We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. ...We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.展开更多
文摘为提高高速公路改扩建工程交通安全风险评估结果的确定性和准确性,建立了基于改进D-S证据理论的相关风险评估模型。首先建立包含24个影响因素的三层级评估指标体系;然后利用云模型(Cloud Model,CM)求出定性指标的基本信度赋值(Basic Probability Assignment,BPA),利用高斯隶属度函数求出定量指标BPA;接着,通过层次分析法确定各评估指标的权重,进而对各指标BPA进行加权;利用D-S证据理论融合加权后的BPA,归一化处理后得到改扩建工程交通安全风险状态评估结果。最后,为验证模型的准确性,选取沪陕高速公路平潮至广陵段高速公路改扩建工程作为实例进行交通安全风险评估。评估结果显示,实例工程的低风险水平隶属度最大,为0.6615,表明该实例总体处于低风险水平,与现有资料和现实情况吻合。同时发现,基于CM、AHP及D-S证据理论的评估模型对各评估指标进行量化、加权、融合后所得到的风险等级隶属度和不确定性有所区别,能更均衡地表示风险的隶属度,量化后的安全风险状态评估结果具有更好的准确性,解决了指标体系中模糊定性指标难以量化表征及指标差异化权重赋值的难题。
文摘We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.