Modeling Transit Bus Fuel Consumption on the Basis of Cycle Properties

Figures & data

Figure 1. Geometric interpretation of the linear model method.

Table 1. Transit buses analyzed in this research

Bus ID	Technology	Manufacturer	Bus Type and Model Year	Engine Type and Model Year	Gross Vehicle Weight (kg)	Available Cycles
32	CNG	John Deere	Orion 2005	RG6081 2005	19,334	16
35	CNG	Cummins	Orion 2005	Cummins CG 2005	19,334	16
37	Hybrid	Allison	New Flyer 2005	Cummins ISL280 2005	18,416	16
39	Diesel	DDC	Orion 1992	DDC S50 2003	17,896	17
41	Diesel	Cummins	New Flyer 2006	Cummins ISM280 2006	18,416	17

Table 2. Average measured properties over five buses for 17 cycles used

Number	Cycle Name	Cycle ID	Velocity (mph)	Acceleration (mph/sec)	Stops/Distance (stops/mi)
1	CARB Idle Cycle	Idle	0.06	0.00	0.00
2	New York Bus Cycle	NYBus	3.54	0.25	18.71
3	Paris Cycle	PARIS	6.68	0.32	12.40
4	Manhattan Cycle	Manhattan	6.86	0.37	9.76
5	Washington Metro Transit Authority Cycle	WMATA	8.43	0.30	6.26
6	New York Composite Cycle	NY-Comp	8.75	0.15	7.21
7	Orange County Transit Authority Cycle	OCTA	12.22	0.41	4.87
8	Central Business District Cycle	CBD	13.08	0.52	6.80
9	Braunschweig Cycle	BRAUN	13.88	0.45	4.19
10	City Suburban Heavy Vehicle Cycle	CSHVC	14.02	0.27	2.29
11	Beeline Cycle	Beeline	14.03	0.43	3.73
12	European Test Cycle Urban	ETCURBAN	14.11	0.28	1.92
13	CARB Transient Cycle	TRANS	15.33	0.28	1.69
14	Urban Dynamometer Driving Schedule	UDDS	18.71	0.20	2.04
15	King County Metro Cycle	KCM	23.35	0.41	1.85
16	Arterial Cycle	ART	25.58	0.55	1.47
17	Commuter Cycle	COMM	44.37	0.18	0.17

Figure 2. Histogram of average percentage error for the prediction of CO₂ mass rate (g/sec).

Table 3. CO₂ mass rate prediction results with lowest average percent error

Bus ID	Cycle 1	Cycle 2	Cycle 3	Percent Error	Average Error (g/sec)	Max Error (g/sec)	SD Error (g/sec)	R ^2
32	Idle	Beeline	KCM	8.48	0.54	1.12	0.37	0.92
35	Idle	PARIS	WMATA	7.53	0.53	1.20	0.37	0.95
37	Idle	OCTA	KCM	8.17	0.51	1.29	0.40	0.98
39	Idle	KCM	ART	8.70	0.83	2.45	0.68	0.93
41	Idle	PARIS	KCM	8.88	0.76	2.33	0.65	0.93
Notes: Metrics used: average velocity and average acceleration.

Table 4. Fuel economy predictions with lowest average percent error

Bus ID	Cycle 1	Cycle 2	Cycle 3	Percent Error	Average Error (mpg)	Max Error (mpg)	SD Error (mpg)	R ^2
32	Idle	Manhattan	OCTA	15.89	0.67	2.61	0.67	0.77
35	Idle	BRAUN	KCM	19.73	0.70	1.57	0.58	0.60
37	Idle	OCTA	COMM	22.26	1.19	2.43	0.93	0.18
39	Idle	Manhattan	KCM	20.34	0.85	2.12	0.76	0.38
41	Idle	Manhattan	KCM	22.17	1.01	2.19	0.77	0.39
Notes: Metrics used: average velocity and average acceleration.

Figure 3. CO₂ mass rate predictions with lowest error for (a) CNG bus 32, (b) CNG bus 35, (c) hybrid bus 37, (d) diesel bus 39, and (e) diesel bus 41.

Figure 4. Frequency of a baseline cycle in predictions with average <10%.

Table 5. Baseline combinations with lower average percentage error for CO₂ (g/sec) prediction

Baseline Cycles Used	Average Percent Error					Average Percent Error	Max Absolute Error (g/sec)
	CNG 32	CNG 35	Hybrid 37	Diesel 39	Diesel 41
Idle OCTA KCM	8.61	7.78	8.17	8.75	9.26	8.51	3.95
Idle PARIS KCM	9.11	7.55	8.89	8.72	8.88	8.63	3.18
Idle OCTA COMM	8.52	7.80	8.38	9.21	9.80	8.74	2.20
Notes: Metrics used: average velocity and average acceleration.

Figure 5. Parity plot for prediction of CO₂ mass rate using idle, OCTA, and KCM as baseline cycles and velocity and acceleration as metrics.

Figure 6. CO₂ mass rate prediction errors using idle, OCTA, and KCM as baseline cycles and average velocity and average acceleration as metrics.

Figure 7. Percentage error ratios when using other metrics combinations. V = velocity, A = acceleration, Std.V = standard deviation of speed, Stops = stops per unit distance, IP = inertial power.

Table 6. CO₂ mass rate prediction results with lowest average percentage error

Bus ID	Cycle 1	Cycle 2	Cycle 3	Average Percent Error	Average Error (g/sec)	Max Absolute Error (g/sec)	SD Error (g/sec)	R ^2
32	Idle	NYBus	CBD	6.08	0.47	1.89	0.49	0.97
35	Idle	NYBus	KCM	8.99	0.77	2.55	0.63	0.94
37	Idle	NYBus	WMATA	6.56	0.46	1.23	0.41	0.98
39	Idle	PARIS	UDDS	9.55	0.94	1.85	0.45	0.95
41	Idle	NYBus	COMM	7.82	0.59	1.42	0.51	0.89
Notes: Metrics used: velocity and stops per distance.

Figure 8. Parity plot for prediction of CO₂ mass rate using idle, NYBus, and KCM as baseline cycles and velocity and stops per distance as metrics.

Figure 9. CO₂ mass rate prediction errors using idle, NYBus, and KCM as baseline cycles and average velocity and stops per distance as metrics.

Table 7. CO₂ mass rate prediction results with lowest average percentage error

Bus ID	Cycle 1	Cycle 2	Cycle 3	Cycle 4	Average Percent Error	Average Error (g/sec)	Max Absolute Error (g/sec)	SD Error (g/sec)	R ^2
32	Idle	NYBus	BRAUN	COMM	4.92	0.32	0.55	0.19	0.91
35	Idle	NYBus	WMATA	COMM	5.65	0.40	1.13	0.33	0.94
37	Idle	NYBus	PARIS	UDDS	6.97	0.48	1.23	0.42	0.98
39	Idle	NYBus	BRAUN	KCM	6.82	0.63	1.63	0.42	0.98
41	Idle	Manhattan	OCTA	UDDS	8.15	0.63	1.33	0.45	0.97
Notes: Metrics used: average velocity, average acceleration, and stops per distance.

Table 8. NO_x mass rate prediction with lowest average percentage error

Bus ID	Cycle 1	Cycle 2	Cycle 3	Average Percent Error	Average Error (g/sec)	Max Error (g/sec)	SD Error (g/sec)	R ^2
32	Idle	CSHVC	COMM	27.76	0.015	0.047	0.013	0.03
35	Idle	ETCURBAN	COMM	14.93	0.011	0.042	0.013	0.29
37	Idle	WMATA	Trans	8.01	0.004	0.017	0.005	0.97
39	Idle	KCM	COMM	10.28	0.005	0.014	0.004	0.58
41	NY-Comp	CBD	ART	10.34	0.003	0.029	0.007	0.58
Notes: Metrics used: average velocity and average acceleration.

Figure 10. Parity plot for prediction of NO_x mass rate using idle, OCTA, and KCM as baseline cycles and average velocity and average acceleration as metrics.

Figure 11. NO_x mass rate prediction errors using idle, OCTA, and KCM as baseline cycles and average velocity and average acceleration as metrics.