應用近似動態規劃法設計捷運線自動列車調控系統

Abstract

捷運系統是由許多條具獨立路權之地面、高架或地下鐵路連結而成的都會區大眾運輸網路，其特點是在都會區人車密集的環境下，可以提供龐大及密集班次的運輸能量以因應繁重的旅運需求、可以精準的控制各列車的離靠站時間及旅運時間、可以提供旅客舒適的候車及乘車環境，今日的捷運系統已經成為世界各大都會區運送旅客的主要交通工具。捷運系統的運輸能量與服務品質，取決於軌道、車輛與車站等基礎建設以及自動化行車監控技術，自動化行車監控技術的主要任務是確保行車安全，其次是調節列車班距以確保運輸能量、掌控列車的離靠站時間與旅運時間以確保服務品質，尤其是當旅客流量巨幅變動或列車的離靠站時間偏離時間表的時候，能迅速使各列車從混亂狀態中恢復運行秩序，以確保系統營運的穩定性。 根據號誌系統的特性，捷運系統的自動化行車監控技術可以大略區分為固定式閉塞區間法(Fixed Block)與移動式閉塞區間法(Moving Block)兩種，閉塞區間法是為了確保系統運能與確保各列車保持安全間距所採取的行車監控技術。固定式閉塞區間法在固定地點佈設軌道電路，把軌道線分隔為許多閉塞區間，行車監控的準則是確保每個閉塞區間只有一列車佔用。移動式閉塞區間法則透過通訊系統傳達各列車所在的位置，按列車的所在位置劃定一個閉塞區間，行車監控的準則是確保每一列車的閉塞區間都不能被其他列車闖入。在自動化行車監控技術之中，自動列車調控系統(Automatic Train Regulation, ATR)負責調節列車班距、掌控列車的離靠站時間與旅運時間、以及確保各列車遵循閉塞區間的行車監控準則，無疑的，自動列車調控系統是最具關鍵性的自動化監控技術。 本論文首先針對捷運行車監控技術的發展過程做回顧，探討的焦點集中於捷運系統設計與營運性能的相關課題，尤其是與自動列車調控系統相關的系統運能、準點率、穩定性、節能省碳等議題。設計自動列車調控系統面對的是一個大規模、高複雜性、高度非線性、限制性、隨機性、時變性的最佳控制問題，傳統的線性最佳控制理論並不適合求解這類型問題，但是文獻顯示許多前輩仍然試圖用線性最佳控制理論尋求解決之道，其艱困不言可喻，因此，自動列車調控系統的設計技術仍然存在許多尚未解決的課題。本論文深入剖析自動列車調控系統的運作環境，並對捷運系統的列車運作過程與能源消耗建立一個適用的系統模型，再運用優化技術、類神經網路、強化學習機制綜合自動列車調控系統的調節器，此調節器具非線性性質，強化學習機制則使其可以自動適應旅客流量等環境條件的變動。 動態規畫法是應用廣泛的優化技術，但是只適合用來處理小規模系統的優化問題，在面對大規模系統時，此方法所隱含的逆向演算程序會引起龐大的演算量以至於難以實現。為了讓動態規畫法能避開逆向演算程序，因而崛起近似動態規畫法(Approximate Dynamic Programming, ADP)，此方法藉由學習過程建立評效器(Critic)，評效器可以預估系統效能的變動趨向，因此可以引導調節器的優化動作，過程中無須採用逆向演算程序，即使面對大規模系統的優化問題，近似動態規畫法也能平順運作。本論文採用近似動態規畫法之中的雙試探動態規畫法(Dual Heuristic Programming, DHP)來優化自動列車調控系統的調節器，我們用感知類神經網路(Multilayer-Perceptron Network, MLP)建構調節器與評效器，透過類神經網路的學習程序達成優化的目標，引用台北市捷運系統的運行數據測試後，證實此設計確實可以優化調節器，但是測試結果亦顯示雙試探動態規畫法的優化效能與系統模型的精確性呈正相關。 由於捷運系統的數學模型都是非常粗略的，優化方法必須有能力排除模型偏差的影響，所以本論文進一步根據雙試探動態規畫法的概念建立自動列車調控系統的適應性最佳控制法(Adaptive Optimal Control, AOC)，此方法引用最小化原理(Pontryagin’s Minimum Principle)推導優化程序，特點是評效器不包含系統模型，因此，在引導調節器的優化動作時，不受模型偏差的影響，經過引用台北市捷運系統的運行數據測試後，發現對於模型偏差的韌度明顯優於雙試探動態規畫法，而且更能逼近理論之最佳解。 考慮列車調控與捷運系統的能源消耗有密切的關係，本論文把捷運系統的能源消耗程序建立成數學模型，並且將其併入列車調控的系統模型，因此，只要訂定適當的性能指標，就可以在優化調節器的時候同時優化節能效率，測試結果顯示，經過優化的調節器其節能效果非常顯著。

A rail rapid transit system in an urban area consists of several at-grade, elevated, or underground railway lines with exclusive right-of-way. Since the rail rapid transit system can provide high transportation capacity with high service frequency to meet heavy traffic demands, provide better transportation service quality, as well as provide a safe and comfortable riding environment for passengers, it has been recognized as an effective solution to traffic congestion problems in metropolitan areas. Nowadays, in the cities where there is an existing rail rapid transit system, it is difficult to conceive how the people could function properly without this mode of transportation. In a modern rail rapid transit system, an automatic train control system (ATC) is responsible for ensuring operation safety, maintaining schedule and headway adherence to meet the required service quality and capacity demands, and particularly for recovering normal operation in the face of passenger flow fluctuations and disturbances resulting in delays. Depending on signaling system design, there are two main types of ATC system: fixed block ATC system and moving block ATC system. The block is a design concept to ensure the safe separation between consecutive trains running along a railway line. In a fixed block ATC system, a railway line is divided into blocks by using track circuits, therewith the safe separations are ensured by inhibiting trains from entering occupied blocks. In a moving block ATC system, instead of deploying track circuits, more precise train positioning can be achieved through a continuous wireless data communication system and the safe separations are ensured by inhibiting other trains from entering the blocks set and moved with trains running along a railway line. No matter what type of ATC system is used in a modern metro, the automatic train regulation (ATR) is definitely the key function of an ATC system in maintaining schedule and headway adherence to ensure reliable operations and required service quality. In this dissertation, a comprehensive review of the developments of train control system is provided first, based primarily on the performance relevant issues of ATR, which includes stability, punctuality, schedule adherence, capacity, de-carbonization, and energy saving as well. Basically, designing ATR is intrinsically a large scale optimal control problem with high nonlinearity, heavy constraints, high complexity, and stochastic characteristics. Hence conventional linear optimization theories would be not appropriate to deal with such a problem, though it can be found in relevant literature that ATR designs have mostly been approached with linear optimization theories. Thus, some issues remain to be further investigated. In this research work, the environment of train regulation is investigated first, and the models for describing the traffic environment and energy consumption resulting from traffic regulation are developed for designing ATR. Thereby, an ATR design is approached by using adequate optimization techniques, neural networks, and reinforcement learning methods so that the designed ATR can adapt to the nonlinearity and fluctuations of the environment. Dynamic programming (DP) is widely used to deal with the optimization problem with a small scale system but always suffers from the “curse of dimensionality” problem with a large scale system because of the backward search method underlying DP. Hence the real implementation of DP is rather intractable. Approximate dynamic programming (ADP) is an emerging technique that turns the real implementation of DP from the difficulty of dimensionality by using an adaptive critic mechanism. A critic in an ADP method is designed to learn to predict system performance as guidance for optimizing a regulator performance without using the backward search method. Thus, the optimization problem with a large scale system can be easily handled by using ADP methods. One ADP method, dual heuristic dynamic programming (DHP) has been successfully employed in this research to optimize the regulator design of ATR, where the regulator and the critic are constructed by using a Multilayer-Perceptron Network (MLP) and adapted via a neural network learning process. The verification of the DHP-based ATR design referring to practical operation data of Taipei metro shows a near optimal design of the regulator is achievable. Nevertheless, the influences of traffic modeling error on the performance of the DHP-based ATR are appreciable because the exact mathematical model for describing the environment is hard to access in real implementation. Thus the capability of coping with the effects of modeling errors is an important issue when dealing with an ATR design. In order to improve the performance of an ATR design in regard to modeling error as well as optimality, an Adaptive Optimal Control (AOC) method is developed in this research work by introducing the Pontryagin’s Minimum Principle (PMP) into a DHP method. The evaluation of ATR designs with field data confirms that the ATR design with AOC method is more robust against traffic modeling error than that with a DHP method and is able to find a more near-optimal solution. This is because the model for predicting the state for critic prediction is no longer necessary in an AOC design. Considering energy consumption is highly dependent on traffic regulation, a model describing traffic environments associated with energy consumption is developed for designing the ATR with energy saving. With the model, the optimal traffic regulation with higher energy efficiency is attainable with adequate tailoring of a performance index for the optimization. Simulation tests with field data also show considerable energy savings in train regulation can be gained via the use of the ATR design with energy saving.