Research Papers: Design Automation

Analyzing Drive Cycles for Hybrid Electric Vehicle Simulation and Optimization

[+] Author and Article Information
Benjamin M. Geller

Department of Mechanical Engineering,
Colorado State University,
Fort Collins, CO 80523
e-mail: BMGeller@gmail.com

Thomas H. Bradley

Department of Mechanical Engineering,
Colorado State University,
Fort Collins, CO 80523

The UDDS is incorporated using the Federal Test Procedure (FTP) configuration which includes a complete UDDS (1375 s) followed by repeating the first 505 s of the UDDS.

An exception is made for the UDDS and FHDS only optimization (cycle set C = 2) where the EPA 55% UDDS and 45% FHDS fuel consumption weighting is applied instead of the equal weighting from Eq. (2).

Comparing Eqs. (9) and (10) shows that the transitional probability matrix shifts from [k1 and k] to [k and k+1], respectively as the method changes from creating the matrix based on observations to using the matrix to predict new cycles.

The UDDS is incorporated using the Federal Test Procedure (FTP) configuration which includes a complete UDDS (1375 s) followed by repeating the first 505 s of the UDDS.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 8, 2014; final manuscript received January 4, 2015; published online February 16, 2015. Assoc. Editor: Matthew B. Parkinson.

J. Mech. Des 137(4), 041401 (Apr 01, 2015) (14 pages) Paper No: MD-14-1227; doi: 10.1115/1.4029583 History: Received April 08, 2014; Revised January 04, 2015; Online February 16, 2015

System design tools including simulation and component optimization are an increasingly important component of the vehicle design process, placing more emphasis on early stages of design to reduce redesign and enable more robust design. This study focuses on the energy use and power management simulations used in vehicle design and optimization. Vehicle performance is most often evaluated in simulation, physical testing, and certification using drive cycle cases (also known as dynamometer schedules or drive schedules). In vehicle optimization studies, the information included in each drive cycle has been shown to influence the attributes of the optimized vehicle, and including more drive cycles in simulation optimizations has been shown to improve the robustness of the optimized design. This paper aims to quantitatively understand the effect of drive cycles on optimization in vehicle design and to specify drive cycles that can lead to robust vehicle design with minimal simulation. Two investigations are performed in service of this objective; investigation 1 tests how different combinations of drive cycles affect optimized vehicle performance and design variables (DV); investigation 2 evaluates the use of stochastic drive cycles for improving the robustness of vehicle designs without adding computational cost to the design and optimization process.

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Fig. 1

Frequency of drive cycle observations in simulation studies

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Fig. 2

Acceleration and velocity ranges for six common drive cycles including complete-cycle averages. Lines represent bounding points while circles represent average data values for each cycle.

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Fig. 3

Pretransmission parallel HEV

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Fig. 4

Simulation design optimization results showing optimized observations of FE (mpg) for different increasing cycle inclusions. Observations shown for designed FE over all included cycles based on the respective objective function and city/highway formulation per cycle sets.

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Fig. 5

P-value of data set comparisons for FE between optimized design sets. All values based on C/H FE comparisons. The city/highway p-values compare each cycle set with the two-cycle set, “Progressive” p-values compare between adjacent cycle sets.

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Fig. 6

Radial plot of mean FE on each cycle, separated by the number of cycles included in the optimization run

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Fig. 7

Optimized vehicle DV for each of the optimized cycle sets. Crosses represent mean values and range expresses +/−1 one standard deviation from the mean. Values are normalized to the searched design space range. P-values are relative to the two-cycle C/H optimized designs (e.g., comparison of cycle set 1&2, 2&3, 2&4, 2&5, 2&6).

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Fig. 8

Structural representation of transitional probability matrices

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Fig. 9

Convergence criteria for Markov cycles. Normalized FE versus optimization iterations (a) and cycle characteristics versus cycle duration (seconds) (b).

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Fig. 10

Box plot of FE on each drive cycle for the six-cycle set and Markov optimizations. Median, 25th and 75th‰, data range, and outliers are represented.

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Fig. 11

Overlay of engine torque and battery SOC over the UDDS for vehicles optimized over one cycle, six cycles, and using Markov cycles

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Fig. 12

Comparison of DV between Markov-cycle and six-cycle set optimized vehicles using box plots. Median, 25th and 75th‰, data range and outliers are represented.

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Fig. 13

Relative measured uncertainty in optimized designs for a variety of FE metrics compared among the six cycle sets and Markov-cycle optimized vehicles

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Fig. 14

Comparison of optimized vehicle attributes




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