混合不确定性分析,使用斯特-沙弗理论对心脏的抽进行混合不确定性分析
Yanyan He1, Nicholas A Battista2, Lindsay D Waldrop3
1Department of Mathematics, and of Computer Science and Engineering, University of North Texas, 1155 Union Circle, Denton, TX, 76203, USA. yanyan.he@unt.edu.
Journal of mathematical biology
|June 16, 2024
概括
这项研究提出了一种新的数字方法,用于心脏动模型中的混合不确定性传播,结合概率和斯特-沙弗理论. 该方法使用信念函数量化关键性能指标中的不确定性,有助于稳健的系统设计.
科学领域:
- 计算流体动力学的流体动力学.
- 不确定性定量化 不确定性定量化
- 生物医学工程 生物医学工程
背景情况:
- 在人工心脏等生物医疗系统中,环静脉送至关重要.
- 准确的建模需要处理随机的 (随机) 和认识的 (基于信念) 不确定性.
- 现有的方法可能无法完全捕捉混合不确定性传播.
研究的目的:
- 用概率和普斯特-沙弗理论引入混合不确定性传播的数值策略.
- 将这一策略应用于心脏系统中围心电平的计算模型.
- 使用信念函数量化对感兴趣量 (QoI) 的不确定性.
主要方法:
- 用随机变量表示随机不确定性,用信念函数表示认识不确定性.
- 通过环静止模型传播混合不确定性.
- 使用物理约束的通用多项式混乱 (gPC) 替代模型来降低计算成本.
- 执行全球敏感性分析以确定关键的不确定因素.
主要成果:
- 开发了一种数值方法,用于在环静电抽水模型中传播混合不确定性.
- 使用信念函数对 QoI (流量,运输成本,工作) 的量化不确定性.
- 灵敏度分析确定了关键的不确定的参数,并将不同静止模型的结果进行了比较.
- gPC替代品有效地近似了完整的模拟,降低了计算成本.
结论:
- 拟议的数值策略有效地处理复杂的生物医学系统中的混合不确定性.
- 信念函数提供了一种强大的方法来表示和传播QI统计中的认识体系不确定性.
- 该方法有助于识别关键设计参数,并提高心脏系统计算模型的可靠性.
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