Energy Institute of Louisiana, University of Louisiana, Lafayette, Louisiana.
Department of Chemical Engineering, University of Louisiana, Lafayette, Louisiana.
Water Environ Res. 2019 Sep;91(9):865-876. doi: 10.1002/wer.1127. Epub 2019 May 6.
The main objective of this study was to demonstrate a computational approach of global sensitivity analysis (GSA) integrated with functional principal component analysis (fPCA) for activated sludge models through aggregation of time-dependent model response patterns into time-independent coefficients of functional principal components (PCs). This proposed approach addresses the main issue of time-varying character of GSA indices when calculated solely on the time-dependent model outputs. The GSA-fPCA methodology was implemented using the rigorous model Activated Sludge Model No. 3 (ASM3) as case study. The approach transforms the time-dependent model outputs into functional PCs prior to calculation of GSA indices to remove the time-varying character of the calculated GSA indices. This work focused on the evaluation of the following key computational factors that may significantly influence the performance of the GSA-fPCA methodology: (a) model parameter sampling range, (b) model simulation period, (c) basis functions system, and (d) state of the system being modeled-batch or continuous activated sludge process. Results show that first few functional PCs capture up to 100% of the curve patterns in the time-dependent model outputs. The sensitivity indices calculated from the PC scores via Morris' GSA technique elucidated parameter sensitivity patterns inherent to the complex mathematical structure of ASM3. PRACTITIONER POINTS: Functional principal components-mediated GSA technique to remove time-varying character of sensitivity indices derived from time-dependent dynamical models. Technique amenable to improving efficiency of capturing response patterns into few functional principal components through various basis functions. Identifying priority parameters for ASM3 model calibration requires specification of target model outputs to which parameter sensitivities are calculated. GSA-fPCA offers a comprehensive numerical approach to manipulating models depending on the intended applications: simple fast-responding models to complex models.
本研究的主要目的是展示一种将全局敏感性分析（GSA）与功能主成分分析（fPCA）相结合的计算方法，通过将时变模型响应模式聚集到时间独立的功能主成分（PC）系数中，对活性污泥模型进行分析。该方法解决了仅基于时变模型输出计算 GSA 指标时存在的主要问题。使用严格模型活性污泥模型 No.3（ASM3）作为案例研究，实现了 GSA-fPCA 方法。该方法在计算 GSA 指标之前，将时变模型输出转换为功能 PC，以去除计算的 GSA 指标的时变特征。本研究重点评估了可能显著影响 GSA-fPCA 方法性能的以下关键计算因素：（a）模型参数采样范围，（b）模型模拟周期，（c）基函数系统，以及（d）所建模系统的状态-间歇或连续活性污泥过程。结果表明，前几个功能 PC 捕获了时变模型输出中多达 100%的曲线模式。通过 Morris 的 GSA 技术从 PC 得分中计算出的敏感性指数阐明了 ASM3 复杂数学结构中固有的参数敏感性模式。实践者关注点：通过功能主成分介导的 GSA 技术去除从时变动态模型中得出的敏感性指数的时变特征。该技术可通过各种基函数来提高将响应模式捕获到少数几个功能主成分中的效率。要确定 ASM3 模型校准的优先级参数，需要指定要计算参数敏感性的目标模型输出。GSA-fPCA 提供了一种全面的数值方法来根据预期应用来操作模型：从简单快速响应模型到复杂模型。
