EVS28 KINTEX, Korea, May 3-6, 25 Pattern Prediction Model for Hybrid Electric Buses Based on Real-World Data Jing Wang, Yong Huang, Haiming Xie, Guangyu Tian * State Key laboratory of Automotive Safety and Energy, Department of Automotive Engineering Tsinghua University, Beijing 84, P. R. China, wang.j.insist@gmail.com Abstract The recognition and prediction of driving pattern is a prerequisite to minimize fuel consumption for plug-in hybrid electric buses with online adaptive energy management strategies. In this work, we present a methodology to develop a driving pattern prediction model from state-of-the-art technologies of cluster, evaluation, and Markov prediction based on the real-world driving speed-time data of a plug-in hybrid electric bus on a fixed route throughout one month. Firstly, we extract the effective driving trips from a large number of irregular data. And by Principal Component Analysis (PCA) for pre-selected 4 feature variables, we select time percent of idling, average velocity and average running velocity composing the optimal feature vectors to partition the driving trips into three significantly different classification with k-means cluster method. The time percent of idling(pti) of the resulted classification are respectively.49,.68 and.832,and the corresponding average velocity are respectively 7.52km/h,4.5km/h and 3.84km/h, and the corresponding average running velocity are respectively 2.6km/h,6.37km/h and 34.28km/h. Secondly, we segment the driving trips into driving snippets between two successive specific idling and also use PCA to get the optimal feature vectors composed by time percent of acceleration, time percent of deceleration and time percent of cruising to cluster the driving snippets into three clusters. Thirdly, we calculate the occurring probabilities of each driving snippets occurring in a specific class of driving trip and build the Markov prediction model of real-world driving cycle. Finally, we use the Markov model to reconstruct the driving cycle. And the smaller error of feature vectors between the reconstructed driving cycle and real-world driving cycle proves the effectiveness of the resulted Markov model. Keywords: Feature extraction, Principal Component Analysis, k-means cluster, Markov model, driving cycle construction Introduction For hybrid buses, in order to fully utilize their advantages of better fuel economy and less emissions, adaptive energy management strategies are designed to assign the output power of engine and battery online[,2,3]. Limited by the hardware conditions of vehicle controllers, the control parameters in such energy management strategies are usually optimized offline and then applied to online control with driving pattern prediction. The more the control parameters matching with the current driving condition, the better the control results, i.e. less fuel consumption and exhaust emission. EVS28 International Electric Vehicle Symposium and Exhibition
In China, European Emission Standard is employed to estimate the engine exhaust emissions of urban vehicles at present. The test cycle, which derived from typical driving conditions in EU or USA, doesn t represent the urban driving cycle in China quite well. Thus, it is necessary to reconstruct a driving cycle representing the real-world driving pattern for offline parameter optimizations, and to build a driving pattern prediction model for online implementation. pattern is a comprehensive description of the road environment and the state of buses. According to the objective of vehicle control, appropriative parameters should be chosen to characterize the driving pattern and further to realize the driving pattern predictive. Ericsson, E [4], used 62 independent parameters which have main effect on fuel consumption and emission to describe 9,23 driving patterns collected in real traffic. And then used factor analysis to reduce the initial 62 parameters to 6 independent driving pattern factors. Murphey, Y [5] extracted 4 parameters from the vehicle speed profile to predict road types by Neural Network (NN), which was trained by standard facility specific driving cycles, such as Freeway LOS, Arterials LOS, and Local Roadways and so on, and applied optimal control parameters which were calculated offline by each standard facility specific driving cycle to the predicted road type. The simulation results displayed this work got 2% fuel saving over the uncontrolled model in test driving cycle, which is also some standard driving cycles. Jeon,S [6] selected 24 parameters related to fuel consumption and emissions to characterize a driving pattern, and used one existing real-word driving cycle and five standard driving cycles as Representative Patterns (RDP) representing general driving patterns to calculate the optimal control parameters by Dynamic Program offline. Then they applied a multi-mode control online by switching the control parameters in each RDP. Won, J [7] primarily selected 4 of the 62 parameters in [5] and then added 7 new parameters for driving pattern recognition. The standard driving cycle also were used to obtain the fuzzy control rules. Above methods all realized the important of the consistency between the control strategies and driving pattern, however, in above research, driving cycles used to obtain offline optimal control parameters were mainly standard driving cycles. However, for real-word driving cycle, the effectiveness of the control parameters in above methods is doubtful and need to be further examined. In this paper, firstly, the speed and accelerate frequency distribution of real-world driving data are analyzed. Secondly, two times of cluster analysis are applied to real-world driving data with optimal feature vector, which is composed of the statistics variables selected by Principal Component Analysis (PCA) from 4 statistics variables related to control goal, i.e. fuel consumption. And real-world driving data are clustered into 3 classes of driving trips and 3 classes of driving snippets. Thirdly, the transition matrix of driving trips and the probability distribution of driving snippets in each class of driving trips are calculated and a Markov driving pattern predictive model are built. Finally, a driving cycle is reconstructed to validate the Markov driving pattern predictive model. 2 Real-world Data Initial Analysis With the help of on-board remote monitoring equipment, real-world driving data of three electric buses during one month were collected, including speed, position, and the state of key components. Daily mileage of every bus is about 5km, and the route is shown in Fig. First, the buses set out from Point A to Point B, then they run four times back and forth through multiple sites between Point B and Point C, and finally return to Point A from Point B. Fig2 displays a typical speed sequence of this real-world data. It can be seen that there are some similar micro-sequence, which is in conformity with the real situation. Figure : The daily route of the hybrid buses EVS28 International Electric Vehicle Symposium and Exhibition 2
ua(km/h) 5 4 3 2.4.6.8.2.4.6.8 2 t(s) x 5 Figure 2: Typical speed sequence of real-world data In order to intuitively learn the characteristics of real-world driving cycle, Fig3 shows the comparison of Speed Accelerate Frequency Distribution (SAFD) between real-word data and 3 representative standard urban driving cycles. From the SAFD of real-world driving cycle, it is obvious that the speed and accelerate are small, which belongs to the category of urban cycle to some extent. However, in Fig3, it can be seen that there are significant difference between SAFD of real-world driving cycle and other standard urban driving cycles. Thus, it is not appropriate to apply standard driving cycle to calculate the optimal control parameters of adaptive energy management strategies offline for the buses running on the real-world route. 3 Statistical Analysis of Realworld Cycle The aim of statistical analysis is to find an appropriate method to segment real-word driving cycles and cluster the partitioned pieces with optimal feature variables, laying the foundation of building Markov model of real-world driving cycle. Four types of method to segment the driving cycle is in detail described in [8]. In this paper, the similar method segment in [9] is adopted. Fig 4 shows the main architecture of this section. Given real-world driving cycle consisting of several driving trips, which are defined as the speed sequence between two successive stops, firstly, real-word driving cycle are divided into 47 driving trips. Then Principle Component Analysis is applied to select the optimal statistics variables from 4 pre-selected statistics variables as feature variables to characterize and cluster the driving trips. Next, the idle time in each driving trip is calculated and an optimal threshold of idle time is determined, which used to segment each driving trip into driving snippets. And the similar method is applied to classify the driving snippets into three distinct classes. RealWord ChinaCity.5.4.3.2. Frequency -.25 -.25.75.75 a(m/s 2 ) 5 25 85 5 65 45 ua(km/h).5.4.3.2. Frequency -.25 -.25.75.75 a(m/s 2 ) 5 25 85 5 65 45 ua(km/h) NEDC FTP.5.4.3.2. Frequency -.25 -.25.75.75 a(m/s 2 ) 5 25 85 5 65 45 ua(km/h).5.4.3.2. Frequency -.25 -.25.75.75 a(m/s 2 ) 5 25 85 5 65 45 ua(km/h) Fig 3 SAFD of real-word driving cycle and standard driving cycles EVS28 International Electric Vehicle Symposium and Exhibition 3
Collected real-world driving data driving trip between two successive stations Principal component analysis and Cluster of driving trips stores statistics variables of each driving trip and each column stands for one statistics variable. Table : Statistics variables of driving trips Name ave.ua ave.run.ua max.ua max.acc Description Average value of speed sequence Average value of speed sequence without idle Maximum speed Maximum acceleration Three typical classes of driving trips max.dec ave.acc Maximum deceleration Average value of acceleration Idletime analysis of driving trips driving snippets between two successive specific stops Principal component analysis and Cluster of driving snippets driving snippets between two successive specific idles Three typical classes of driving snippets Fig 4 Architecture of statistics analysis of real-world driving cycle 3. Trips Cluster 3.. Statistics variables In order to find the optimal statistics variables which can best characterize the driving trips, considering the goal of adaptive energy management strategies, 4 statistics variables related to fuel consumption are pre-selected. The pre-selected statistics variables are listed and described in Table. And the value of 4 statistics variables for 47 driving trips are calculated to form the driving trip database, in which each row ave.dec RMS.a PKE PTA PTD PTI Ave. idling Average value of deceleration Root mean square of acceleration For every accelerate process, PKE = (ua end ua start ) /s percentage of cycle time for acceleration percentage of cycle time for deceleration percentage of cycle time for cruising percentage of cycle time for idling stop number of idling per kilometer 3..2 Principal component analysis PCA is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components, which keep as much of the variability in the original observations data as possible. Because 4 statistics variables are in different units, the normalization is applied before PCA. In this paper, statistics variables are normalized with Equation (). x = x x min () x max x min Where x are column vectors of driving trip database, and x min and x max are respectively minimum and maximum element of x. Fig5 display the results of PCA for driving trips. In Fig5 (a), all the driving trips are irregularly distributed on the plane composed by the first and EVS28 International Electric Vehicle Symposium and Exhibition 4
the second principle component. It can be seen that there is not distinct clusters. The reason possibly is that the number of statistics variables, being of no great importance on clustering, in 4 pre-selected statistics variables is large so as to cover the statistics variables playing the key role on clustering. Considering the variance of statistics variables with top 3 load coefficient in first principle component account a larger proportion in the whole variance, they were selected to implement the cluster. 3..3 Cluster of driving trips According to Fig5 (b), PTI, ave.ua and ave.run.ua are selected as feature variables to form the optimal feature vector to character the driving trips. Then K-means cluster method is employed to realize the classification, using Euclidean distance between the feature vectors of driving trips to evaluate their dissimilarity. Fig6 (a) shows the result of driving trips clustering with the optimal feature vector. There are distinct 3 clusters, which respectively has 34, 93and 2 samples in the space composed by PTI, ave.ua, and ave.run.ua. And the within-distance and between-distance of 3 driving trip clusters are shown in Table2. Where, the within-distance of the cluster is the average Euclidean distance of feature vectors for all the driving trips in this driving trip cluster, as shown in Equation (2)and (3),the between-distance is the Euclidean distance of feature vectors of two cluster centers. Obviously, within-distance is smaller than between-distance. D i = N i m=,n=,m n d m,n N i i =,2,3 (2) d m,n = k j= (x mj x nj ) 2 (3) Where, D i is the within-distance of driving trip cluster i. d m,n is the Euclidean distance of feature vectors for two driving trips in driving trip cluster i. In Equation (3), x mj is the feature variables j in the feature vector of driving trip m. The silhouette value of each driving trip cluster is shown in Fig6 (b), and the more close to of the silhouette value means the better result of the cluster while the negative silhouette value means a not appropriate cluster. In Fig6 (b), it can be seen the cluster and cluster3 is perfect classes with most of silhouette value close to, and only a few driving trips has lower silhouette value in cluster2, but there is no negative silhouette value. Fig6 (c) and Table3 evaluate the clustering result of driving trips from another perspective. Fig6 (c) graphically depicts the degree of dispersion of samples in 3 resulted clusters and the mean of feature variables of 3 resulted clusters respectively displayed in Table3. (a) Distribution of the driving trips with PCA (b) Load coefficient of each variables in the first principle component (a) Load 2nd Principal Component.6.5.4.3.2. -. -.2 ave.run.ua 6 4 2 4.3.2. -. -.2 -.3 -.4 - -.5.5 st Principal Component The First Principal Component max.accmax.decave.acc ave.dec RMS.a PKE PTA PTD PTI Ave.idlingmax.ua ave.uaave.run.ua Feature Variable Fig 5 Results of PCA for driving trips 2 ave.ua Distribution of the driving trips in the space constructed by selected feature variables Fig 6 Cluster results of driving trips (to be continued in next page).5 EVS28 International Electric Vehicle Symposium and Exhibition 5
Cluster 2 3.2.4.6.8 Silhouette Value (b) Silhouette Value of driving trips clusters.8.8.8.6.4 ave.ua.6.4 ave.run.ua.6.4.2.2.2 3.2 Snippets Cluster The driving trips can be regard as the series of several driving snippets which are defined as the speed sequence between two successive specific idling. Considering the traffic condition, the idling time is different with different time and different trips. By analyzing of the idling time for all driving trips, the threshold of idling time is set to 2s to be used to segment each driving trip into driving snippets. Finally, 777 driving snippets is produced to form the driving snippets database. The similar method as the cluster of driving trips is employed to cluster the driving snippets. By PCA, PTA, PTD, are selected as the feature variables to form the optimal feature vectors to cluster the driving snippets into 3 classes, as Fig 7(a) shown. Fig 7(b) and Fig7(c) shows there are some driving snippets with an inappropriate cluster, and some samples are a little far from the cluster center, but the number of these abnormal samples is small and in the allowable range. The distance of driving snippets clusters and mean feature variables are respectively displayed in Table 4 and Table5. 2 3 2 3 2 3.9.8 (c) Boxplot of driving trips clusters Fig 6 Cluster results of driving trips.7.6.5.4.3 Table 2 Distance and sample number of driving trips cluster Between Distance Within Distance samples number Cluster Cluster2 Cluster3.7.2.7.59.2.59.22.9.224 34 93 2 Table 3 Mean feature variables of driving trips cluster ave.ua ave.run.ua Cluster.49 4.78 6.565 Cluster2.68 7.295 2.953 Cluster3.832 3.28 32.58.2..2.3 (a) Distribution of the driving snippets in the space constructed by selected feature variables Cluster 2 3 PTA (b) Silhouette Value of driving snippets clusters.4 Fig 7 Cluster results of driving snippets (to be continued in next page)..5 Silhouette Value.2.3 PTD EVS28 International Electric Vehicle Symposium and Exhibition 6
PTA (c) Boxplot of driving snippets clusters Fig 7 Cluster results of driving snippets Table 4 Distance and sample number of driving snippets cluster Between Distance Within Distance samples number.8.6.4.2 2 3 PTD Cluster Cluster2 Cluster3.359.496.359.332.496.332.36.23.23 2 333 324 Table 5 Mean feature variables of driving snippets cluster PTA PTD Cluster.24.26.438 Cluster2.278.27.736 Cluster3.93.42.82 4 Markov model.8.6.4.2 2 3 4. Transition Matrix Based on the results of driving trips cluster and driving snippets. The transition probability of driving trips and the frequency of each type of driving snippets in each driving trips are calculated. Table 6 shows the transition probability matrix of driving trips, in which the sum of each row is. The frequency probability matrix of different driving snippets in each driving trips clusters is displayed in Table 7, in which the sum of each row is also. For Hidden Markov Model (HMM), the state which is a Markov process is not directly visible, but the output, defined as emissions, is dependent on the state and visible. Each state has a probability distribution over the emissions by a.8.6.4.2 2 3 general stochastic process. Therefore, the emissions sequence generated by an HMM gives some information about the sequence of states and the model []. For the online adaptive energy management strategies of plug-in hybrid electric buses, the optimal control parameters should be switched with different classes of driving trips rather than driving snippets, because if the objective distance is too short, the calculated optimal control will be electric running to get minimum fuel consumption, which is not available for the buses with a long route. Thus, the class of the current driving trip is desired to be known during the buses running. However, it is difficult to directly and accurately predict the long driving trip online, but the driving snippets with shorter distance are relatively easy to obtain. Table 6 Transition probability matrix of driving trips cluster cluster2 cluster3 trip cluster trip cluster2 trip cluster3.23.538.23.22.7.88.444.278.278 Table 7 Transition probability matrix of driving trips cluster cluster2 cluster3 snippet cluster snippet cluster2 snippet cluster3.58.24.72.335.295.37.333.468.99 In this paper, assuming the transition between different classes of driving trips in a fixed route is a Markov process, the process of driving pattern predicting is abstracted as Hidden Markov Model (HMM). Based on above analysis, driving trips are regarded as the state in HMM, and driving snippets are regarded as the emissions of HMM. The transition matrix of driving trips are state transition matrix and the probability distribution of driving snippets in each driving trips forms emissions matrix. While operating online, the historical driving data are segmented into several driving snippets and classified into right driving snippets clusters by Euclidean distance of feature vectors to EVS28 International Electric Vehicle Symposium and Exhibition 7
obtain the current emissions sequence. Then based on HMM and emissions sequence, the current probable state will be calculated. 4.2 Reconstruction In order to validate the accuracy of HMM, a driving cycle is reconstructed, as shown in Fig8.The evaluation function is defined as Equation (4) N i= e i (4) E = Where, e i is the error of a selected statistics variable, listed in Table, between reconstructed driving cycle and real-world driving cycle. E is the sum of errors for all selected statistics variables. The process of reconstruction is iterated with 5 times and the reconstructed driving cycle with minimum value of evaluation function is regard as the final determined driving cycle. Fig 8 shows the final reconstructed driving cycle,whose evaluation function value is 9.. ua/km/h 5 4 3 2 5 5 2 25 t/s Fig 8 Reconstructed driving cycle based on HMM 5 Conclusion In this paper, statistical analysis is implemented for real-word driving data of 3 hybrid electric buses with a fixed-route. The realworld driving cycle is divided into driving trips by two successive stops and then further segmented into driving snippets by two successive specific idling. By PCA, the optimal statistics variables are selected to group the driving trips and driving snippets into 3 classes respectively. Finally, based on the transition matrix between driving trips and the frequency of driving snippets in each driving trips, the HMM of driving cycle is built,which can be applied to realize the driving pattern recognition online, and a driving cycle is reconstructed to validate the HMM. The result shows that the error between the reconstructed real-world driving cycle and real-word driving cycle is 9.. 6 Acknowledgment This work is supported by the National Basic Research Program of China, The Energy Consumption and Control Strategy Research of Electric Powertrain for Distributed Drive Electric Vehicles. References [] Gu, B.O. and G. Rizzoni. An adaptive algorithm for hybrid electric vehicle energy management based on driving pattern recognition. ASME 26 International Mechanical Engineering Congress and Exposition. 26: American Society of Mechanical Engineers. [2] Lee, T. and Z. Filipi, Real-World Pattern Recognition for Adaptive HEV Supervisory Control: Based on Representative Cycles in Midwestern US. 22, SAE International. [3] Musardo, C., et al., A-ECMS: An adaptive algorithm for hybrid electric vehicle energy management. European Journal of Control, 25. (4): p. 59--524. [4] Ericsson, E. Independent driving pattern factors and their influence on fuel-use and exhaust emission factors. Transportation Res. Part D 6, 325-34,2. [5] Murphey, Y., et al., Intelligent Hybrid Vehicle Power Control-Part II: Online Intelligent Energy Management. 23 [6] Jeon, S., et al., Multi-mode driving control of a parallel hybrid electric vehicle using driving pattern recognition. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 22. 24(): p. 4-49 [7] Won, J. and R. Langari, Intelligent energy management agent for a parallel hybrid vehicle-part II: torque distribution, charge sustenance strategies, and performance results. Vehicular Technology, IEEE Transactions on, 25. 54(3): p. 935 953 [8] Dai, Z., Niemeier, D., Eisinger, D., 28. Cycles: a New Cycle-building Method that Better Represents Real-world Emissions. UC Davis-Caltrans Air Quality Project. University of California, Davis. [9] Andre, M., Hickman, J., Hassel, D., and Joumard, R. (995). " cycles for emission measurements under European conditions." SAE Technical Paper Series, the Engineering Society for Advanced Mobility, Detroit, Michigan. [] Rabiner, L.R., 989. A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE,77(2):257-286. EVS28 International Electric Vehicle Symposium and Exhibition 8
Authors Jing Wang, received B.S. degree in China Agricultural University in 22, and is currently a graduate student in Department of Automotive Engineering of Tsinghua University. My main research field is online optimal energy management for hybrid electric bus based on driving pattern recognition. EVS28 International Electric Vehicle Symposium and Exhibition 9