Enabling Higher Dimensionality of Temporal-Spatial Analysis Applied to Linear Scheduling of Construction Operations Based on Singularity Functions in Structural Engineering

该项目的目的是研究建筑和其他行业如何超越当前关键路径算法调度的概念限制，并更好地将其项目信息整合到二维中。现有的线性调度方法迄今仍然基本上是图形表示，因为缺乏全面的潜在数学基础，无法在如此高的维度上应用分析算法。为了解决这个问题，研究将利用数学类奇异函数固有的多功能性，并开发一种独立的新方法来分析和优化线性和重复的项目时间表。这个项目的可行性植根于线性表中基于离散几何的活动描述，基于奇异函数的有价值的数学性质，以及它们在结构分析中对各种荷载下的梁的现有应用。奇点函数是非常可取的，因为它们提供了一种灵活的方法，可以在单个数学表达式中对感兴趣的现象进行建模，这些数学表达式可能包含许多不同复杂程度的组件，但仍然可以用基本的几何和代数技能手动解决，以验证计算机计算。对国家首都地区重大项目进行详细进度分析的真实案例研究将有助于验证和确认。IT工具和相关的教育材料将为当前的项目经理、未来的项目经理和他们在课堂上的教育者以及其他研究人员带来扩展的分析能力。PI将把这项研究的成果带到美国天主教大学（CUA）的建筑、建筑和工程职业机会指导项目和各种工程预科暑期项目中，积极地让他们的选民，包括青年、妇女和少数民族，参与教育推广活动，帮助他们建立技能和对自己能力的信心。指数会与专业及学术界分享研究成果，包括在学术刊物发表研究成果、在重要会议上介绍研究进展和成果，以及利用教材为业界专业人士提供持续教育培训，以促进新方法的采用。这些材料将被整合到中国建筑学院以实践为导向的综合建筑课程中。所有材料将被放置在一个网站上，以便及时发布。新的进度分析实验室将成为一个孵化器，可以引导进一步的创新，实现完全信息集成和信息驱动的项目管理的长期愿景，并将为其研究生提供宝贵的研究经验。总体而言，该项目将加深对建筑项目在时间和空间维度之间相互作用的信息内容的理解，并将改进基础设施和资本建设设施的规划、分析和执行，以维持高质量的现代生活。建筑行业和其他行业中线性或重复性项目的利益相关者将能够通过更好的干扰检测、减少返工和优化的操作顺序，从提高资源利用率、更有效的现场布局、更安全的工作场所中获得经济效益。该项目对社会福利的预期贡献将是：(a)促进更好的决策，从而节省成本和时间；(b)培养年轻工程师成为学术界和建筑业的高素质进入者；(c)发展PI的研究、教学和服务领域，以实现富有成效的未来。

The objective of this project is to investigate how construction and other industries can move beyond the current conceptual limitations of the critical path method algorithm for scheduling and better integrate their project information in two dimensions. The existing linear scheduling method thus far has remained an essentially graphical representation for lack of a comprehensive underlying mathematical basis that would allow applying an analytical algorithm at such higher dimensionality. To address this issue, the research will utilize the inherent versatility of the mathematical class of singularity functions and develop a self-contained new method of analyzing and optimizing linear and repetitive project schedules. The feasibility of this project is rooted in the discrete geometry-based activity description in linear schedules, in the valuable mathematical properties of singularity functions, and in their existing application to beams under various loads in structural analysis. Singularity functions are very desirable as they present a flexible means of modeling a phenomenon of interest in a single mathematical expression that may contain numerous components of different degree of complexity, but can still be solved manually with basic geometry and algebra skills to verify computer calculations.Real-world case studies with detailed schedule analyses of major projects in the national capital region will serve for verification and validation. An IT tool and associated educational materials will bring the expanded analytical capabilities to current project managers in the field, to future project managers and their educators in the classroom, and to other researchers. The PI will bring the fruits of this research to the Career Opportunities in Architecture, Construction, and Engineering mentoring program and to various pre-engineering summer programs at The Catholic University of America (CUA) to actively involve their constituents, including youth, women, and minorities, in educational outreach activities that will help building their skills and confidence in their abilities. The PI will share outcomes of the research with the professional and academic communities by publishing in scholarly publications, presenting the progress and results at premier conferences, and using the educational materials in continuing education training for industry professionals to facilitate the adoption of the new method. The materials will be integrated into the comprehensive practice-oriented construction curriculum at CUA. All materials will be housed on a website for timely dissemination. The new schedule analysis laboratory will become an incubator that can lead to further innovations toward the long-term vision of a fully information-integrated and information-driven project management and will give its graduate students valuable research experience.Overall, this project will generate a deeper understanding of the informational content of construction projects in their interplay between the temporal and spatial dimensions and will lead to improved planning, analysis, and execution of creating the infrastructure and the capital constructed facilities that sustain the high quality of modern life. The stakeholders of projects of linear or repetitive nature in the construction industry and in other industries will be able to benefit economically from improved resource utilization, more efficient site layout, safer workplaces through better interference detection, reduced rework, and optimized sequencing of operations. The anticipated contributions of this project to society's welfare will be (a) facilitating better decision making that can yield cost and time savings, (b) grooming young engineers into highly qualified entrants into academia and construction, and (c) developing the PI's research, teaching, and service areas for a productive future.