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TBO模式下终端区进场交通流优化模型与仿真分析

1. 南京航空航天大学 民航学院, 南京 211106;
2. 克兰菲尔德大学 航空中心, 贝德福德郡 MK430AL

Optimizing arrival traffic flow in airport terminal airspace under trajectory based operations
ZHANG Honghai1, TANG Yiwen1, XU Yan2
1. College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Centre for Aeronautics, Cranfield University, Bedford MK430 AL, United Kingdom
Abstract: Continuously increasing traffic demand and gradually saturated airspace are promoting a transformation which will shift future air traffic management system to a refined management mode with Trajectory Based Operation (TBO) as its core. Conforming to the TBO concept and current air route structure in busy terminal airspace, traffic flow optimization models corresponding to short-cut directly fly arrival mode and merge-point arrival mode with TBO characterized are proposed respectively. Charles de Gaulle Airport is taken as an example to build the terminal airspace simulation environment. Based on actual flight plans and radar data, four-dimensional flight trajectories are generated and optimized by the two models. According to the simulation outcomes, analysis and comparisons of traffic flow characteristics for the two models are carried out. The results show that the models can effectively avoid potential aircraft conflicts and maintain a safe and efficient traffic flow operation in terminal airspace by implementing trajectory selection, time slot rescheduling, dynamic separation, sequence exchange, etc. It reveals traffic flow characteristics under the TBO mode and provides theoretical support for the future air traffic management strategy centered on the four-dimensional trajectory.
Keywords: air traffic management    terminal airspace    trajectory-based operation    traffic flow characteristics    simulation and optimization

1 TBO模式下截点直飞进场优化模型 1.1 模型介绍

 图 1 截点直飞方式进场航路构型 Fig. 1 Route structure of short-cut direct fly arrival model

 图 2 巴黎戴高乐机场场面结构图 Fig. 2 Surface structure of Charles de Gaulle Airport
1.2 数学建模 1.2.1 决策变量

 $\begin{array}{l} x_{f,t}^{k,j} = \\ \left\{ {\begin{array}{*{20}{l}} {1,{\rm{ 航班 }}f{\rm{ 的 }}k{\rm{ 航迹于 }}t{\rm{ 时刻前已到达 }}j{\rm{ 位置点 }}}\\ {0,{\rm{ 否则}}} \end{array}} \right.\\ z_f^k = \left\{ {\begin{array}{*{20}{l}} {1,{\rm{ 航班 }}f{\rm{ 选取 }}k{\rm{ 航迹 }}}\\ {0,{\rm{ 否则 }}} \end{array}} \right. \end{array}$

 时间变量定义 T1 T2 T3 T4 T5 t时刻之前已经到达 0 0 1 1 1 t时刻恰好到达 0 0 1 0 0
1.2.2 优化模型

 ${\rm{min}}({\rm{Ar}}{{\rm{r}}_{{\rm{ cost }}}} + \lambda {\rm{De}}{{\rm{p}}_{{\rm{ cost }}}})$ （1）
 $\begin{array}{l} {\rm{Ar}}{{\rm{r}}_{{\rm{ cost }}}} = ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{a}} + {C_{\rm{p}}})D_{{\rm{ Ent }}}^{{\rm{ arr }}} + ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{a}})D_{{\rm{ Hold }}}^{{\rm{ arr }}} + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{g}})D_{{\rm{Gnd}}}^{{\rm{arr}}} \end{array}$ （2）
 $\begin{array}{l} {\rm{De}}{{\rm{p}}_{{\rm{ cost }}}} = {C_{\rm{d}}}D_{{\rm{Gate}}}^{{\rm{dep}}} + ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{g}})D_{{\rm{Gnd}}}^{{\rm{dep}}} + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{g}} + {C_{\rm{p}}})D_{{\rm{Rwy}}}^{{\rm{dep}}} \end{array}$ （3）
 $\left\{ \begin{array}{l} D_{{\rm{Ent}}}^{{\rm{arr}}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {\sum\limits_{j = J_f^{{\rm{Ent}}}} {\sum\limits_{t \in T_f^j} {(t - \tau _f^j)(x_{f,t}^{k,j} - x_{f,t - 1}^{k,j})} } } \\ D_{{\rm{ Hold }}}^{{\rm{ arr }}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {\sum\limits_{j = J_f^{{\rm{Rwy}}}} {\sum\limits_{t \in T_f^j} {(t - \tau _f^j)(x_{f,t}^{k,j} - } } } \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} x_{f,t - 1}^{k,j}) - D_{{\rm{Ent}}}^{{\rm{arr}}}\\ D_{{\rm{Gnd}}}^{{\rm{arr}}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {\sum\limits_{j = J_f^{{\rm{Gate}}}} {\sum\limits_{t \in T_f^j} {(t - \tau _f^j)(x_{f,t}^{k,j} - x_{f,t - 1}^{k,j})} } } - \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} D_{{\rm{Hold}}}^{{\rm{arr}}} - D_{{\rm{Ent}}}^{{\rm{arr}}} \end{array} \right.$ （4）
 $\left\{ \begin{array}{l} D_{{\rm{Gate}}}^{{\rm{dep}}} = \sum\limits_{f \in {F_{{\rm{dep}}}}} {\sum\limits_{j = J_f^{{\rm{Gate}}}} {\sum\limits_{t \in T_f^j} {(t - \tau _f^j)(x_{f,t}^{k,j} - x_{f,t - 1}^{k,j})} } } \\ D_{{\rm{Gnd}}}^{{\rm{dep}}} = \sum\limits_{f \in {F_{{\rm{dep}}}}} {\sum\limits_{j = J_f^{{\rm{Taxi}}}} {\sum\limits_{t \in T_f^j} {(t - \tau _f^j)(x_{f,t}^{k,j} - {\kern 1pt} {\kern 1pt} x_{f,t - 1}^{k,j})} } } \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} - D_{{\rm{Gate}}}^{{\rm{arr}}}\\ D_{{\rm{Rwy}}}^{{\rm{dep}}} = \sum\limits_{f \in {F_{{\rm{dep}}}}} {\sum\limits_{j = J_f^{{\rm{Rwy}}}} {\sum\limits_{t \in T_f^j} {(t - \tau _f^j)(x_{f,t}^{k,j} - } } } \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} x_{f,t - 1}^{k,j}) - D_{{\rm{Gnd}}}^{{\rm{dep}}} - D_{{\rm{Gate}}}^{{\rm{dep}}} \end{array} \right.$ （5）
 $\sum\limits_{k \in {K_f}} {z_f^k} = 1,\forall f \in F$ （6）
 $x_{f,\underline T _f^{k,j} - 1}^{k,j} = 0,\forall f \in F,\forall k \in {K_f},\forall j \in J_f^k$ （7）
 $x_{f,\bar T_f^{k,j}}^{k,j} = z_f^k,\forall f \in F,\forall k \in {K_f},\forall j \in J_f^k$ （8）
 $\begin{array}{l} x_{f,t}^{k,j} - x_{f,t - 1}^{k,j} \ge 0,\forall f \in F,\forall k \in {K_f},\\ \quad {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall j \in J_f^k,\forall t \in T_f^{k,j} \end{array}$ （9）
 $\begin{array}{l} x_{f,t + \hat t_f^{k,j{j^\prime }}}^{k,{j^\prime }} - x_{f,t}^{k,j} \le 0,\forall f \in F,\forall k \in {K_f},\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall t \in T_f^{k,j},j = J_k^{(i)},{j^\prime } = J_k^{(i + 1)}:\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall i \in [1,n_f^k) \end{array}$ （10）
 $\begin{array}{l} x_{f,t + u_f^{k,j{j^\prime }}\hat t_f^{k,j{j^\prime }}}^{k,{j^\prime }} - x_{f,t}^{k,j} \ge 0,\forall f \in F,\forall k \in {K_f},\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall t \in T_f^{k,j},j = J_k^{(i)},{j^\prime } = J_k^{(i + 1)}:\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall i \in [1,n_f^k) \end{array}$ （11）
 $\sum\limits_{f \in F} {\sum\limits_{k \in {K_f}} {\sum\limits_{t \in T_f^{k,j} \cap T_p^j} {x_{f,t}^{k,j} - x_{f,t - 1}^{k,j} \le 1} } } ,\forall j \in J,\forall p \in P$ （12）
 $\begin{array}{*{20}{l}} {x_{f,t}^{k,j} \in \{ 0,1\} ,\forall f \in F,\forall k \in {K_f},\forall j \in J_f^k,}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall t \in T_f^{k,j}} \end{array}$ （13）
 $z_f^k \in \{ 0,1\} ,\forall f \in F,\forall k \in {K_f}$ （14）

 $\begin{array}{l} ({x_n} - {x_{n - 1}}) + ({x_{n - 1}} - {x_{n - 2}}) + \cdots ({x_2} - {x_1}) = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {x_n} - {x_{n - 1}} \end{array}$

2 TBO模式下融合点进场优化模型 2.1 模型介绍

 图 3 融合点方式进场航路构型 Fig. 3 Route structure of point-merge arrival model
 图 4 融合点方式进场排序边示意图 Fig. 4 Sequence leg structure of point-merge arrival model

2.2 数学建模 2.2.1 决策变量

 $\omega _{f,t}^j = \left\{ {\begin{array}{*{20}{l}} {1,{\rm{ 航班 }}f{\rm{ 于 }}t{\rm{ 时刻到达 }}j{\rm{ 位置点 }}}\\ {0,{\rm{ 否则 }}} \end{array}} \right.$

 $h_{f,{f^\prime }}^j = \left\{ {\begin{array}{*{20}{l}} {1,{\rm{ 航班 }}f{\rm{ 比 }}{f^\prime }{\rm{ 先到达 }}j{\rm{ 位置点 }}}\\ {0,{\rm{ 否则 }}} \end{array}} \right.$

2.2.2 优化模型

 ${\rm{min}}({\rm{Ar}}{{\rm{r}}_{{\rm{ cost }}}} + \lambda {\rm{De}}{{\rm{p}}_{{\rm{ cost }}}})$ （15）
 $\begin{array}{l} {\rm{Ar}}{{\rm{r}}_{{\rm{ cost }}}} = ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{a}} + {C_{\rm{p}}})D_{{\rm{Ent}}}^{{\rm{arr}}} + ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{a}})D_{{\rm{Hold}}}^{{\rm{arr}}} + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{s}})D_{{\rm{Seq}}}^{{\rm{arr}}} + ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{g}})D_{{\rm{Gnd}}}^{{\rm{arr}}} \end{array}$ （16）
 $\begin{array}{l} {\rm{De}}{{\rm{p}}_{{\rm{ cost }}}} = {C_{\rm{d}}}D_{{\rm{ Gate }}}^{{\rm{dep}}} + ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{g}})D_{{\rm{ Gnd }}}^{{\rm{dep}}} + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ({C_{\rm{d}}} + C_{\rm{f}}^{\rm{g}} + {C_{\rm{p}}})D_{{\rm{Rwy}}}^{{\rm{dep}}} \end{array}$ （17）
 $\left\{ \begin{array}{l} D_{{\rm{Ent}}}^{{\rm{arr}}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {\sum\limits_{j = J_f^{{\rm{Ent}}}} {(\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \tau _f^j)} } \\ D_{{\rm{Hold}}}^{{\rm{arr}}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {\sum\limits_{j = J_f^{{\rm{Seq}}}} {(\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \tau _f^j)} } - D_{{\rm{Ent}}}^{{\rm{arr}}}\\ D_{{\rm{Seq}}}^{{\rm{arr}}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {{q_f}} \\ D_{{\rm{Gnd}}}^{{\rm{arr}}} = \sum\limits_{f \in {F_{{\rm{arr}}}}} {\sum\limits_{j = J_f^{{\rm{Gate}}}} {(\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \tau _f^j)} } - D_{{\rm{Hold}}}^{{\rm{arr}}} - D_{{\rm{Seq}}}^{{\rm{arr}}} \end{array} \right.$ （18）
 $\left\{ \begin{array}{l} D_{{\rm{Gate}}}^{{\rm{dep}}} = \sum\limits_{f \in {F_{{\rm{dep}}}}} {\sum\limits_{j = J_f^{{\rm{Gate}}}} {(\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \tau _f^j)} } \\ D_{{\rm{Gnd}}}^{{\rm{dep}}} = \sum\limits_{f \in {F_{{\rm{dep}}}}} {\sum\limits_{j = J_f^{{\rm{Taxi}}}} {(\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \tau _f^j)} } - D_{{\rm{Gate}}}^{{\rm{dep}}}\\ D_{{\rm{Rwy}}}^{{\rm{dep}}} = \sum\limits_{f \in {F_{{\rm{dep}}}}} {\sum\limits_{j = J_f^{{\rm{Rwy}}}} {(\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \tau _f^j)} } - D_{{\rm{Gnd}}}^{{\rm{dep}}} - D_{{\rm{Gate}}}^{{\rm{dep}}} \end{array} \right.$ （19）
 $\sum\limits_{t \in T_f^j} {\omega _{f,t}^j} = 1,\forall f \in F,\forall j \in {J_f}$ （20）
 $\begin{array}{l} \sum\limits_{t \in T_{{f^\prime }}^{j\prime }} t \omega _{f,t}^{{j^\prime }} - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j \ge \hat t_f^{k,j{j^\prime }},\forall f \in F,\forall (j,{j^\prime }) \in \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {J_f},{j^\prime } = j + 1 \end{array}$ （21）
 $\begin{array}{l} \sum\limits_{t \in T_{{f^\prime }}^{j\prime }} t \omega _{f,t}^{{j^\prime }} - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j \ge u_f^{k,j{j^\prime }}\hat t_f^{k,j{j^\prime }},\forall f \in F,\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall (j,{j^\prime }) \in {J_f},{j^\prime } = j + 1 \end{array}$ （22）
 $\begin{array}{l} \sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{f,t}^j - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j \ge S_{(f,{f^\prime })}^j,\forall j \in {J^{\rm{A}}},\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall (f,{f^\prime }) \in {F_j},f \ne {f^\prime } \end{array}$ （23）
 $\begin{array}{l} \left| {\sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j} \right| \ge S_{(f,{f^\prime })}^jh_{f,{f^\prime }}^j + S_{({f^\prime },f)}^j(1 - \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} h_{f,{f^\prime }}^j),\forall j \in {J^{\rm{B}}},\forall (f,{f^\prime }) \in {F_j} \end{array}$ （24）
 $\begin{array}{*{20}{c}} {\left| {\sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j + {q_f} - (\sum\limits_{t \in T_f^j} t \omega _{f,t}^j + {q_{{f^\prime }}})} \right| \ge S_{(f,{f^\prime })}^jh_{f,{f^\prime }}^j + }\\ {S_{({f^\prime },f)}^j(1 - h_{f,{f^\prime }}^j),\forall j \in {J^{\rm{C}}},\forall (f,{f^\prime }) \in {F_j}} \end{array}$ （25）
 $\left\{ {\begin{array}{*{20}{l}} {\sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j < {M_0}h_{f,{f^\prime }}^j}\\ {\sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j \ge {M_0}(1 - h_{f,{f^\prime }}^j)} \end{array}} \right.$ （26）
 $\left\{ \begin{array}{l} (\sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j - \sum\limits_{t \in T_f^j} t \omega _{f,t}^j) + {M_{\rm{B}}}a_{f,{f^\prime }}^j \ge S_{(f,{f^\prime })}^jh_{f,{f^\prime }}^j + S_{({f^\prime },f)}^j(1 - h_{f,{f^\prime }}^j),\forall j \in {J^{\rm{B}}},\forall (f,{f^\prime }) \in {F_j}\\ (\sum\limits_{t \in T_f^j} t \omega _{f,t}^j - \sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j) + {M_{\rm{B}}}a_{f,{f^\prime }}^j \le {M_{\rm{B}}} - \left[ {S_{(f,{f^\prime })}^jh_{f,{f^\prime }}^j + S_{({f^\prime },f)}^j(1 - h_{f,{f^\prime }}^j)} \right],\forall j \in {J^{\rm{B}}},\forall (f,{f^\prime }) \in {F_j} \end{array} \right.$ （27）
 $\left\{ \begin{array}{l} \sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j + {q_f} - (\sum\limits_{t \in T_f^j} t \omega _{f,t}^j + {q_{{f^\prime }}}) + {M_{\rm{C}}}a_{f,{f^\prime }}^j \ge S_{(f,{f^\prime })}^jh_{f,{f^\prime }}^j + S_{({f^\prime },f)}^j(1 - h_{f,{f^\prime }}^j),\forall j \in {J^{\rm{C}}},\forall (f,{f^\prime }) \in {F_j}\\ \sum\limits_{t \in T_f^j} t \omega _{f,t}^j + {q_{{f^\prime }}} - (\sum\limits_{t \in T_{{f^\prime }}^j} t \omega _{{f^\prime },t}^j + {q_f}) + {M_{\rm{C}}}a_{f,{f^\prime }}^j \le {M_{\rm{C}}} - [S_{(f,{f^\prime })}^jh_{f,{f^\prime }}^j + S_{({f^\prime },f)}^j(1 - h_{f,{f^\prime }}^j)],\forall j \in {J^{\rm{C}}},\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \forall (f,{f^\prime }) \in {F_j} \end{array} \right.$ （28）
 ${\omega _{f,t}^j \in \{ 0,1\} ,\forall f \in F,\forall j \in {J_f},\forall t \in T_f^j}$ （29）
 ${h_{f,{f^\prime }}^j \in \{ 0,1\} ,\forall j \in {J^{\rm{B}}} \cup {J^{\rm{C}}},\forall (f,{f^\prime }) \in F}$ （30）
 ${a_{f,{f^\prime }}^j \in \{ 0,1\} ,\forall j \in {J^{\rm{B}}} \cup {J^{\rm{C}}},\forall (f,{f^\prime }) \in F}$ （31）
 ${{q_f} \in [0,n],\forall f \in {F^{{\rm{arr}}}}}$ （32）

3 仿真实验及结果分析 3.1 仿真实验 3.1.1 实验设计

 图 5 仿真实验总体框架与流程 Fig. 5 Overall frameworks and processes of simulation experiment

3.1.2 数据来源

 图 6 仿真实验原始数据示意图 Fig. 6 Source of raw data for simulation experiment

 空中距离间隔/海里 空中时间间隔/s 地面时间间隔/s 前机 后机 前机 后机 前机 后机 重型机 中型机 重型机 中型机 进场 离场 重型机 4 5 重型机 82 118 进场 15 60 中型机 3 3 中型机 60 70 离场 30 120
3.1.3 实验假设

 目标函数 约束条件 参数设置 截点直飞模型 融合点模型 参数设置 截点直飞模型 融合点模型 延误成本 1 1 最大延误/s 750 750 惩罚成本 1 1 排序边延误/s 600 地面燃油成本 0.5 0.5 场面滑行间隔/s 45 45 空中燃油成本 2 2 空中时间间隔/s 120 见表 3 进离场偏好 2:1 2:1 跑道穿越间隔/s 60 见表 3

3.1.4 过程控制

 图 7 滑动时间窗方法示意图 Fig. 7 Schematic of sliding window method

 图 8 根据模型构建的BlueSky仿真运行场景 Fig. 8 BlueSky simulation environment built based on the model

3.2 结果分析 3.2.1 冲突分析

 图 9 仿真场景中飞行计划在各位置点处的冲突数 Fig. 9 Conflicts at each waypoint of flight plan scenario in simulation enviroment

3.2.2 间隔分析

 图 10 近似传统运行的进场方式及2种模型优化前后的时隙分配结果 Fig. 10 Time slots rescheduling results of approximately traditional operation and two optimization models

3.2.3 延误分析

 时段/时 截点直飞模型 融合点模型 近似传统运行的进场方式 区外延误/s 延误恢复/s 进场延误/s 进场数/架次 区外延误/s 航路延误/s 融合区延误/s 进场数/架次 延误时间/s 进场数/架次 06-07 6 275 11 300 -5 025 45 880 935 805 46 1 045 21 07-08 18 990 11 590 7 400 51 1 645 2 215 2 920 50 10 700 58 08-09 2 600 1 985 615 31 615 575 690 35 4 540 34 09-10 4 750 3 705 1 045 27 35 440 230 25 3 670 28 10-11 6 865 10 390 -3 525 50 705 1 590 690 48 1 840 38 11-12 1 075 2 355 -1 280 25 100 595 435 25 3 580 33

3.2.4 流量分析

 图 11 跑道入口处进场交通流流量 Fig. 11 Number of arrival aircraft at runway entrance

4 结论

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http://dx.doi.org/10.7527/S1000-6893.2020.23844

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#### 文章信息

ZHANG Honghai, TANG Yiwen, XU Yan
TBO模式下终端区进场交通流优化模型与仿真分析
Optimizing arrival traffic flow in airport terminal airspace under trajectory based operations

Acta Aeronautica et Astronautica Sinica, 2020, 41(7): 323844.
http://dx.doi.org/10.7527/S1000-6893.2020.23844