# Development of Driving Cycle Construction for Hybrid Electric Bus: A Case Study in Zhengzhou, China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The HEB Original Driving Data Acquisition

#### 2.1. The Selection of Test Route and Test HEB

#### 2.1.1. Test Route Selection

- Hybrid electric bus is the only choice to drive on the test route.
- The test route should include both traditional and rapid bus routes.Bus rapid transit (BRT) is a new type of public transport system running between the railway and traditional bus transportation. BRT uses the special bus route to achieve rail transit mode operation, and it has been applied widely in China. The driving states of buses in the BRT routes are totally different from those in the traditional bus routes. Therefore, the construction of an urban driving cycle which fuses traditional bus route and rapid bus route is consistent with the actual operation situation of Chinese urban buses.
- The selected bus route should cover congested and fluent urban regions.

#### 2.1.2. Test Bus Selection

#### 2.2. The Driving Data Acquisition System

^{2}1σ, linearity is 0.01%, and the total range is 100 m/s

^{2}.

#### 2.2.1. Velocity and Acceleration Measurement

#### 2.2.2. Road Slope Estimation

- Primarily, eliminate slope calculated values with low velocity to avoid the denominator of Equation (1) being close to 0.
- Carry out filtering. If the calculated slope values are higher than 9% [25], then replace them with those of the previous sampling time.
- Perform average filtering against the processed slope values to smooth out the sawtooth signals.

## 3. Original Data Preprocessing

#### 3.1. Velocity Fragment Division

#### 3.1.1. Velocity Threshold Determination

#### 3.1.2. Acceleration Threshold Determination

^{2}), which indicates that the HEB drives at a uniform velocity when the acceleration is in the interval of (−0.1, 0.1). Considering that the road bump may magnify the measurement error of acceleration, the selection value of final acceleration threshold can approximately rise to 0.15 m/s

^{2}.

#### 3.1.3. Basis of Velocity Fragment Division

#### 3.2. Fragement State Cluster Distribution

#### 3.2.1. Calculation of Required Power and Nominal Velocity

_{0}(a > 0.15) denotes the required power of acceleration fragment when bus acceleration a > 0.15 m/s

^{2}, P

_{0}(a ≤ 0.15) represents the required power of non-acceleration fragment when a ≤ 0.15 m/s

^{2}. u

_{a}is the bus velocity, i is the road slope, G is the bus gravity, f is the rolling resistance coefficient, C

_{D}is the drag coefficient, A is the bus windward area, and η

_{T}means the bus powertrain mechanical efficiency.

^{2},

^{2},

#### 3.2.2. State Cluster Distribution

#### 3.3. Calculation of the Markov Transfer Matrix

_{ij}(n) denotes the one step transfer probability at moment n.

_{ij}is the time of velocity fragment transferring from state i at time t − 1 to state j at time t.

#### 3.4. The Statistical Anlysis of Original Data

#### 3.4.1. Characteristic Parameter Matrix of Original Data

_{0}is then constructed to represent the original data. The PM (performance measure) value is the differences in characteristic parameters between the driving cycle and original data, which is normalized and used to represent the differentiating degree.

#### 3.4.2. Calculation of PM Value

- Count the characteristic parameters of driving cycle candidates n and construct the n × 16 matrix M.
- Obtain the absolute differentiating value matrix pm through each row of matrix M minus the original characteristic M
_{0}:$$pm=\left|{M}_{\left(n\times 16\right)}-{\left\{\begin{array}{c}1\\ 1\\ \vdots \\ 1\end{array}\right\}}_{\left(n\times 1\right)}\times {M}_{0\left(1\times 16\right)}\right|$$ - Normalize pm. Normalization is necessary for totally different parameter ranges, which can be deduced as$$P{M}_{\left(k,i\right)}=\frac{p{m}_{\left(k,i\right)}-p{m}_{i\mathrm{min}}}{p{m}_{i\mathrm{max}}-p{m}_{i\mathrm{min}}}\hspace{1em}\hspace{1em}i\in \left(1,16\right),\hspace{1em}\hspace{1em}k\in \left(1,n\right)$$
_{i}_{max}is the maximum value of the matrix pm’s ith column, while pm_{i}_{min}is the minimum one. - Sum the elements in the kth row in the matrix PM
_{(k,i)}to obtain the PM value of the driving cycle.

#### 3.4.3. Sufficient Proof of the Original Data

## 4. Driving Cycle Construction

#### 4.1. Construction of Start Part

#### 4.2. Construction of Middle Part

- Confirm the current state cluster and the transfer probability, which are determined according to the Markov transfer matrix T.$$P\left(X\left(n\right)=j|X\left(n-1\right)=i\right)={P}_{ij}$$
- Generate a random number r in the interval of (0, 1), if r meets the in-equation as follows:$$\sum _{j=0}^{q-1}{P}_{ij}}<r\le {\displaystyle \sum _{j=0}^{q}{P}_{ij}}\hspace{1em}\hspace{1em}(q\le 7)$$
- Determine the velocity fragments whose velocity differences in current and next state clusters are below 0.5 km/h. The one which has the minimum velocity difference will be the next determined velocity fragment.
- The sampling points which are used in the start part construction will not be used in the middle part construction, and 10 middle part candidates are constructed for optimal selection.

#### 4.3. Construction of End Part

- The velocity of the sampling points that are 10 s prior to the checkpoint is above velocity threshold 0.7 km/h.
- The velocity sampling points which are 5 s later than the checkpoint are below the velocity threshold 0.7 km/h.
- If both the above conditions are met, set the checkpoint at the time t, then the sampling points in the time interval of (t − 114, t + 5) will be chosen as the end part candidates.
- Check all sampling points in the first 60 s of every end part candidate, determine 10 whose velocities in sampling points are closest to the terminal velocity of the constructed middle part, and then set these points as the start times of the 10 end part candidates.

#### 4.4. Construction of Driving Cycle

## 5. Validation of ZZUDC as a Driving Cycle

#### 5.1. Comparison between the Driving Cycles Based on Markov and Traditional Micro-Trip

#### 5.2. Comparison between ZZUDC and Other International Cycles

#### 5.2.1. Dynamic Programming

#### 5.2.2. Comparison between the Statistical Characters of Various Driving Cycles

#### 5.3. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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State 1 | State 2 | State 3 | State 4 | State 5 | State 6 | State 7 | Total | |
---|---|---|---|---|---|---|---|---|

State 1 | 7430 | 1878 | 508 | 167 | 14 | 0 | 0 | 9997 |

Probability | 0.7432 | 0.1879 | 0.0508 | 0.0167 | 0.0014 | 0 | 0 | 1 |

… | ||||||||

Probability |

**Figure 9.**Comparison of VAPDs: (

**a**) VAPD of the original data. (

**b**) VAPD of the constructed driving cycle.

**Figure 11.**Normalization results: (

**a**) normalizations of 8 cycles in 15 statistical items; (

**b**) normalizations of ZZUDC and MANHATAN; (

**c**) normalizations of ZZUDC and WVUCITY.

Route | B17 | 906 |
---|---|---|

Single transit operation distance | 15 km | 21 km |

Bus stops | 27 | 36 |

Single transit operation time | 2.5–3 h | 3.5–4 h |

Test acquisition time | 7:00–9:00; 10:00–12:00; 16:00–18:00 | 7:00–11:00; 14:00–18:00 |

Parameters | Values | Parameters | Values |
---|---|---|---|

Length | 12.0 m | Engine displacement | 6494 mL |

Width | 2.55 m | Engine rated power | 155/2500 kW/rpm |

Height | 3.05 m | Traction motor rated power | 95/1800 kW/rpm |

Wheel base | 6.10 m | Maximum velocity | 85 km/h |

Outfit quality | 12,400 kg | Capacity of power battery packs | 72 Ah |

Velocity (km/h) | 0–0.4 | 0.4–0.7 | 0.7–1 | 1–1.5 | 1.5–2 | 2–2.5 | 2.5–3 | 3–3.5 | 3.5–4 |

Probability Distribution (%) | 50.01 | 17.32 | 9.36 | 7.85 | 4.70 | 3.36 | 2.80 | 2.42 | 2.20 |

Acceleration Absolute Value | 0–0.05 | 0.05–0.1 | 0.1–0.15 | 0.15–0.2 | 0.2–0.25 | 0.25–0.3 | 0.3–0.35 | >0.35 |

Probability Distribution (%) | 82.09 | 9.92 | 2.59 | 1.23 | 0.75 | 0.60 | 0.49 | 2.33 |

State 1 | State 2 | State 3 | State 4 | State 5 | State 6 | State 7 | Total | |
---|---|---|---|---|---|---|---|---|

State 1 | 7430 | 1878 | 508 | 167 | 14 | 0 | 0 | 9997 |

Probability | 0.7432 | 0.1879 | 0.0508 | 0.0167 | 0.0014 | 0 | 0 | 1 |

… | ||||||||

Probability |

No. | Characteristic Parameters | Statistic | No. | Characteristic Parameters | Statistic |
---|---|---|---|---|---|

1 | Proportion of stop time | 24.09% | 9 | Maximum acceleration | 4.507 |

2 | Proportion of uniform time | 19.91% | 10 | Acceleration standard deviation | 0.5944 |

3 | Proportion of acceleration time | 30.31% | 11 | Minimum slope | −4.59° |

4 | Proportion of deceleration time | 25.69% | 12 | Maximum slope | 5.61° |

5 | Velocity standard deviation | 13.67 | 13 | Average slope | 0.54° |

6 | Maximum velocity | 53.762 | 14 | Minimum road power | −32.6027 |

7 | Average velocity | 14.8962 | 15 | Maximum road power | 627.1849 |

8 | Minimum acceleration | −5.399 | 16 | Average road power | 24.7528 |

PM Values Sorted by Size | PM Values of Candidate Start Parts | PM Values of Candidate Middle Parts | PM Values of Candidate End Parts |
---|---|---|---|

1 | 2.510540671 | 4.739681266 | 2.501163991 |

2 | 2.569868781 | 7.319837123 | 2.737829385 |

3 | 2.628233751 | 8.021323306 | 3.613194073 |

4 | 2.653348204 | 8.472976857 | 4.692183328 |

5 | 2.668761563 | 9.019943662 | 4.924311752 |

6 | 2.945562042 | 9.504009244 | 5.055707237 |

7 | 3.040904642 | 9.904238173 | 5.510211213 |

8 | 3.257100981 | 10.28213778 | 6.020786659 |

9 | 3.285076105 | 10.68241299 | 7.054115036 |

10 | 3.327682241 | 11.13303276 | 7.404858184 |

…… | |||

912 | 7.463476789 | ||

923 | 7.508530394 |

Characteristic Parameters | Original Data | Markov | Micro-Trip |
---|---|---|---|

Proportion of stop time | 24.09% | 22.93% | 32.51% |

Proportion of uniform time | 19.91% | 14.97% | 16.80% |

Proportion of acceleration time | 30.31% | 33.32% | 27.30% |

Proportion of deceleration time | 25.69% | 28.78% | 23.39% |

Velocity standard deviation | 13.67 | 13.556 | 13.742 |

Maximum velocity | 53.762 | 49.634 | 48.489 |

Average velocity | 14.896 | 14.961 | 13.688 |

Minimum acceleration | −5.399 | −5.399 | −2.777 |

Maximum acceleration | 4.507 | 4.031 | 2.459 |

Acceleration standard deviation | 0.594 | 0.700 | 0.542 |

Minimum slope | −5.154 | −3.398 | −4.888 |

Maximum slope | 5.152 | 4.789 | 4.762 |

Average slope | 0.021 | −0.233 | −0.486 |

Minimum road power | −32.602 | −32.603 | −31.314 |

Maximum road power | 308.165 | 217.185 | 137.080 |

Average road power | 24.753 | 26.871 | 21.619 |

Statistical items | ZZUDC | CTUB | LA92 | IM240 | JN1015 | UDDS | MANHATTAN | WVUCITY |
---|---|---|---|---|---|---|---|---|

Time (s) | 1184 | 1314 | 1436 | 241 | 661 | 1370 | 1090 | 1408 |

Mileage (km) | 4.919 | 5.898 | 15.797 | 3.152 | 4.164 | 11.921 | 3.324 | 5.319 |

Average acc. (m/s^{2}) | 0.459 | 0.299 | 0.699 | 0.5452 | 0.548 | 0.6375 | 0.6432 | 0.4201 |

Average dec. (m/s^{2}) | −0.512 | −0.431 | −0.787 | −0.833 | −0.604 | −0.752 | −0.836 | −0.551 |

Idling proportion (%) | 22.93 | 29.00 | 17.061 | 4.979 | 31.467 | 19.197 | 38.349 | 34.943 |

Uniform proportion (%) | 14.97 | 36.606 | 15.460 | 26.141 | 20.121 | 27.226 | 12.294 | 25.213 |

Acc. proportion (%) | 33.32 | 37.367 | 35.097 | 40.249 | 24.962 | 28.102 | 27.156 | 21.591 |

Dec. proportion (%) | 28.78 | 26.027 | 32.382 | 28.631 | 23.449 | 25.474 | 22.202 | 18.253 |

Maximum velocity (km/h) | 45.634 | 60 | 108.15 | 91.25 | 69.97 | 90.72 | 40.71 | 57.65 |

Average velocity (km/h) | 14.961 | 16.16 | 39.60 | 47.08 | 22.68 | 31.32 | 10.98 | 13.60 |

Maximum acc. (m/s^{2}) | 2.167 | 0.914 | 3.085 | 1.4752 | 0.7933 | 1.4667 | 2.0559 | 1.1433 |

Minimum dec. (m/s^{2}) | −3.292 | −1.042 | −3.934 | −1.565 | −0.833 | −1.467 | −2.503 | −3.237 |

RMS^{1} of acc. (m/s^{2}) | 0.700 | 0.333 | 0.795 | 0.705 | 0.424 | 0.621 | 0.605 | 0.380 |

Fuel consumption (L/100 km) | 20.509 | 14.985 | — | — | 17.710 | — | 21.288 | 15.419 |

Electricity consumption (kwh/100 km) | 12.772 | 9.8581 | — | — | 9.081 | — | 12.474 | 13.326 |

^{1}Root mean square.

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## Share and Cite

**MDPI and ACS Style**

Peng, J.; Jiang, J.; Ding, F.; Tan, H.
Development of Driving Cycle Construction for Hybrid Electric Bus: A Case Study in Zhengzhou, China. *Sustainability* **2020**, *12*, 7188.
https://doi.org/10.3390/su12177188

**AMA Style**

Peng J, Jiang J, Ding F, Tan H.
Development of Driving Cycle Construction for Hybrid Electric Bus: A Case Study in Zhengzhou, China. *Sustainability*. 2020; 12(17):7188.
https://doi.org/10.3390/su12177188

**Chicago/Turabian Style**

Peng, Jiankun, Jiwan Jiang, Fan Ding, and Huachun Tan.
2020. "Development of Driving Cycle Construction for Hybrid Electric Bus: A Case Study in Zhengzhou, China" *Sustainability* 12, no. 17: 7188.
https://doi.org/10.3390/su12177188