[论文解读] On the estimation of sorption isotherm coefficients using the optimal experiment design approach

Julien Berger, Thomas Busser+2 more|arXiv (Cornell University)|Apr 15, 2017

Hygrothermal properties of building materials被引用 1

一句话总结

本研究提出一种最优实验设计（OED）方法，通过最小化模型与数据之间的差异，精确估算木材纤维材料的三个分配等温线系数。结合基于敏感度的OED与内点算法，并为两种不同的湿度阶跃实验分别设置成本函数，该方法降低了参数不确定性，提升了模型精度，尤其在更可靠地捕捉湿气吸附与解吸行为方面优于以往研究。

ABSTRACT

This paper deals with an inverse problem applied to the field of building physics to experimentally estimate three sorption isotherm coefficients of a wood fiber material. First, the mathematical model, based on convective transport of moisture, the optimal experiment design (OED) and the experimental set-up are presented. Then measurements of relative humidity within the material are carried out, after searching the OED, which is based on the computation of the sensitivity functions and a priori values of the unknown parameters employed in the mathematical model. The OED enables to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs, ensuring the best accuracy for the identification method and, thus, for the estimated parameter. Two experimental procedures were identified: i) single step of relative humidity from 10% to 75% and ii) multiple steps of relative humidity 10-75-33-75% with an 8-day duration period for each step. For both experiment designs, it has been shown that the sensor has to be placed near the impermeable boundary. After the measurements, the parameter estimation problem is solved using an interior point algorithm to minimize the cost function. Several tests are performed for the definition of the cost function, by using the L_2 or L_infty norm and considering the experiments separately or in the same time. It has been found out that the residual between the experimental data and the numerical model is minimized when considering the discrete Euclidean norm and both experiments separately. It means that two parameters are estimated using one experiment while the third parameter is determined with the other experiments. Two cost functions are defined and minimized for this approach. Moreover, the algorithm requires less than 100 computations of the direct model to obtain the solution. In addition, the OED sensitivity functions allow to capture an approximation of the probability distribution function of the estimated parameters. The determined sorption isotherm coefficients enable to calibrate the numerical model and fit better the experimental data, reducing the discrepancies usually reported in the literature that underestimate the moisture adsorption and overestimate the desorption processes.

研究动机与目标

• 为解决建筑建材中分配等温线参数估算不准确的挑战，特别是针对木材纤维材料。
• 减少文献中湿气吸附被低估而解吸被高估的差异。
• 开发一种最优实验设置，通过敏感度分析最大化参数识别精度。
• 通过识别最优传感器位置和边界条件，更精确地校准湿气传输模型。
• 通过最小化分配等温线参数的不确定性，提高建筑物理数值模拟的可靠性。

提出的方法

• 本研究采用基于对流湿气传输的数学模型，模拟木材纤维中的瞬态湿气扩散。
• 利用敏感度函数和先验参数值，通过最优实验设计（OED）从20种可能的实验设计中选择最佳实验配置。
• 测试了两种实验程序：单步湿度变化（10%至75%）和多步循环（10-75-33-75%，每步8天）。
• 通过内点算法进行参数估算，该算法最小化基于L₂范数的成本函数。
• 针对每项实验分别评估成本函数，使用离散欧几里得范数以最小化实验数据与模型预测之间的残差。
• 利用OED生成的敏感度函数，近似估计参数的概率分布，从而增强不确定性量化。

实验结果

研究问题

• RQ1 单步（10%至75%）与多步湿度循环（10-75-33-75%）实验设计中，哪一种能更准确地估算分配等温线系数？
• RQ2 在湿气传输实验中，传感器应放置在何处才能最大化参数识别精度？
• RQ3 成本函数范数选择（L₂与L∞）及实验分组方式如何影响参数估算性能？
• RQ4 与传统实验设计相比，OED方法是否能降低参数估算的不确定性并改善模型拟合？
• RQ5 所提出方法在多大程度上减少了文献中普遍存在的对木材纤维材料吸附过程低估和解吸过程高估的偏差？

主要发现

• 最优实验设计表明，传感器必须靠近不透湿边界布置，以最大化敏感度和参数精度。
• 单步（10%至75%）和多步（10-75-33-75%）湿度实验均有效，但为每项实验分别设置成本函数可获得更优结果。
• 采用离散欧几里得范数（L₂）并独立处理各项实验，可最小化模型预测与实验数据之间的残差。
• 内点算法在少于100次直接模型评估内即实现收敛，表明其计算效率高。
• OED敏感度函数使估计参数的概率分布得以近似，支持不确定性量化。
• 校准后的模型更准确地捕捉湿气吸附与解吸行为，减少了以往研究中报告的系统性偏差。