基於系統韌性最佳化之相依基礎設施災後修復作業

Abstract

相依基礎設施系統遭受災害之後，需要透過修復作業以回復其原始功能，本研究宗旨即為討論相依基礎設施系統的災後修復作業，並以最小化修復過程中的系統韌性為目標。為計算、規劃系統內損壞元件的修復排程並以系統韌性評估該基礎設施系統的效能，本研究考慮由道路、電力及電信系統所組成、包含各系統間複雜交互關係的相依基礎設施系統，提出以網路流為基礎的混合整數二次規劃模式。模式中以各系統提供的服務需求未滿足量評估系統的韌性損失，並將目標函數定義為最小化整體修復過程中的任性損失與需求資訊不完整的懲罰項。其中，模式透過網路流計算各基礎設施系統中的服務遞送量與受損元件修復的可行選項，並以決策變數描述系統中元件功能狀態，而其數值隨時間的變化即為修復受損元件的時序。其中，本研究與既有文獻不同處為考慮資訊傳遞與修復過程的相依性。資訊傳遞的相依性涵蓋因通訊中斷而導致需求資訊的不完整，本研究以邏輯限制式、期望系統性能損失與迭代修復過程進行考量。修復過程的相依性則與修復班隊基地能否透過路網與各基礎設施系統損壞節線連通有關，本研究係利用網路流於模式中計算，而此種相依性將直接影響到修復排程的可行性。為展示模式的能力與說明相依性對修復過程造成的影響，本研究以臺灣新北市土城區為基礎進行案例分析，利用參考當地管線資料所建立的多層相依基礎設施網路進行數值實驗，並設想兩種不同型態的破壞模式，以說明資訊傳遞與修復過程的相依性對修復過程的影響。實驗結果顯示本模式可透過系統性的觀點評估相依基礎設施系統的韌性，進而以系統韌性最佳化的角度規劃修復作業。

This study proposes the problem of restoring interdependent infrastructure systems after disaster impact, seeking to minimize the resilience loss and the penalty for the incomplete information of the amount of demand throughout the horizon of a restoration schedule. In order to solve the proposed problem, this study develops a mixed integer quadratic programming model, which applies the network flow method to describe the dynamics of commodity delivery, restoration crews and functional states of components in the interdependent infrastructure systems, including the roadway, electric power, and telecommunication systems. The performance of each system is defined based on the met demand for relevant service to assess resilience loss, and the objective function is defined to minimize the expected unmet demand throughout the recovery phase. This model also reflects several types of interdependencies. First, the cyber interdependency is factored by the logical constraints, the expected performance loss, and the iterative process when updating the state of certainty for the demand. Then, the restoration interdependency is addressed through the network flow method to determine the connectivity of the restoration crews from restoration depots to the disrupted components of different systems in the roadway network, which can directly affect the feasibility of a restoration schedule. In order to exemplify the capability of the model, this study conducts numerical experiments using test infrastructure networks built based on the infrastructure systems in Tucheng District, New Taipei City, Taiwan and conceives two cases of different patterns of system disruption. The results of the experiments demonstrate that the proposed model can optimize the restoration schedule based on the assessment of system resilience from a holistic perspective.