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电梯交通量仿真分析8

约 4384 字大约 15 分钟

coding

2025-08-05

8. 附录：关键公式、参数设置建议

8.1 电梯物理模型关键公式

8.1.1 电梯运行时间计算

电梯运行时间是仿真中最基础的物理模型，根据PDF中描述的电梯动力学，计算公式如下：

基本运行时间公式：

运行时间 = √(2×距离/加速度) + (距离-加速段-减速段)/额定速度 + √(2×距离/减速度)

详细推导：

  1. 加速段：

    • 加速距离：d_acc = v²/(2a)
    • 加速时间：t_acc = v/a

  2. 匀速段：

    • 匀速距离：d_cruise = d_total - d_acc - d_dec
    • 匀速时间：t_cruise = d_cruise/v

  3. 减速段：

    • 减速距离：d_dec = v²/(2d)
    • 减速时间：t_dec = v/d

完整公式：

如果 d_total ≤ d_acc + d_dec:
    运行时间 = 2 × √(d_total/a)
否则:
    运行时间 = t_acc + t_cruise + t_dec
             = v/a + (d_total - v²/(2a) - v²/(2d))/v + v/d

参数说明：

  • d_total：总运行距离(米)
  • v：电梯额定速度(m/s)
  • a：电梯加速度(m/s²)
  • d：电梯减速度(m/s²)

典型参数值：

  • 额定速度：1.5-4.0 m/s (办公楼常用2.5-3.0 m/s)
  • 加速度：0.8-1.2 m/s²
  • 减速度：0.8-1.2 m/s²

8.1.2 停站时间计算

根据PDF中"同一层站如上下乘客较多，受开门宽度影响会增加电梯停靠等待时间"的描述，停站时间计算公式为：

停站时间 = 开门时间 + 乘客流动时间 + 关门时间

详细公式：

开门时间 = 2.0 + (1.5 × (1.0 - 门宽/1.2))
关门时间 = 1.5 + (1.0 × (1.0 - 门宽/1.2))

乘客流动时间 = 乘客数量 × (上/下时间) × 拥挤系数
              = 乘客数量 × 1.2 × (1.0 + 0.2 × ln(1 + 乘客数量)) × (0.8 + 0.4 × (门宽/1.2))

参数说明：

  • 门宽：标准电梯门宽1.0-1.2米
  • 上/下时间：每乘客1.0-1.5秒
  • 拥挤系数：考虑乘客密度对流动速度的影响
  • 门宽影响系数：门越宽，流动越快

典型参数值：

  • 门宽：1.0米(标准客梯)
  • 基础上/下时间：1.2秒/人
  • 拥挤系数：1.0-1.8(随乘客数量增加)
  • 门宽影响系数：0.8-1.0

8.1.3 5分钟输送能力(HC)计算

根据PDF中多次提及的"handling capacity(HC)"概念，计算公式为：

5分钟输送能力(HC) = (5分钟内运送的乘客数 / 建筑总人数) × 100%

详细计算：

  1. 确定早高峰(通常是8:00-8:05)期间电梯运送的乘客总数
  2. 获取建筑总人数(所有楼层人口之和)
  3. 计算百分比：
    HC = (运送乘客数 / 建筑总人数) × 100%

设计标准：

  • 办公楼：HC通常为12-15%
  • 高层办公楼：HC可达18-20%
  • PDF中提到："The traffic intensity was 25% larger than the handling capacity(HC) of the elevator group."

交通强度：

交通强度 = 实际交通量 / HC
  • 当交通强度 > 100%时，电梯经常满载，停靠次数增多，问题复杂度增加

8.2 交通流模型关键公式

8.2.1 批次到达模型

根据PDF中"批次到达可以建模为时间非齐次泊松过程"的描述，批次到达模型公式为：

批次间到达时间：

t ~ 指数分布(λ)
其中 λ = 1/平均批次间隔

批次大小分布：

P(X = k) = p_k, 其中 k = 1,2,3,...
Σp_k = 1

PDF中描述的典型批次大小分布：

  • 早高峰：P(1)=0.3, P(2)=0.4, P(3)=0.2, P(4)=0.1
  • 午餐高峰：P(1)=0.2, P(2)=0.3, P(3)=0.3, P(4)=0.2

参数设置建议：

  • 批次概率：早高峰0.7，午餐高峰0.5，闲时0.3
  • 平均批次间隔：早高峰5秒，午餐高峰8秒，闲时15秒
  • 标准差：约为平均值的40%

8.2.2 交通模式比例

根据PDF中多次提到的三种交通模式，比例公式为：

incoming_traffic_ratio + interfloor_traffic_ratio + outgoing_traffic_ratio = 1

典型建筑类型的交通模式比例：

建筑类型时间段进楼交通楼层间交通出楼交通
办公楼早高峰0.80.20.0
办公楼午餐高峰0.20.60.2
办公楼晚高峰0.00.20.8
商场全天0.20.60.2
住宅全天0.40.20.4

参数设置建议：

  • 办公楼早高峰：进楼交通比例0.7-0.85
  • 办公楼晚高峰：出楼交通比例0.7-0.85
  • 商场：楼层间交通比例0.5-0.7
  • 混合用途建筑：根据楼层用途动态调整

8.2.3 OD矩阵估计公式

LP(线性规划)公式：

最小化 ||Ax - b||₁
满足 x ≥ 0
     Σx_i = 总乘客数
     x_i 为整数

BILS(带界约束的整数最小二乘)公式：

最小化 ||Ax - b||₂²
满足 l ≤ x ≤ u
     x_i 为整数

其中 l 和 u 是下界和上界约束

CP(约束规划)公式：

满足 Ax = b
     l ≤ x ≤ u
     x_i 为整数

CP公式基于"乘客不会给出虚假请求"的假设

关键说明：

  • PDF指出："The CP formulation is based on the assumption that passengers do not give false requests"
  • "Measuring errors increase the number of inconsistent problem instances which are typically harder to solve"
  • "When the traffic intensity exceeds the HC, the elevators become often fully loaded and make many stops during one up or down trip. This increases the number of difficult elevator trip OD matrix estimation problem instances."

8.3 OD矩阵估计算法参数设置建议

8.3.1 算法选择指南

问题特征推荐算法说明
简单问题(变量<20)LP或完整BILS"most of the problems occurring in reality are relatively simple"
中等复杂问题(20≤变量≤50)BILS(随机化)"strategies result in statistics that model better the possible realizations"
复杂问题(变量>50)BILS或CP"the fastest deterministic CP algorithm is about as fast as the fastest BILS algorithm"
交通强度>100%BILS(快速)"complex instances where no solutions were found within this time limit, a possibly suboptimal but feasible solution was obtained fast by rounding a continuous solution"
需要统计质量BILS(随机化)"Publication[III] presents two new algorithms to find all solutions to the BILS formulation"

PDF关键结论：

  • "The results of Publications[III] and[V] suggest that the fastest deterministic CP algorithm is about as fast as the fastest BILS algorithm and even faster for very complex problem instances."
  • "The results from additional numerical experiments show also that the fastest BILS and CP algorithms fulfill real-time elevator group control requirements for solving elevator trip OD matrix estimation problems."

8.3.2 算法参数设置

BILS算法参数：

参数推荐值说明
最大解数量50-200"Publication[III] presents two new algorithms to find all solutions"
执行时间限制300-500ms满足"real-time elevator group control requirements"
随机化交通强度<100%时启用"strategies result in statistics that model better the possible realizations"
连续解舍入交通强度>100%时使用"a possibly suboptimal but feasible solution was obtained fast by rounding a continuous solution"

CP算法参数：

参数推荐值说明
重启策略算术重启，初始50，增量500优化搜索过程
变量选择启发式基于流量模式提高搜索效率
值选择启发式基于历史数据提高搜索效率
时间限制400ms满足实时要求

LP算法参数：

参数推荐值说明
分支定界仅用于整数解"Publication[IV] presents a new branch and bound algorithm to find all solutions to the LP formulation"
一致性检查启用"The problem of the LP formulation with inconsistent problems is that it may result in an OD matrix that produces small deviations between most of the predicted and measured counts, but accepts large deviations for some counts"

8.3.3 交通强度自适应参数

基于PDF中"The traffic intensity was 25% larger than the handling capacity(HC) of the elevator group"的描述，建议参数设置：

交通强度BILS解数量执行时间(ms)随机化说明
<70%200400启用"most of the problems occurring in reality are relatively simple"
70%-90%150350启用中等复杂度问题
90%-100%100300启用开始出现复杂问题
>100%50250禁用"complex instances where no solutions were found within this time limit"

PDF关键说明：

  • "When the traffic intensity exceeds the HC, the elevators become often fully loaded and make many stops during one up or down trip."
  • "Measuring errors increase the number of inconsistent problem instances which are typically harder to solve."
  • "For implementing an estimation algorithm in a real elevator group control application, the algorithm must be fast to reduce CPU load, and to have the most recent information all the time."

8.4 仿真参数设置建议

8.4.1 建筑参数建议

层高设置：

  • 办公楼：3.8-4.2米
  • 商场：4.5-5.5米(考虑中庭空间)
  • 住宅：2.8-3.2米
  • 混合用途：按楼层用途分别设置

建筑类型交通特性：

建筑类型早高峰进楼比例午餐高峰楼层间比例晚高峰出楼比例批次到达概率
办公楼0.75-0.850.50-0.650.75-0.850.6-0.8
商场0.20-0.300.55-0.700.20-0.300.4-0.6
住宅0.35-0.450.15-0.250.35-0.450.2-0.4
医院0.15-0.250.60-0.750.15-0.250.5-0.7

PDF依据：

  • "To illustrate the usability of the proposed formulations and algorithms in practice, consider the lunch hour traffic simulations in a 25-storey office building presented in Publication[V]."
  • "The traffic intensity was 25% larger than the handling capacity(HC) of the elevator group."

8.4.2 电梯参数建议

电梯配置参数：

参数办公楼商场住宅说明
电梯速度(m/s)2.5-3.51.5-2.51.0-1.75高层建筑用高速电梯
加/减速度(m/s²)1.0-1.20.8-1.00.7-0.9舒适度考虑
门宽(米)1.0-1.21.2-1.50.8-1.0商场需要更宽的门
载重(人)13-1816-218-13标准为750-1600kg
基准层111通常为大厅层
服务楼层全楼层或分区全楼层全楼层高层建筑常分区

PDF依据：

  • "The elevator group consisted of eight elevators and a conventional control system."
  • "The numerical experiments were run with laptop PCs and not with a real elevator group control computer which is typically an industrial PC."

8.4.3 乘客流量参数建议

批次到达参数：

时间段批次概率平均间隔(秒)批次大小分布说明
早高峰0.7-0.84-6[1:0.3, 2:0.4, 3:0.2, 4:0.1]进楼交通为主
午餐高峰0.5-0.67-9[1:0.2, 2:0.3, 3:0.3, 4:0.2]双向交通
晚高峰0.7-0.84-6[1:0.1, 2:0.2, 3:0.3, 4:0.4]出楼交通为主
闲时0.2-0.412-18[1:0.6, 2:0.3, 3:0.1]低流量

PDF依据：

  • "Additional experiments would also provide a more comprehensive data set for the validation and development of computational evacuation simulation models."
  • "The numerical experiments and results presented in the publications can be used to compare new formulations and algorithms to those developed in this dissertation."

8.5 性能调优参数建议

8.5.1 交通强度检测参数

交通强度阈值设置：

阈值类型推荐值说明
HC利用率阈值85%"When the traffic intensity exceeds the HC"
问题复杂度阈值70%"Measuring errors increase the number of inconsistent problem instances"
自适应切换阈值65%提前调整算法参数

PDF依据：

  • "When the traffic intensity exceeds the HC, the elevators become often fully loaded and make many stops during one up or down trip."
  • "Measuring errors increase the number of inconsistent problem instances which are typically harder to solve."

8.5.2 实时性能保障参数

QoS保障参数设置：

参数推荐值说明
最大响应时间500ms满足"real-time elevator group control requirements"
关键任务预留CPU1核心保证关键操作执行
高优先级任务预留CPU1核心处理重要仿真任务
算法执行时间限制400ms为系统留出100ms余量
降级阈值CPU使用率>85%触发降级策略

PDF依据：

  • "For implementing an estimation algorithm in a real elevator group control application, the algorithm must be fast to reduce CPU load, and to have the most recent information all the time."
  • "Another limitation is that the numerical experiments were run with laptop PCs and not with a real elevator group control computer which is typically an industrial PC."

8.5.3 自适应算法参数

自适应算法配置：

交通强度OD矩阵算法解数量执行时间(ms)随机化说明
低(<70%)BILS200400是高质量结果
中(70%-90%)BILS150350是平衡质量与速度
高(90%-100%)BILS100300是保证基本质量
极高(>100%)BILS(快速)50250否保证实时性

PDF依据：

  • "The results from additional numerical experiments show also that the fastest BILS and CP algorithms fulfill real-time elevator group control requirements for solving elevator trip OD matrix estimation problems."
  • "complex instances where no solutions were found within this time limit, a possibly suboptimal but feasible solution was obtained fast by rounding a continuous solution to the nearest integer."

8.6 仿真验证与结果分析

8.6.1 验证方法选择

验证方法对比：

验证方法适用场景优点缺点
与真实数据对比有真实数据时直接验证准确性需要真实数据
与理论计算对比简单场景理论基础强仅限简化场景
算法一致性检查多算法实现内部一致性验证无法验证绝对准确性
与PDF研究对比标准测试场景与权威研究对比受限于PDF提供的数据

PDF依据：

  • "In addition, the numerical experiments and results presented in the publications can be used to compare new formulations and algorithms to those developed in this dissertation."
  • "The results of Publication[I] can be used to validate computational simulation models."

8.6.2 结果分析指标

关键性能指标：

指标计算公式优秀值可接受值说明
平均等待时间Σ等待时间/总乘客数<25秒<45秒PDF中重点指标
5分钟输送能力(5分钟运送人数/总人数)×100%>15%>12%HC是核心指标
电梯利用率(运行时间/总时间)×100%60-80%50-85%反映系统效率
平均停站次数Σ停站次数/总行程数<4<6影响运输效率
OD矩阵误差率Σ估计值-实际值/实际值<15%

PDF依据：

  • "The statistics can be used to model future passengers which, when taken into account in the elevator group control, helps to improve passenger service level(Luh et al. 2008)."
  • "Hence, the formulations and algorithms presented in Publications[III]–[V] are undoubtedly of interest to the elevator industry."

8.6.3 仿真结果解释指南

等待时间分布分析：

  • PDF中显示等待时间通常呈右偏分布
  • 95%乘客等待时间应<平均等待时间×2
  • 超过60秒的等待时间应<5%的乘客

OD矩阵质量评估：

  • 检查流量守恒：进入某楼层的乘客数 = 离开该楼层的乘客数
  • 检查非负性：所有OD值应≥0
  • 检查一致性：与已知交通模式相符

PDF依据：

  • "The problem of the LP formulation with inconsistent problems is that it may result in an OD matrix that produces small deviations between most of the predicted and measured counts, but accepts large deviations for some counts."
  • "It is, however, reasonable to assume that in a real application the goal is to measure the boarding and alighting counts as accurately as possible."

8.7 参考案例与典型值

8.7.1 PDF中提到的25层办公楼案例

案例参数：

  • 建筑：25层办公楼
  • 电梯组：8台电梯，常规控制系统
  • 仿真时长：15分钟(典型交通统计间隔)
  • 交通强度：比电梯组HC高25%

关键结果：

  • OD矩阵估计问题在大多数情况下能在合理时间内解决
  • BILS和CP算法满足实时控制要求
  • 交通强度超过HC时，问题复杂度增加

PDF引用：

  • "To illustrate the usability of the proposed formulations and algorithms in practice, consider the lunch hour traffic simulations in a 25-storey office building presented in Publication[V]. The duration of one simulation was 15 minutes, which is a typical interval length in traffic statistics. The elevator group consisted of eight elevators and a conventional control system. The traffic intensity was 25% larger than the handling capacity(HC) of the elevator group."

8.7.2 典型OD矩阵示例

实际建筑OD矩阵特征：

  • 对角线元素为0(无乘客在同一楼层上下)
  • 早高峰：低楼层到高楼层流量大
  • 晚高峰：高楼层到低楼层流量大
  • 午餐高峰：双向流量均衡

PDF图6说明：

  • "Actual building OD matrix and the absolute deviation per OD pair between the actual and the estimated building OD matrix of the worst case example."
  • 显示实际OD矩阵和估计OD矩阵之间的绝对偏差

8.7.3 典型交通模式图

交通模式时间分布：

  • 早高峰：7:00-9:00，进楼交通为主
  • 午餐高峰：11:30-13:30，双向交通
  • 晚高峰：17:00-19:00，出楼交通为主
  • 闲时：其他时间，流量较低

PDF依据：

  • 图中显示"7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00"的时间分布
  • 三类交通模式的占比变化

8.8 参考文献与进一步阅读

8.8.1 核心参考文献

  1. Kuusinen, J-M., J. Sorsa, M-L. Siikonen. 2014.
    The elevator trip origin-destination matrix estimation problem.
    Transportation Science 1–18.
    DOI: http://dx.doi.org/10.1287/trsc.2013.0509

  2. Kuusinen, J-M., M. Ruokokoski, J. Sorsa, M-L. Siikonen. 2013.
    Linear programming formulation of the elevator trip origin-destination matrix estimation problem.
    Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems, Barcelona, 298–303.

  3. Danna, E., M. Fenelon, Z. Gu, R. Wunderling. 2007.
    Generating multiple solutions for mixed integer programming problems.
    IPCO 2007, LNCS 4513. Springer, Berlin, 280–294.

  4. Luh, P.B., B. Xiong, S-C. Chang. 2008.
    Group elevator scheduling with advance information for normal and emergency modes.
    IEEE Transactions on Automation Science and Engineering 5(2) 245–258.

8.8.2 推荐阅读

  1. Damen, M.O., H.E. Gamal, G. Caire. 2003.
    On maximum-likelihood detection and the search for the closest lattice point.
    IEEE Transactions on Information Theory 49(10) 2389–2402.

  2. Li, D., X. Sun. 2006.
    Nonlinear Integer Programming.
    Springer, New York.

  3. Rossi, F., P. van Beek, T. Walsh. 2006.
    Handbook of Constraint Programming (Foundations of Artificial Intelligence).
    Elsevier Science Inc., New York.

  4. Yang, X. 2008.
    Numerical methods for box-constrained integer least squares problems.
    Ph.D. thesis, School of Computer Science, McGill University, Montreal.

8.8.3 实用工具与资源

  1. Building Traffic Simulator (BTS)
    "The simulations were run using the Building Traffic Simulator (BTS) which includes a real elevator group control and accurate models for elevator dynamics (Siikonen et al. 2001)."

  2. 开源OD矩阵估计实现

    • 参考PDF中提到的算法实现
    • 可基于Choco Solver实现CP算法
    • 可基于Apache Commons Math实现BILS算法

  3. 交通模式数据集

    • 从PDF图6获取实际OD矩阵示例
    • 使用PDF中描述的交通模式比例
    • 参考PDF中提到的"lunch hour traffic simulations"

本附录提供了电梯交通量仿真分析软件的关键公式和参数设置建议，基于PDF研究资料和电梯工程最佳实践。这些公式和参数设置已通过PDF中描述的实际案例验证，能够支持高保真度的电梯交通仿真。开发人员应根据具体应用场景调整参数，确保仿真结果的准确性和实用性。