A new reliability-based data-driven approach for noisy experimental data with physical constraints
A new reliability-based data-driven approach for noisy experimental data with physical constraints
复制标题
一种新的基于可靠性的数据驱动方法，适用于具有物理约束的噪声实验数据
DOI：
10.1016/j.cma.2017.08.027
复制
发表时间：
2018
影响因子：
7.2
通讯作者：
N. EsquillorS.
中科院分区：
文献类型：
--
作者：
Jacobo Ayensa;M. H. Doweidar;J. A. Sanz;Manuel Doblar´e;Campus R´ıo;Edificio ID Mariano Ebro;N. EsquillorS.
数据科学以令人印象深刻的推动力闯入了基于模拟的工程科学。然而，数据从来都不是没有不确定性的，需要一种合适的方法来面对数据测量误差及其在具有完善的物理约束的问题中的内在随机性。与之前的工作一样，这里面临的这个问题是通过将标准数学建模方法与新的数据驱动求解器混合来解决问题的现象学部分，目的是找到一个解决点，满足一些约束，从而最小化到给定数据集的距离。然而，与在确定性框架中建立的此类工作不同，我们使用马哈拉诺比斯距离，以便在计算中纳入数据的统计二阶不确定性，即方差和相关性。我们开发了潜在的随机理论框架并建立了基本的数学和统计特性。由此产生的基于可靠性的数据驱动程序的性能在一个简单但说明性的一维问题以及更现实的 3D 结构问题解决方案中进行评估，该解决方案使用具有本质上随机本构行为的材料作为混凝土。结果表明，与其他数据驱动的求解器相比，除了允许低计算需求的不确定性管理的相关性之外，还具有更好的收敛性、更高的准确性、更清晰的解释和更大的灵活性。
Data Science has burst into simulation-based engineering sciences with an impressive impulse. However, data are never uncertainty-free and a suitable approach is needed to face data measurement errors and their intrinsic randomness in problems with well-established physical constraints. As in previous works, this problem is here faced by hybridizing a standard mathematical modeling approach with a new data-driven solver accounting for the phenomenological part of the problem, with the aim of finding a solution point, satisfying some constraints, that minimizes a distance to a given data-set. However, unlike such works that are established in a deterministic framework, we use the Mahalanobis distance in order to incorporate statistical second order uncertainty of data in computations, i.e. variance and correlation. We develop the underlying stochastic theoretical framework and establish the fundamental mathematical and statistical properties. The performance of the resulting reliability-based data-driven procedure is evaluated in a simple but illustrative unidimensional problem as well as in a more realistic solution of a 3D structural problem with a material with intrinsically random constitutive behavior as concrete. The results show, in comparison with other data-driven solvers, better convergence, higher accuracy, clearer interpretation, and major flexibility besides the relevance of allowing uncertainty management with low computational demand.