628. It
turns out that our utility curve is concave, which indicates that we are risk averse. It is consistent
since we, as a company, aim at having a sustainable development and thus give a higher value to
ensuring we get relatively high revenues than gambling for a doubled profit with uncertainty.
Note: The curve is consistent is the way that we effectively have:
u($12000000) = 0.5 (u($0) + u($37802189))
1. Identifying and Modeling the Uncertainty in our Design Analysis
Model
The parameters that introduce the most uncertainty into the parallel-hybrid vehicle’s
performance are:
1. Drag Coefficient
2. Drag Area
3. Air density
4. Driver mass
5. Friction Coefficient
6. Wheel Radius
7. Battery State of Charge
8. Glider Mass
9. Motor Resistance R
10. Car Mass
11. Driver Throttle
12. Air Speed
They were selected because these parameters will influence the performance of the vehicle and
are not fundamentally known. In other words, these parameters are not completely certain and
they will influence how the vehicle performs.
The Drag Coefficient (Cd ) is unknown at this stage because the geometry of the car is unknown.
Most vehicles have a Cd above .3, but not more than .4. For hybrid vehicles, since they are
designed to be more fuel efficient, have lower than average Cd . For our analysis, an upper bound
of .34 was used with a lower bound of .3. The most likely value of Cd for our vehicle is .32.
These values are loosely based on the Honda Civic 2012 hybrid.
Drag Area (Ad ) is similar to the Cd in that it is unknown at this stage because the geometry of the
vehicle is unknown in m2 , an upper bound of 2.4 and lower bound of 2 were used. The most
likely valued is 2.2 m2 . These estimates are also loosely based on the Honda Civic.
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The Air Density will have an impact on the performance of the vehicle. The air density at any
given location is not constant, so this variable is very useful to have in an uncertainty calculation.
A most likely value of 1.29 kg/m3 was used because it is the density of air at 0 C and 1 atm. An
upper bound of 1.35 kg/m3 and a lower bound of 1.25 kg/m3 were used to have a range of likely
densities that the vehicle can encounter.
Driver Mass will obviously be a variable that cannot be predicted with certainty. Although it is
small compared to the overall weight of the vehicle, the weight of the driver can still impact the
performance of the vehicle. The selection of 100 kg for most likely, and upper and lower bounds
of 130 kg and 50 kg were selected based on reasonable weights of drivers.
The Friction Coefficient takes into account the losses the vehicles’ drivetrain will experience
during operation. It is set based on the Dymola model configuration. Its’ value ranges from .01 to
.02 and is most likely at .015. These changes could be due to manufacturing of the vehicle and
the fact that every system has frictional losses.
The Radius corresponds to the wheel radius. Most vehicles has a few sizes of wheels as options,
and this variable will take that variation into account. The radius range is from 10.5 in. to 15 in.
with 10.5 in. wheels being the most likely based on this car’s market. For simplicity, it’s
assumed that the variation in the wheel diameter is continuous.
Initial State of Charge (SOC) of the battery will have a huge impact on how the vehicle performs
over the UDDS cycle. Obviously, if the battery starts out with a higher charge a substantially
smaller amount of fuel could be saved. For our test, the SOC can vary from 0 to 1 (0 being
depleted and 1 being fully charged) and the most likely value will be a value of .5 (half charge).
The Glider Mass corresponds with the weight of vehicle minus the drivetrain. The drivetrain
individual component masses are calculated at a different point in the analysis. The glider mass
can range from 500 to 1200 kg, with a most likely value of 900 kg. These values are fairly
standard for small vehicles.
The Motor Resistance parameter allows for uncertainty in the quality of the motor. If it is isn’t
built properly, it may have a higher resistance. The range is from .04 to .06 Ohms with a most
likely value of .05 Ohms.
Another parameter that could potentially have a large impact on the performance of the vehicle is
the driver’s response to the throttle. The Driver Throttle parameter accounts for a how much
more does the driver presses the pedal more than required. It has a minimum value of 0 (the
driver presses the pedal as required exactly) and a maximum value of 1 (the driver always
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presses the paddle at maximum). Most drivers won’t press it that much, and a lot won’t get the
exact pedal position, so a value of 0.15 is most likely to happen.
Finally, the Air Speed is uncertain. For our test, the airspeed has a range of -2 to 2 m/s, with -2
being in the direction of the vehicle. The most likely value is 0 m/s.
Figure 2 Setup for uncertain variables
Figure 2 shows the setup for uncertain variables. The Model Center connection was linked to the
quick wrap and the survey results. The Generic Driver Tool allowed us to examine the effects of
uncertainty on our hybrid-vehicle. The maximum values of the design parameters (200 kW
engine power, 70 kW motor power and 50 AmpHr battery capacity) were used to examine just
the effect of the uncertainty. Figure 3 shows the model center setup for LHS.
Figure 3 Model center setup for LHS
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Figure 4 Design variables histogram for 100 LHS runs
Figure 4 shows the Design variables histogram for 100 LHS runs. For 100 Latin-Hypercube
Sample (LHS) runs, the histograms review the effect of uncertainty. The design variable
distribution is based on the best guess estimates for the uncertainty. For example, most drivers do
not drive aggressively so the distribution is biased towards non-aggressive drivers (lower throttle
coefficient). The LHS run for 1000 samples returned similar results, with the utility. Figure 5
shows the design variables histogram for 1000 LHS runs. It is also observed that the drag
coefficient, drag area, glider mass, air speed and friction coefficient are evenly distributed.
However it is observed that the radius is shifted towards the right. The reason is because most
commonly vehicles have 15’’ rim diameter and hence occurrences of 16’’ and higher are rare.
Furhter the driver mass is also on the higher end. This also makes sense as most drivers weigh
mostly 80 kgs and higher.
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Figure 5 Design variables histogram for 1000 LHS runs
The survey tie-in was used to determine the demand and utility of the different parameters.
Figure 6 and 7 shows the demand 100 and 1000 LHS runs respectively. Figure 8 and 9 shows the
utility 100 and 1000 LHS runs respectively.
Figure 6 Demand 100LHS runs
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Figure 7 Demand 1000 LHS runs
Figure 8 Utility 100 LHS runs
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Figure 9 Utility 1000 LHS runs
Figure 10 Sensitivity analysis for our model
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It is observed from Figure 10 that the most influential uncertain variables are the Radius of
the wheel, the Driver throttle, the glider mass, the driver mass and Initial SOC. Each of this is
explained below:
Wheel Radius: We know that rotational speed ω = v/r. This means that for producing the
same linear speed v with a larger wheel radius requires lesser ω. This means that the rotational
speed of the engine and motor can be less to produce a given linear velocity. This makes a
significant impact on two design variables namely acceleration time and top speed. With a larger
wheel radius the top speed increases and acceleration time decreases greatly hence an increase in
utility and demand can be obtained. Further a larger radius increases the torque requested as
shown in Eq 3. hence decreases the fuel efficiency. Thus due to these reasons the wheel radius is
the most important uncertain variable.
[𝑇𝑒 (𝑘)+𝑇𝑚 (𝑘)]𝑖𝑛 (𝑘)𝑖𝑓 𝜂
𝑟𝑤
= 𝜆𝑀[𝑣(𝑘 + 1) − 𝑣(𝑘)] + 𝑐𝑟 𝑀𝑔 cos 𝜃𝑘 + 𝑆𝑐𝑑 𝜌𝑎
𝑣̅ 2
2
(3)
Driver Throttle: How much the driver presses on the throttle determines the linear velocity of
the vehicle, the acceleration and the fuel efficiency. This however does not play as big an impact
as wheel radius because even a bad driver may actually press just enough throttle position at
times hence the overall effect gets mitigated to an extent. Further most drivers don’t
unnecessarily press the throttle too much and hence its effect is less than that of wheel radius.
Glider mass: The glider mass plays a crucial role in increasing the overall mass of the
vehicle. The increase in mass of the vehicle decreases the top speed as more torque is needed to
drive the vehicle. The acceleration time increases as more energy needs to be expended to take
the vehicle to 60MPH. Further the overall fuel efficiency also decreases. The effect of Glider
mass can be observed from Eq 3. The mass affects only the 𝜆𝑀[𝑣(𝑘 + 1) − 𝑣(𝑘)] and 𝑐𝑟 𝑀𝑔
factor hence its effect is less than that of radius.
Driver mass: The driver mass like the glider mass plays an important role however since the
scale is lower it plays a lower influential factor than glider mass.
Initial SOC: Since the initial SOC directly affects the fuel efficiency its affect plays an
important role in the demand of the HEV. For example a higher initial SOC of battery requires
less fuel to complete the UDDS cycle. However since the SOC affects the top speed and
acceleration time only when the battery is depleted its effect plays a less important role.
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2. Elicit a Detailed CDF for the Most Significant Uncertain Variables
For our project, the factors determine the utility and demand are the top speed, acceleration,
and the fuel efficiency. Thus, we select the uncertain variables that will mostly affect those three
factors. The following five uncertain variables are picked, Driver Mass, Glider Mass, Battery
Initial State of Charge (SOC), Throttle Deviation, and Wheel Radius. For the entire simulation
and analysis, the UDDS cycle is always tracked. Given that condition, intuitively the Driver
Mass and Glider Mass will affect the top speed, acceleration, and the fuel efficiency; the Battery
Initial SOC and Throttle Deviation will affect the fuel efficiency; and the Wheel Radius will also
affect the top speed, acceleration and the fuel efficiency. The detailed elicitation process for all
the five uncertain variables is presented in the following.
2.1 Driver Mass
As part of the total mass when the vehicle is running, driver mass will affect the vehicle top
speed, acceleration and fuel efficiency. To determine the CDF of the driver mass, the questions
that were asked include:
1) What’s the weight range of the driver?
2) What’s the age range of the driver, which could affect the driver mass significantly?
3) Would most drivers be male or female?
4) What’s the average weight of the driver?
The male average weight in U.S. is around 88 kg and for female is 74 kg. The male driver
amount is much larger than the female. Therefore, we have 84 kg corresponding to the average
driver weight. The maximum weight selected is 200 kg which should correspond to probability
of 1 and a weight of 0 should correspond to 0 probability as there cannot be negative weights. A
person over this weight is not able to fit in this Honda Civic Hybrid Car comfortably. Besides,
we consider that it has little probability that a child under 16 will drive this car, but a too little
kid will not. We also assume that most people i.e. 98% weigh below 150 Kgs. With the above
information, the CDF of the driver mass is as Fig. 11 (a) and the corresponding PDF is as Fig. 11
(b).
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(a) CDF of Driver Mass
(b) PDF of Driver Mass
Figure 11 Driver Mass Probability
The CDF of driver mass has a fast increase between 50 kg and 100 kg. This is intuitively
understandable because most of the adult weights are falling within this range. Above and below
this range, the CDF will have a relative small change. Correspondingly, the PDF has a peak
value between 50 kg and 80kg.
2.2 Glider Mass
As part of the total mass, similarly to the driver mass, the glider mass will also affect all three
vehicle parameters: top speed, acceleration and fuel efficiency. To determine the CDF of the
driver mass, the questions that were asked include:
1) What’s the mass range of the glider?
2) What’s the average glider mass?
The glider mass is the main part of the total mass. Intuitively, it has more effect on vehicle
performance than the driver mass. By checking the available vehicle parameters on market, the
glider mass covers the range between 400 kg to 1700 kg, with the average around 800 kg. We
assume that there exists no glider for an automobile that is less than 300 kgs hence this
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corresponds to probalility of 0. Further the heaviest weighs around 1800 kgs as obtained from
FASTSim this corresponds to 1 probability. Most vehicles have an approximate glider mass of
900 kgs hence this was chosen to be 0.75. Therefore, the CDF and PDF of glider mass are shown
as Figure 12.
(a) CDF of Glider Mass
(b) PDF of Glider Mass
Figure 2. Glider Mass Probability
The glider mass CDF has a fast increase between 600 kg and 900 kg, since most of the vehicle
on market have the glider mass in this range. Correspondingly, the PDF has a peak between 600
kg and 900 kg.
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2.3 Battery Initial SOC
The battery initial SOC will affect the vehicle fuel efficiency. If the battery is fully charged
before the UDDS cycle starts, the vehicle could more efficiently run the engine and have the
motor output the desired power difference. However, if the battery initial SOC is very low, the
engine will run most of the time and hence the fuel efficiency will drop. To determine the CDF
of battery initial SOC, the following questions are asked:
1) Could the users leave the battery fully discharged?
2) What’s the maximum limit for the SOC of a charged battery?
3) Would most users leave the SOC below or above 50% SOC?
4) How many would leave their battery at low SOC?
The battery SOC ranges from 0 to 1. When driving a hybrid car, people usually keep their
battery at a relative high SOC. We run our model from 0.2 to 0.8 SOC as between these values
the open circuit voltage remains a constant. A zero and one SOC should correspond to 0 and 1
probability respectively. Anything below 0.2 SOC would effectively mean no motor power
hence this is 0.05 and since anything above 0.8 corresponds to full SOC this value 0.95. But very
few people will fully charge or deplete the battery. Then the corresponding CDF and PDF for
battery initial SOC are shown in Figure 13.
(a) CDF of Battery Initial SOC
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(b) PDF of Battery Initial SOC
Figure 13. Battery Initial SOC Probability
CDF shows that most users leave their battery SOC between 0.2 and 0.8. More people will
prefer to have the SOC above 0.5. Therefore, the CDF has faster increase between 0.6 and 0.8
than between 0.2 and 0.6. Correspondingly, the PDF has a peak between 0.6 and 0.8. The area
between 0.6 and 0.8 is larger than that between 0.2 and 0.6.
2.4 Throttle Deviation
For a specific UDDS cycle, the controller will decide how much output power should be
generated from the engine. However, it is almost not possible that the driver is always able to
press the pedal at the corresponding throttle position. With this throttle deviation, the engine will
not be able to run most efficiently, and thus the fuel efficiency will drop. This deviation will be
resulted from the drivers’ habit and controllability of the vehicle. Therefore, the following
questions are asked to derive the CDF:
1) How likely is it for a driver to press the gas pedal at full throttle all the time?
2) What percentage of drivers could figure out the exact throttle position for the car?
3) Would most drivers press the pedal more than required by a large amount?
The throttle position ranges from 0 to 1 and this corresponds to probability of 0 and 1
respectively. The driver is not possible to always press the pedal for the exact right throttle
position. However, most drivers should be able to control it reasonably well. Therefore, the
throttle deviation CDF and PDF are shown in Figure 14.
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(a) CDF of Throttle Deviation
(b) PDF of Throttle Deviation
Figure 14. Throttle Deviation Probability
Most of the drivers could control the pedal well enough, with little deviation though.
Therefore, the corresponding CDF has large value at 0.5, and it increases faster between 0.1 and
0.2 than between 0.2 and 0.5 The PDF has a peak between 0.1 and 0.2. After 0.2, it decreases
slowly. This is matching the CDF changing trend.
2.5 Wheel Radius
With a relative large wheel size, the vehicle speed could be faster, and this will affect the
vehicle top speed, acceleration, and fuel efficiency. To determine the CDF of the wheel radius,
the questions that were asked include:
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1) What’s the typical wheel radius range of the car in market?
2) What’s the wheel radius of most cars?
The car wheel radius range was found to be between 11.05 and 15 inches. Since the car we
designed (Honda Civic) is a small passenger car, therefore, most likely the wheel radius is also
relative smaller. Most automobiles use 15’’ rims hence this is the most common this corresponds
to 0.96 probability. We assume the minimum to be 11.05’’ in radius and maximum is 30’’
diameter this corresponds to 0 and 1 respectively. The wheel radius CDF and PDF are shown in
Figure 15.
(a) CDF of Wheel Radius
(b) PDF of Wheel Radius
Figure 15. Wheel Radius Probability
The CDF has a fast increase under 12.45. This is intuitively understandably since the
passenger car we designed is a small one, thus a relative small size wheel is most likely being
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selected. The PDF has this shape because most wheels’ radius is 11.35 inches, and almost no
wheel has a size below that. Also some wheels have size between 11.35 and 12.45 inches. Fewer
wheels have size larger than that.
3. Determining the Distribution of the Output of our Model
A Monte Carlo simulation of 1000 runs was performed on our model. Figure 16 shows the
Model Center model used with the appropriate variables CDF’s integrated. The Latin-Hypercube
Sampling Tool examined the effect of uncertainty, in specified variables, on the performance of
our parallel-hybrid vehicle. The Latin-Hypercube Sampling Tool has the 12 uncertain parameters
embedded in it, and they are shown in Figure 17. The five uncertain parameters with associated
CDF’s and PDF’s are Glider Mass, Initial State of Charge of the Battery, Throttle sensitivity of
the Driver, Wheel Radius, and Driver Mass and they are linked separately as excel spreadsheets
with the variables from the LHS Tool tying them in. The distribution data was entered directly
into the LHS Tool, and is shown in Figure 18.
Figure 16 Model Center model used with the appropriate variables CDF’s integrated
The ModelCenter layout links the uncertain variables (with CDF’s and from LHS) to the
input of the QuickWrap which contains the Dymola simulation of our parallel-hybrid vehicle.
The Script handles to cost caluclations based on the values of the design parameters, and those
values coupled with the performance tie in to the Demand Spreadsheet. Therefore we can
examine the effects of uncertainty on our demand, profit, and utility.
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Figure 17 Latin-Hypercube Sampling Tool that has the 12 uncertain parameters embedded in it
Figure 18 The distribution data that was entered directly into the LHS Tool
Figure 17 and 18 show the input of the uncertain variables. The uncertain parameters were:
●
●
●
●
●
●
●
●
●
●
●
●
Drag Coefficient
Drag Area
Air density
Driver mass
Friction Coefficient
Wheel Radius
Battery State of Charge
Glider Mass
Motor Resistance R
Car Mass
Driver Throttle
Air Speed
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However, the five parameters with the greatest influence on the behavior of the car are the Glider
Mass, Initial State of Charge of the Battery, Throttle sensitivity of the Driver, Wheel Radius, and
Driver Mass. Figure 19 shows the histograms for each of the uncertain variables and the
performance attributes under uncertainty simulation.
Figure 19 Histograms of uncertain variables based on previously assigned distributions
Figure 20. Histogram of Top Speed of Vehicle
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Figure 20. shows the distribution of Top Speed of Vehicle The top speed of the vehicle (in
MPH) is expected to be around 154 MPH. Our vehicle, even under uncertainty, will likely have a
substantial amount of power, and the effect of drag on the vehicle is going to be fairly consistent
even with variations in Cd and surface are. The top speed values far away from 154 MPH are still
possible, but those values clearly correspond to extreme values of power either in a high power
or low power case.
Figure 21. Histogram of Acceleration Time of Vehicle
Figure 21 shows the distribution of Acceleration Time of Vehicle. The acceleration times for our
vehicle are around 5 seconds. Although that is a quick time, our vehicle will most likely have a
powerful powertrain, and the mass is held fairly low because modern cars average weight has
been decreasing. Also, the demand survey responds well to quickly accelerating cars and this
output helps with our demand, profit, and utility.
Figure 22 Histogram of MPG of Vehicle
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Figure 22 shows the distribution of MPG of Vehicle. Expected values of MPG are centered
around 27 MPG. For a hybrid, this is a fairly low value but it is better than the average car, and is
high enough to generate demand. The vehicle does have configurations that get significantly
higher and moderately lower values. The vehicle configurations with higher MPG also help to
drive demand, whereas the lower values certainly drive demand down to some degree.
Figure 23 Data explorer data
Figure 23 shows the data explorer data. The data explorer allowed the examination of the
variables as the 1000 runs progressed. There is consistent demand for our vehicle for various
configurations of the drivetrain. There are a large number of cases with a demand value around
.03, and those values of demand are the most likely based on Figure 24. There are cases with
very low (0) demand, and cases with relatively high demand (.1), but there are occurrences with
significantly less than a demand around .03. Our group expected our vehicle to have some
demand, as sales of hybrid cars do command marketshare. The demand is not outstanding
because our vehicles’ performance simply didn’t pull enough demand from the survey responses.
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Figure 25 Demand Histogram for HEV
The profit output was positive for almost all cases run. The profit values tended to be grouped
around $2,500,000 for the car’s total sales in the market. There are cases with higher or lower
profits, and this variation makes sense because the car’s performance is uncertain and the survey
results are not going to perfectly reflect the sales of the vehicle in reality. However, we can say,
with a high degree of certainty, that our vehicle will be profitable. The histogram is shown in
Figure 26. Our profit histogram is based on our vehicle cost model versus the amount of money
consumers were willing to pay for a hybrid vehicle. Since our cost model and vehicle
performance are competitive with vehicles on the market that are profitable, our consistent profit
makes sense. In addition, not having a high profit makes sense as the components in a hybrid
vehicle are quite expensive.
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Figure 26 profit histogram for HEV
The expected utility follows the same trend as the profit in that there are some cases with a
negative utility, but most likely the vehicle will have a positive utility. Since the majority of
vehicle arrangements had positive demand and positive profit, a consistently positive utility is
logical as shown in Figure 27.
Figure 27. Histogram of Utility for HEV
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Figure 28 Histogram of Cost
Figure 28 shows the histogram of the cost with all the uncertain parameters. Cost (this due to
that the parameters affecting the cost are engine power, motor power, Amphr and voltage. Since
the voltage varies due to the change in resistance the cost will vary only if the resistance changes.
In these runs, the resistance is constant hence there is very little variation in cost.
The following figures show the MCS runs with most important uncertain variables.
Figure 29 Histogram of MPG obtained from MC Simulation of most important uncertain variables.
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Figure 30 Histogram of Top Speed obtained from MC Simulation of most important uncertain variables.
Figure 31 Histogram of Acceleration Time obtained from MC Simulation of most important uncertain variables.
Figure 29-31 shows the Histogram of MPG, Top Speed and Acceleration Time obtained from
MC Simulation of most important uncertain variables. It is observed that they are not
significantly different from those obtained using all the uncertain variables.
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Figure 32 Histogram of Demand obtained from MC Simulation of most important uncertain variables
Figure 33 Histogram of Utility obtained from MC Simulation of most important uncertain variables
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Figure 33 Histogram of Cost obtained from MC Simulation of most important uncertain variables
Figure 34 Histogram of Profit obtained from MC Simulation of most important uncertain variables
Figure 32-34 shows the Histogram of Demand, Utility, Cost and profit obtained from MC
Simulation of most important uncertain variables. It is observed that except for Cost the other
are not significantly different from those obtained using all the uncertain variables.
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4. Exploring the design space
A deterministic study on the maximum utility was conducted to explore the design space.
The three parameters what were used are the motor power, engine power, and battery capacity
(AmpHr). The engine power varies from 50KW to 250KW (the range was increased in order to
eliminate the occurrence of a maxima in the boundary of the constraints (inactive constraint).
The motor power changes from 5KW to 70KW. As for the battery, it changes from 1AmpHr to
50AmpHr. Figure 35 shows a snapshot of the tool used to explore the design space. Six levels of
a full factorial were conducted using the Engine power and motor power at different battery
capacities (1, 10, 20, 30, 40, and 50 AmpHr).
Figure 35 Snapshot of the DOE tool
After conducting the DOE, the plot of the results is shown from Figure 36 to Figure 41.
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Figure 36 Utility plot at 1 AmpHr
Figure 37 Utility plot at 10 AmpHr
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Figure 38 Utility plot at 20 AmpHr
Figure 39 Utility plot at 30 AmpHr
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Figure 40 Utility plot at 40 AmpHr
Figure 41 Utility plot at 50 AmpHr
The figures show that the utility surface is smooth with no discontinuities, which is helpful
later in the optimization task. From the data obtained from the figures, the maximum
deterministic utility is achieved at 170KW engine power, 31KW motor power and 10AmpHr
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battery capacity.
By looking at the graphs, the design range can be minimized in order to
simplify the optimization task to the ranges shown in Table 1.
Table 1 Reduced design range
Parameter
Range
Engine power (KW)
(130-210)
Motor power (KW)
(18-44)
Battery size (AmpHr)
(1-20)
5. Updating Project Web-page
Figure 42 shows the updated web page
(a)
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(b)
(c)
35
(d)
Figure 42 Updated web page
References
[1] Drag Coefficient Estimates: theautochannel.com, Honda Civic Wheel Sizes: cars.com,
http://www.bridgestonetire.com/catalog
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