Integrated optimization model of pedestrian-public transit emergency evacuation
-
摘要: 针对大型公共场所突发事件提出了运用公共交通进行紧急疏散的集成优化模型。模型将紧急疏散问题抽象为行人交通流和公共交通网络的双层优化网络, 第1层引导撤离人员从事发地点(建筑物等) 到达指定的乘车点(公交站等), 第2层优化公交车从场站出发, 途经各乘车点, 最后运输撤离人员到达安全地点。利用基于禁忌搜索的两阶段启发式算法对模型进行求解和验证。验证结果表明: 在一个有328人需要疏散的网络中, 共使用8辆公交车完成疏散。目标函数中每一项权重的变化对模型输出结果基本没有影响, 模型具有很强的鲁棒性。对比CPLEX优化软件, 启发式算法能够在1h内求解出近似最优解, 并且近似最优解与最优解的误差小于15%。模型充分考虑了撤离人员分配与公交路径优化之间的交互影响, 实现了在紧急疏散时行人交通流与公共交通网络的组织最优。Abstract: Aiming at emergent event in large-scale public, an integrated optimization model of emergency evacuation was developed based on public transit.In the model, the problem of emergency evacuation was summarized as a two-level optimization network including pedestrian traffic flow and public transit network.The first-level framework guided evacuees from accident sites (e.g.buildings) to designated pick-up points (e.g.bus stops).The second-level framework properly dispatched and routed a fleet of buses at different transit depots to the pick-up points, and transported evacuees to safe places finally.Integrated optimization model was tested and verified by using a two-stage heuristic algorithm based on tabu search.Verification result indicates that 8 buses are used for the evacuation of all 328 people in the network.The output result of integrated optimization model is not sensitive to the change of weight assignment of objective function, so the model has strong robustness.Comparing with the optimization software of CPLEX, heuristic algorithm can get near optimum solution in 1 h, and the error between near optimum solution and optimal solution is less than 15%.The interactions betweenevacuees distribution and bus route optimization are fully considered in the model.The pedestrian traffic flow and the public transit network during evacuation process are concurrently optimized.
-
Key words:
- public transit /
- emergent event /
- emergency evacuation /
- pedestrian /
- integrated optimization model /
- tabu search
-
0. Introduction
The variation range of metal pushing belt continuously variable transmission (CVT) can reach only about 5~6 because of its limit in structures, which makes it unfit for the control requirement of optimal drivability and fuel economy when engine output and the driven condition of vehicle change in a large range[1-2]. By using hydraulic torque converter at start-up and low speed, a lager range of speed ratio of CVT can be get; and the ability of less impact, big torque at low speed and good fitness to outside load helps vehicle start up steadily and have good drivability at low speed[3]. However, because of the low efficiency even on the coupling stage, torque converter should lock up when vehicle drives on normal condition for improving transmission efficiency.
Most of vehicles with torque converters determine whether to lock up or unlock by jugging the vehicle speed, which influences the using effect of torque converter on some special conditions, such as cooling machine, braking and so on[4-5]. So it is necessary to suitably set the unlocking and lock-up conditions for the improving transmission efficiency, the start-up and driving performances at low speed. In order to improve the fuel economy of vehicle under the unlocking condition of torque converter, torque converter should work in the optimal economic region with engine before lock-up according to the control damands of CVT.
1. Lock-up and unlocking
1.1 Lock-up
The conversion of torque converter from unlocking to lock-up should carry out on the condition that the work of torque converter at start-up and low speed has been completed and vehicle speed have reached a limit value, in addition to considering cooling water temperature and the speed difference between turbine and impeller[6]. Torque converter should lock up at high speed, driver avoids the continual conversion between unlocking and lock-up under complex road condition, but eusure lock-up in time on good road station (vehicle speed reaches 30 km·h-1). Torque converter should lock up when engine has warmed up and is able to bear every working condition, and the cooling water temperature is higher than the set value, 50 ℃~60 ℃. Torque converter can reduce impact and increase torque under special condition or driving intention if the speed difference between turbine and impeller is larger. It is suitable for lock-up when the speed difference between turbine and impeller lowers a set value (transmission ratio is more than 0.7), or it will cause impact.
1.2 Unlocking
The conversion of torque converter from lock-up to unlocking is because of the decrease of vehicle speed to a limit value (25 km·h-1). Decreasing vehicle speed is resulted from the driving intention because road state needs the working of torque converter for torque transmission. In addition to considering such special conditions as closing throttle to decrease the speed or the intention to decrease the speed by braking, torque converter should lock up to reduce emission and improve fuel economy.
The conversion of torque converter from lock-up to unlocking is determined by the change of vehicle speed, and the special conditions about the driving intention and working conditions are considered. The convertsion logic is shown in fig. 1.
Torque converter lock up when vehicle runs at high speed (exceed 30 km·h-1), the engine has warmed up (engine cooling water temperature exceeds 50 ℃~60 ℃) and the speed difference between turbine and impeller is little (transmission ratio exceeds 0.7). Torque converter unlock when vehicle starts up, runs under city complex road conditions at low speed (under 25 km·h-1), and the driver closes the throttle or brakes. In addition to considering the interval between vehicle speed limit values of unlocking and lock-up for torque converter, the constantly conversion of lock-up and unlocking is avoided when vehicle speed waves in small range. In fig. 1, unlocking state is continued when transiting from unlocking region to buffer area, lock-up state is conti-nued when transiting from lock-up region to buffer area.
2. Speed Ratio control
On the normal working state of torque converter, torque converter has large torque, well automatic adaptability, good shock absorption and buffering performances at start-up and low speed, so that vehicle starts up quickly and steadily and has good accelerating performance. But except the above stages, up to the lock-up region of torque converter, torque converter influences the efficiency of driveline, and the influencing degree has a direct relation with the speed ratio of torque converter[7]. In order to improve transimission efficiency of torque converter in the region, firstly, torque converter should match well with engine according to its characteristics, then, according to the common features of engine and toruqe converter, the adjustment of speed ratio can improve the fuel economy of vehicle.
2.1 Common working properties
The common work focus of engine and torque converter is the intersectant point of between torque curves and load curves, when engine has small loads (the throttle opening angles of vehicle start-up are α1~α4), and torque converter has small transmission ratios, the ratios are 0, 0.1, 0.2, and the torque of the point is maximum. It is a steady point of common work, as the equation (1) shows
ΤΤ=kiΤe (1)
Vehicle fuel economy at start-up and low speed is considered and the superposition degree between the workaround of low oil consumption of engine and the high-efficiency area of torque converter is studied, then the best economic common workingarea of engine and torque converter is confirmed (fig. 2), as the equation (2) shows
beΤ=be/ηi (2)
2.2 Speed ratio control
At start-up and low speed, the CVT ratio is largest, and the torque is furtherly improved. Because torque converter has well automatic adaptability, good shock absorption and buffering performance, vehicle can start-up quickly and steadily and has good accelerating performance at low speed.After the stages of start-up and low speed, the economy problem of engine and torque converter common work needs to be considered. Adjusting the speed ratio of CVT can make engine work in economic area and torque converter work round the highest efficiency point, thus the best economy of engine and torque converter common working can be carried out[8-9].
Studied CVT is mental pushing belt CVT, the speed ratio adjustment of CVT is carried out by the change of pulse-width modulation (PWM) driving signal for speed ratio control's proportional electromagnetic valve, and the change of the driving signal will lead to put different forces to the movable part of initiative belt wheel, so that it running radius is changed, thus CVT's speed ratio will be changed.
At different throttle opening angles, the relation between the fuel consumption rate of engine and torque converter common work and the speed radio of torque converter is expressed as
beΤ=f(ne)/f(i) (3)
By experiments, the common economic working line of engine and torque converter can be achieved, the speed ratios of torque converter are taken as abscissa, engine loads are taken as ordinate, the points of the common working lowest fuel consumption rate of engine and torque converter are labelled. According to the economic line, at different throttle opening angles, the object speed ratios of torque converter can be got. Using engine speed signal and CVT's input speed signal that have the same output speed as torque converter, the real speed ratios of torque converter can be calculated.Taking the difference value between the real speed ratio and the object speed ratio of torque converter as input, the PWM driving signal's change value of speed ratio control's proporational electromagnetic valve is calculated by PID controller and exported to carry out the ratio adjustment of CVT. By the ratio adjustment of CVT, the matching relationship between engine and torque converter-transmission-road load will be changed to make the real speed ratio of torque converter reach the object speed ratio, and to improve the fuel economy of vehicle. The ratio control process of torque converter is shown in fig. 3.
The proportion coefficient kp and differential coefficient kD of PID controller are set to less values, and the integral coefficient kI is set to bigger value, so that the overshoot can be reduced, the system's steady precision under steady condition can be improved, and the inhibiting ability to disturbance can be increased.
3. Process of lock-up control
The unlocking process of torque converter is converting mechanical transmission into hydraulic transmission. The converting process is smooth depending on the good active suitability to the external load of torque converter. The lock-up process of torque converter is converting hydraulic transmission into mechanical transmission. Although under common situation, the error between pump impeller speed and turbo speed is less, the lock-up without control will reducing the stabilization of vehicle and the useful life of lock-up clutch, especially under uncommon situation. For example, acceleration or the condition variety of road causes the huge error between pump impeller speed and turbo speed, which will bring the vibration or slippage between friction plates of lock-up clutch.
The lock-up process of torque converter is assumed as two sections, the slippage section and the quick engagement section[10]. There are two points should be considered in the slippage section, the impact degree and the friction work. In the quickly engagement section, there are not the impact degree and the friction work because the speeds of friction plates are equal. It's just making quick engagement and enhancing the transmitted torque. The engagement of lock-up clutch will be controlled according to the principles of stabilizing engine rotation and optimizing the performance of the impact and sliding friction work in the slippage section. The engagement process of lock-up clutch is also the increasing process of the clutch's positive pressure. The positive pressure increase is made by the PWM duty ratio change of high-speed on-off valve.
Engine torque is supposed to a constant in a short time, it is mainly affected by the change rate of pump impeller torque. Therefore, when the ratio is constant, it is surely affected by the change rate of the clutch's positive pressure, as the equation shows
Jednedt=dΤBdt=didtΤΤ=ΤΤf(i,dpdt) (4)
The impact degree of vehicle is defined by the following equation
j=d2vdt2=ri0icvtΙtd2ωΤdt2=ri0icvtΙtf(ωB-ωΤ,dpdt) (5)
It shows that the impact degree is surely affected by the change ratio of the pressure during lock-up when the error between pump impeller and turbo is constant.
The lock-up signal of torque converter can is measured. When the lock-up demand is satisfied, the lock-up is started, and the engagement control in slippage section begins. Whether the slippage section is over, the quick engagement start is determined through whether the error between pump impeller and turbo is in a small area (considering the measuring error of the actual speed). Firstly, according to the principle of optimizing the performance of impact and sliding friction work, the basic duty ratio is determined, and according to the principle of stabilizing engine rotation, the real-time duty ratio is modified based on the error between real engine speed measured by sensor and object engine speed determined by throttle angle. Finally, the real duty ratio is get. The control process is shown in fig. 4.
Fig. 5 shows the lock-up fuzzy controller based on the above control strategies[11]. The impact degree of vehicle and engine speed error are fuzzificated and input the controller. The impact degree of vehicle means the principle of optimizing performance of impact and sliding friction work. PWM signal is adjusted in real-time according to the change of impact degree. If the impact degree is big, the change rate of PWM signal should be reduced, on the contrary, the change rate of the PWM signal should be increased to the target value of optimizing performance of impact and sliding friction work. Engine speed error means the principle of stabilizing engine rotation. According to the error between object speed and real speed, PWM signal in real-time is adjusted. If the real speed is smaller than the object speed, the change rate of PWM signal should be reduced, on contrary, the change rate of PWM signal should be increased to the target value of stabilizing engine rotation, meanwhile, jointing well with the adjusting ratio aimed at the best work point of engine. Finally, the result of the fuzzy inference is converted into control signal (the change rate of PWM signal) of high-speed on-off valve through defuzzification.
The fuzzy controller is planar. The inputs are the error between the object speed and the real speed and the imapct degree obtained from the CVT output speed after handling. The output is the change rate of the duty ratio of high-speed on-off valve. The language values of the speed error and the impact degree are NL (negative big), NS (negative small), ZO (zero), PS (positive small) and PL (positive big). The language values of the change rate of the duty ratio are also PL, PS, ZO, NS and NL. The relations between the language values of the speed error and the change rate of the duty ratio and between the impact degree and the change rate of the duty ratio are established. And then, the fuzzy rules are made up by using product strategy.
The experiments are executed under two different lock-up states. Fig. 6 shows the engagement controls, input speeds and output speeds of lock-up clutch during accelerating slowly and quickly. In fig. 6, line 1 means the input speed (equalling to engine speed), line 2 means the output speed. Torque converter is affected obviously by the states. When the big change rate of throttle angle causes vehicle speed reaching the lock-up value, the error between pump impeller and turbo will increase, and the demanding torque transmitted by lock-up clutch will increase also. Aimed at the change of torque converter, the engagement process is adjusted by the control strategies. In fig. 6 (b), the error is bigger. In order to avoid impact, the engagement time is prolonged.The 1.92 s in fig. 6 (b) is bigger than the 1.38 s in fig. 6 (a). In order to transmit bigger torque effectively, when the slippage ends, the duty ratio is 63.2% in fig. 6 (b), it is bigger than 49.8% in fig. 6 (a). The fig. 6 shows also that when the demanding torque transmitted by lock-up clutch reaches the biggest point, for the purpose of stabilizing engine rotation, the duty ratio changes are not obvious sometime. Under the two situations, the change of object engine speed is only resulted from throttle angle change, however, it is stable, meanwhile, the change trend of the output speed is smooth. Through analyzing the experiment data, the designed controller performs excellent and it satisfies the control demands.
4. Conclusion
The rational transition between the unlocking and lock-up states of hydraulic torque converter for vehicle with CVT is beneficial to make the most of its working characteristics and improve the transmission efficiency when vehicle runs at medium or high speed, moreover, it meets the running requirements of vehicle on special conditions.The speed ratio is regulate to change the output load of the converter. The PID control strategy designed for vehicle running at low speed can achieve the optimal economy of engine and converter working together. The designed fuzzy controller with two inputs can optimize performance of impact and slipping friction work and stabilize engine speed.
Nomenclatures
ai throttle angle
T cooling water temperature
t time
TT turbo torque (N·m)
ki torque coeffient
Te engine torque (N·m)
beT common working fuel consumption rate of engine and torque converter[g· (kW·h)-1]
be fuel consumption rate of engine[g· (kW·h)-1]
ηi transmission efficency of torque converter
ne engine speed (r·min-1)
i speed ratio of torque converter
Je engine moment of inertia (kg·m2)
TB pump impeller torque (N·m)
p clutch positive pressure (N·m-2)
j impact degree of vehicle (m·s-3)
v vehicle speed (km·h-1)
r rolling radius of driving wheel (m)
i0 main speed ratio
icvt CVT speed ratio
It equivalent inertia of output axle conver-ted from vehicle inertia rigid connectedwith CVT output axle (kg·m2)
ωT turbo speed (r·min-1)
ωB pump impeller speed
-
表 1 节点和车辆信息
Table 1. Node and vehicle information
表 2 每个建筑物中需撤离人数
Table 2. Evacuee number at each building
表 3 每个乘车点的容量
Table 3. Capacity of each pick-up point
表 4 建筑物到乘车点的距离
Table 4. Distances from buildings to pick-up points
表 5 车辆网络的距离矩阵
Table 5. Distance matrix of vehicular network
表 6 分配结果
Table 6. Assignment result
表 7 每辆公交车的疏散路径和总疏散量
Table 7. Routing plan and total evacuee number of each bus
表 8 权重对总疏散量的影响
Table 8. Effect of objective weights on total evacuee numbers
表 9 不同情景的计算结果
Table 9. Calculation results of different scenarios
-
[1] 胡红, 蒋光胜, 杨孝宽, 等. 基于Link-node仿真的北京奥运应急交通疏散预案研究[J]. 北京工业大学学报, 2007, 33 (11): 1187-1192. https://www.cnki.com.cn/Article/CJFDTOTAL-BJGD200711016.htmHU Hong, JIANG Guang-sheng, YANG Xiao-kuan, et al. Study on emergency evacuation plan based on link-node simulation for Beijing Olympics[J]. Journal of Beijing University of Technology, 2007, 33 (11): 1187-1192. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-BJGD200711016.htm [2] 姜长杰, 韦献兰. TransCAD与TransModeler在港口突发特大事故应急交通疏散问题方面的研究与应用[J]. 水运工程, 2008 (6): 60-63. https://www.cnki.com.cn/Article/CJFDTOTAL-SYGC200806019.htmJIANG Chang-jie, WEI Xian-lan. Application of TransCAD and TransModeler to research on traffic evacuation for emergency events in port[J]. Port and Waterway Engineering, 2008 (6): 60-63. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-SYGC200806019.htm [3] LIU Y, CHANG G L, LAI X, et al. CAPEVACUATION: the corridor-based emergency traffic evacuation system for Washington DC[C]//Intelligent Transportation Society of America. Proceedings of the 14th World Congress on Intelligent Transportation Systems. Beijing: Intelligent Transportation Society of America, 2007: 1-8. [4] LIU Y, CHANG G L, LIU Y, et al. Corridor-based emergency evacuation system for Washington DC: system development and case study[J]. Transportation Research Record, 2008 (2041): 58-67. [5] ELMITINY N, RAMASAMY S, RADWAN E. Emergency evacuation planning and preparedness of transit facilities: traffic simulation modeling[J]. Transportation Research Record, 2007 (1992): 121-126. [6] NAGHAWI H, WOLSHON B. Performance of multi-modal evacuation traffic networks: a simulation based assessment[C]//TRB. Proceedings of the 90th Annual Meeting of Transportation Research Board. Washington DC: TRB, 2011: 1-21. [7] NAGHAWI H, WOLSHON B. Operation of multimodal transport systems during regional mass evacuations[C]//TRB. Proceedings of the 90th Annual Meeting of Transportation Research Board. Washington DC: TRB, 2011: 22-38. [8] MASTROGIANNIDOU C, BOILE M, GOLIAS M, et al. Using transit to evacuate facilities in urban areas: a microsimulation based integrated tool[C]//TRB. Proceedings of the 88th Annual Meeting of Transportation Research Board. Washington DC: TRB, 2009: 1-15. [9] PERKINS J A, DABIPI I K, HAN L D. Modeling transit issues unique to hurricane evacuations: North Carolina's small urban and rural areas[R]. Greensboro: North Carolina A & amp; amp; T State University, 2001. [10] SAYYADY F. Optimizing the use of public transit system in no-notice evacuations in urban areas[D]. Starkville: Mississippi State University, 2007. [11] SAYYADY F, EKSIOGLU S D. Optimizing the use of public transit system during no-notice evacuation of urban areas[J]. Computers and Industrial Engineering, 2010, 59 (4): 488-495. doi: 10.1016/j.cie.2010.06.001 [12] EKSIOGLU B, VURAL A V, REISMAN A. The vehicle routing problem: a taxonomic review[J]. Computers and Industrial Engineering, 2009, 57 (4): 1472-1483. doi: 10.1016/j.cie.2009.05.009 [13] MARGULIS L, CHAROSKY P, FERNANDEZ J, et al. Hurricane evacuation decision-support model for bus dispatch[C]//LACCEI. The Fourth LACCEI International Latin American and Caribbean Conference for Engineering and Technology. Mayaguez: LACCEI, 2006: 1-9. [14] HE S, ZHANG L, SONG R, et al. Optimal transit routing problem for emergency evacuations[C]//TRB. Proceedings of the 88th Annual Meeting of Transportation Research Board. Washington DC: TRB, 2009: 32-45. [15] CHEN C C, CHOU C S. Modeling and performance assessment of a transit-based evacuation plan within a contraflow simulation environment[J]. Transportation Research Record, 2009 (2091): 40-50. [16] CHAN C P. Large scale evacuation of carless people during short-and long-notice emergency[D]. Tucson: The University of Arizona, 2010. [17] 滕靖, 徐瑞华. 城市轨道交通突发事件下公交应急联动策略[J]. 铁道学报, 2010, 32 (5): 13-17. https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201005003.htmTENG Jing, XU Rui-hua. Bus dispatching strategies in urban rail emergent events[J]. Journal of the China Railway Society, 2010, 32 (5): 13-17. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TDXB201005003.htm [18] 王泽. 台风灾害下区域疏散公交集结点选址和车辆路径规划[D]. 哈尔滨: 哈尔滨工业大学, 2010.WANG Ze. Public transit assembly stations location and vehicle routing plans for regional evacuation under the typhoon disaster[D]. Harbin: Harbin Institute of Technology, 2010. (in Chinese). [19] 徐梁, 宋瑞. 自然灾害下的公交疏散路线模型[J]. 物流技术, 2011, 30 (6): 147-150, 154. https://www.cnki.com.cn/Article/CJFDTOTAL-WLJS201111046.htmXU Liang, SONG Rui. Bus evacuation route model in event of natural disaster[J]. Logistics Technology, 2011, 30 (6): 147-150, 154. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-WLJS201111046.htm [20] LIAO Fei-xiong, ARENTZE T, TIMMERMANS H. Multistate supernetworks: recent progress and prospects[J]. Journal of Traffic and Transportation Engineering: English Edition, 2014, 1 (1): 13-27. doi: 10.1016/S2095-7564(15)30085-4 [21] CHAPMAN J R, NOYCE D A. Influence of roadway geometric elements on driver behavior when overtaking bicycles on rural roads[J]. Journal of Traffic and Transportation Engineering: English Edition, 2014, 1 (1): 28-38. -