Xin Q. Diesel Engine System Design

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Table 3.7 Coefﬁcient of variation of the engine system response of the Monte Carlo simulation cases

Case 1 Case 2 Case 3 Case 4 Case 4S Case 5 Average of

ﬁve cases

Engine brake power 0.58% 0.58% 0.59% 0.57% 0.57% 0.58% 0.58%

BMEP 0.58% 0.58% 0.59% 0.57% 0.57% 0.58% 0.58%

Gross pumping loss PMEP 1.59% 1.48% 1.48% 1.40% 1.40% 1.30% 1.45%

360∞ gross IMEP

0.57% 0.55% 0.55% 0.54% 0.54% 0.51% 0.55%

Engine delta P 1.95% 1.91% 1.82% 1.78% 1.78% 1.63% 1.82%

BSFC 0.28% 0.27% 0.28% 0.30% 0.30% 0.31% 0.29%

Peak cylinder gas pressure (maximum of all

cylinders)

2.60% 2.29% 2.38% 2.28% 2.28% 1.94% 2.30%

Peak cylinder gas temperature 0.96% 0.81% 0.76% 0.78% 0.78% 0.64% 0.79%

EGR rate 1.23% 1.16% 1.08% 1.10% 1.10% 1.02% 1.12%

Intake manifold gas temperature 0.68% 0.80% 0.73% 0.79% 0.79% 0.83% 0.77%

A/F ratio 2.11% 1.78% 1.65% 1.64% 1.64% 1.25% 1.69%

Intake manifold oxygen mass fraction 0.84% 0.65% 0.55% 0.63% 0.63% 0.50% 0.63%

Exhaust manifold gas temperature 1.27% 1.03% 0.97% 0.99% 0.99% 0.79% 1.01%

HP compressor outlet temperature 1.30% 1.18% 1.10% 1.12% 1.12% 1.21% 1.18%

Intake manifold boost pressure 1.80% 1.51% 1.48% 1.36% 1.36% 1.05% 1.44%

Exhaust manifold pressure 1.62% 1.36% 1.34% 1.23% 1.23% 1.04% 1.32%

Intake manifold mixture volumetric efﬁciency 0.07% 0.09% 0.10% 0.10% 0.10% 0.10% 0.09%

Total exhaust restriction (pressure drop) 10.95% 11.26% 11.25% 11.41% 11.41% 12.08% 11.39%

Engine coolant heat rejection 0.67% 0.71% 0.74% 0.72% 0.72% 0.75% 0.71%

Total engine coolant plus CAC heat rejection 0.81% 0.82% 0.86% 0.80% 0.80% 0.82% 0.82%

EGR cooler heat rejection 1.22% 1.17% 1.14% 1.14% 1.14% 1.22% 1.18%

Charge air cooler heat rejection 2.99% 2.75% 2.53% 2.31% 2.31% 2.12% 2.54%

HP-stage turbocharger actual speed 1.47% 1.05% 1.08% 1.16% 1.16% 1.23% 1.20%

LP-stage turbocharger actual speed 1.38% 1.26% 1.25% 1.39% 1.39% 1.43% 1.34%

Notes: The coefﬁcient of variation is computed as the ratio of standard deviation to mean of the samples. The average of ﬁve cases includes

Cases 1, 2, 3, 4 and 5.

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287Optimization techniques in diesel engine system design

The oscillating data of the distribution in the gures are the raw data of the

Monte Carlo simulation with 1000 random samples. The smooth curves of

the distributions are the tted results by using the normal distribution. The

probability distribution of the raw data is obtained by using 100 bins that span

over the entire range of the sample values for a given parameter. Fewer bins

make the distribution appear less oscillating but may exhibit ‘step changes’

in the shape of the probability distribution curve because more samples

1 2 3

4% fueling

derating

Constant

at 77 °F

Six sigma range = 3%

variation of rated fueling

Engine fuel

ﬂow rate

Probability density functionProbability density functionProbability density function

Probability density function

Probability density

function

2.5

1.5

0.5

450

400

350

300

250

200

150

100

0.25

0.2

0.15

0.1

0.05

70 80 90 100 110 120 130 140 150 160

LP-stage compressor inlet air temperature

(°F)

15 15.5 16 16.5 17

Engine compression ratio

1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15

HP-stage normalized turbine area (mass multiplier)

0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

EGR valve opening (ﬂow coefﬁcient)

–1 0 1 2 3 4 5 6 7 8 9 10 11 12

HP turbine wastegate opening (mm)

Constant

at zero

(fully

closed)

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

3.24 Input data in Monte Carlo simulation for engine system design.

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288 Diesel engine system design

will fall into each bin. In contrast, more bins make the distribution appear

more oscillating and may even exhibit zero probability at certain parameter

values because some bins may not have samples at all. The degree of the

data oscillation is related to the number of bins used for data display, and

does not indicate simulation accuracy. It is the number of samples in the

Monte Carlo simulation that affects accuracy.

Figure 3.25 shows an example of the response parameters, displayed

with both raw data of the Monte Carlo simulation and the tted normal

distribution curves. Figure 3.26 shows the probability distribution curves of

all important response parameters in engine performance. Table 3.7 shows

the calculated coefcients of variation for the responses of all six cases. A

summary of this investigation is given as follows.

1. The variation range of each response parameter can be clearly observed

from this study (Table 3.7 and Fig. 3.26). It should be noted that the

variation range of the response is governed by the assumptions made

in the variation ranges of the input factors shown in Table 3.6.

2. The shapes of the probability distributions of a given response parameter

at different ambient conditions are different. This indicates the effect of

the shapes of the probability distributions of the input factors (especially

the turbine wastegate opening and the EGR valve opening), and the effect

of complex nonlinear engine behavior at different ambient conditions.

0.015

0.01

0.005

Probability density function

1800 2000 2200 2400 2600 2800 3000

Peak cylinder gas pressure (maximum of all cylinders, psia)

Design

limit

Raw data of Monte Carlo simulation

Normal distribution ﬁt

1: 0 ft 77 °F

4: 5500 ft 100 °F

2: 0 ft 100 °F

5: 10,000 ft 85 °F

3: 0 ft 122 °F

3.25 Output data illustration in Monte Carlo simulation – ﬁtting the

raw data with normal distribution.

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289Optimization techniques in diesel engine system design

3. Different engine performance parameters exhibit their extreme values

at different ambient conditions. For example, peak cylinder pressure

has its worst (highest) value in Case 1 (sea level, 77∞F), while exhaust

manifold temperature reaches its worst (highest) value in Case 5 (10,000

feet, 85∞F) even with 4% fueling derating. Different types of engine

design constraints or limits are marked on Fig. 3.26 as examples. The

probability distributions of the responses can be checked against these

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

0.20

0.15

0.10

0.05

0.00

0.02

0.015

0.01

0.005

500

400

300

200

100

Probability density function

17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0

BMEP (bar)

Six sigma range = 3.5%

variation of rated power

Engine brake power

Raw data of Monte Carlo simulation

Normal distribution ﬁt

–3.1 –3.0 –2.9 –2.8 –2.7 –2.6 –2.5 –2.4 –2.3 –2.2 –2.1

Gross pumping loss PMEP (bar)

1000 1200 1400 1600 1800 2000

Engine delta P (mbar)

21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5

360-deg gross IMEP (bar)

0.35 0.36 0.37 0.38 0.39

BSFC (lb/(hp.hr))

3.26 Output data in Monte Carlo simulation – probabilistic engine

system design.

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290 Diesel engine system design

3.26 Continued

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

0.015

0.01

0.005

0.03

0.025

0.02

0.015

0.01

0.005

Probability density function

2400 2500 2600 2700 2800 2900

Peak cylinder gas temperature (°F)

1900 2100 2300 2500 2700 2900

Peak cylinder pressure (maximum of all cylinders, psia)

Design

limit

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

1.5

0.5

500

400

300

200

100

Probability density function

15 16 17 18 19 20 21

A/F ratio

16.0% 16.5% 17.0% 17.5% 18.0% 18.5%

Intake manifold oxygen mass fraction

5 5

Design

limit

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

1.5

1.0

0.5

0.0

0.4

0.3

0.2

0.1

0.0

Probability density function

28 29 30 31 32 33 34 35 36 37 38

EGR rate (%)

140 150 160 170 180 190 200 210

Intake manifold gas temperature (°F)

4 4

Design

limit

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291Optimization techniques in diesel engine system design

3.26 Continued

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

0.05

0.04

0.03

0.02

0.01

0.15

0.1

0.05

Probability density function

300 350 400 450 500

HP-stage compressor outlet temperature (°F)

1000 1100 1200 1300 1400

Exhaust manifold gas temperature (°F)

Design

limit

Design

limit

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

Probability density function

4.5 5.0 5.5 6.0

Exhaust manifold pressure (bar, absolute)

3.0 3.5 4.0 4.5

Intake manifold boost pressure (bar, absolute)

Design

limit

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

700

600

500

400

300

200

100

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Probability density function

88% 89% 90% 91% 92%

Intake manifold mixture volumetric efﬁciency

3 4 5 6 7 8 9 10 11 12 13

Total exhaust restriction (inch Hg)

Design

limit

Diesel-Xin-03.indd 291 5/5/11 11:46:16 AM

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292 Diesel engine system design

design limits to assess the probability of failure and reliability issues.

4. Case 4S illustrates a typical sensitivity analysis on the effect of design or

calibration changes. Case 4S has a much lower exhaust restriction pressure

drop compared with Case 4. This gives higher peak cylinder pressure

in Case 4S due to its higher engine air ow rate. The sensitivity of the

probability distribution shape of the engine response to the probability

distributions of the input factors can be analyzed by this method.

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

1: 0 ft 77 °F

3: 0 ft 122 °F

5: 10,000 ft 85 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

2: 0 ft 100 °F

4: 5500 ft 100 °F

4S: 5500 ft 100 °F

0.004

0.003

0.002

0.001

0.0005

0.0004

0.0003

0.0002

0.0001

0.0005

0.0004

0.0003

0.0002

0.0001

0.003

0.002

0.001

0.007

0.006

0.005

0.004

0.003

0.002

0.001

0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

Probability density functionProbability density function

Probability density function

22000 22500 23000 23500 24000 24500 25000

Total engine coolant plus CAC heat rejection (Btu/min)

18000 18500 19000 19500 20000 20500 21000

Engine coolant heat rejection (Btu/min)

6000 6500 7000 7500 8000 8500

EGR cooler heat rejection (Btu/min)

80,000 90,000 100,000 110,000 120,000 130,000

HP-stage turbocharger speed (rpm)

2800 3000 3200 3400 3600 3800 4000 4200

Charge air cooler heat rejection (Btu/min)

70,000 75,000 80,000 85,000 90,000 95,000

LP-stage turbocharger speed (rpm)

Design

limit

Design

limit

Design

limit

Design

limit

Design

limit

3.26 Continued

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293Optimization techniques in diesel engine system design

5. This Monte Carlo simulation combines multiple engine operating

conditions (i.e., at different ambient conditions) on one probability

distribution chart to compare them conveniently. Similar plotting can

be conducted by combining different engine speeds or loads on one

probability chart.

6. Such a probabilistic analysis in engine system design provides much

more information than the traditional deterministic approach in order

to evaluate variability, reliability and safety margins in design.

3.5 References and bibliography

3.5.1 References and bibliography on DoE and

optimization

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P, Grove D M and Wynn H P (eds), Statistics for Engine Optimization, Professional

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engine using cycle analysis and Taguchi methods’, SAE paper 891895.

Bates R A, Fontana R, Randazzo C, Vaccarino E and Wynn H P (2000), ‘Empirical

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P, Grove D M and Wynn H P (eds), Statistics for Engine Optimization, Professional

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John Wiley & Sons, New York.

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diesel vehicles through the use of DOE and optimization techniques’, SAE paper

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Carey W R (1992), Tools for Today’s Engineer: Strategy for Achieving Engineering

Excellence, the 38th L. Ray Buckendale Lecture, SAE SP-913, SAE paper 920040,

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Courteille E, Mortier F, Leotoing L and Ragneau E (2005), ‘Multi-objective robust design

optimization of an engine mounting system’, SAE paper 2005-01-2412.

Dvorak T M and Hoekstra R L (1996), ‘Optimizing internal combustion engine performance

through response surface methodology’, SAE paper 962525.

Edwards S P, Grove D M and Wynn HP (eds) (2000), Statistics for Engine Optimization,

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Experiments: Principles and Applications, Umetrics AB, Sweden.

Fowlkes W Y and Creveling C M (1995), Engineering Methods for Robust Product

Design: Using Taguchi Methods in Technology and Product Development, Addison-

Wesley Publishing Company, Reading, MA.

Gardner T P (1992), ‘Investigation of the effects of engine design parameters on diesel

combustion and emissions using Taguchi methods’, SAE paper 920116.

Goh T N (1994), ‘Taguchi methods in practice: an analysis of Hoh’s paradox’, Quality

and Reliability Engineering, 10(5), 417–421.

He Y and Rutland C (2004), ‘Application of articial neural networks in engine modelling’,

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294 Diesel engine system design

Hunter C E, Gardner T P and Zakrajsek C E (1990), ‘Simultaneous optimization of diesel

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‘Robust optimization of an automobile valvetrain using a multi-objective genetic

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Technical Conference, Chicago, IL, September 2–6.

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study of manufacturing variation effects on diesel injector design with emphasis on

emissions’, SAE paper 2004-01-1560.

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SAE paper 2004-01-0038.

Mallamo F, Badami M and Millo (2004), ‘Application of the design of experiments

and objective functions for the optimization of multiple injection strategies for low

emissions in CR diesel engines’, SAE paper 2004-01-0123.

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Product Optimization Using Designed Experiments, 2nd edn, John Wiley & Sons,

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trains’, SAE paper 2001-01-0668.

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SAE paper 961907.

Shayler P J, Dow P I, Hayden D J and Horn G (2000), ‘Using neural networks in the

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Publishing, Suffolk, pp. 145–161.

Siddall J N (1982), Optimal Engineering Design: Principles and Applications, Marcel

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Whiter Plains, NY.

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emission reduction of heavy duty diesel engine’, SAE paper 2005-01-1099.

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295Optimization techniques in diesel engine system design

economy investigation on a small DI diesel using Taguchi methods’, SAE paper

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in the design of engine components’, SAE paper 2008-01-0219.

3.5.2 References and bibliography on probability, robust

design, and reliability-based design optimization

Catania A E, d’Ambrosio S, Guenna G M, Petrolo D, Pilo L and Strazzullo L (2007),

‘New modeling for reliable evaluation of parameter variability effects on vehicle fuel

consumption’, SAE paper 2007-01-0328.

Chan K Y, Kokkolaras M, Papalambros P, Skerlos S J and Mourelatoes Z (2004),

‘Propagation of uncertainty in optimal design of multilevel systems: piston-ring/

cylinder-liner case study’, SAE paper 2004-01-1559.

Courteille E, Mortier F, Leotoing L and Ragneau E (2005), ‘Multi-objective robust design

optimization of an engine mounting system’, SAE paper 2005-01-2412.

Daniels C and Miazgowicz K (2007), ‘Incorporating design variation into a 1-D analytical

model of a 4.6L-4V Ford engine for improving performance projections’, SAE paper

2007-01-4098.

Dave A and Hampson G J (2003), ‘Robust engine design using engine simulations’,

SAE paper 2003-01-0371.

Dinsmore M L and Unglenieks R (2005), ‘Acoustical optimization using quasi-Monte

Carlo methods and SEA modeling’, SAE paper 2005-01-2431.

Dodson B and Schwab H (2006), Accelerated Testing: A Practitioner’s Guide to Accelerated

and Reliability Testing, SAE International, Warrendale, PA.

Donders S, d’Ippolito R, Auweraer H V, Hack M, Tzannetakis N, Farkas L and Desmet

W (2007), ‘Uncertainty-based design in automotive and aerospace engineering’, SAE

paper 2007-01-0355.

Ejakov M A, Yeager D A and Kayupov M (2003), ‘Reliability and robustness analysis

of engine ring-pack performance’, SAE paper 2003-01-1221.

Evans M, Hastings N and Peacock B (2000), Statistical Distributions, 3rd edn, John

Wiley & Sons, New York.

Farizal F and Nikolaidis E (2007), ‘Assessment of imprecise reliability using efcient

probabilistic reanalysis’, SAE paper 2007-01-0552.

Fowlkes W Y and Creveling C M (1995), Engineering Methods for Robust Product

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