Multiscale Design under Uncertainty
Author: Yin, Xiaolei
Supervisor: Chen, Wei
Institution: Northwestern University, Evanston, Illinois
With the advances in physical, biological and material sciences, multiscale theories and models have been developed to gain a holistic understanding of physical phenomena at a system level by intelligently and efficiently combining the underlying physical mechanisms at multiple scales across the atomic, molecular, microscopic, and macroscopic scales. Building upon the advancements of multiscale modeling, Multiscale design is an emerging research paradigm that aims for achieving exceptional system performance through concurrent design of materials and product across multiple scales. However, challenges remain in the design of multiscale systems due to the complexity of multiscale analysis, coupled information exchanges, various uncertainty sources (especially those due to the random nature of materials), and the complexity of multiscale/multidisciplinary decision making. The objective in this dissertation is to develop formulations and efficient solution strategies for multiscale design under uncertainty, with a special emphasis on designing integrated hierarchical material and product systems.
To meet the challenges and facilitate multiscale design under uncertainty, design formulations and methods are first developed for generic research topics including the enhancement of probabilistic design optimization and statistical sensitivity analysis for hierarchical systems. In particular, new formulations that take into account the non-fixed variances are developed and integrated into the Sequential Optimization and Reliability Assessment (SORA) method. The developed formulations are generic enough to be extended and utilized in other probabilistic optimization strategies that involve the Most Probable Point (MPP) estimations. To facilitate the application of Statistical Sensitivity Analysis (SSA) to complex engineering systems with a hierarchical structure, a Hierarchical Statistical Sensitivity Analysis (HSSA) method is developed to manage the complexity of designing hierarchical engineering systems. A top-down strategy is introduced to invoke the SSA of critical submodels and later the SSA results at each individual scale are aggregated to measure the global impact of local submodel parameters without using additional samples. For multiscale design under uncertainty involving hierarchical materials and product design, efforts have been made to first develop computational methods for identifying critical material microstructure parameters with respect to material properties. A predictive stochastic volume element method is developed for studying material microstructure-property relations considering material random microstructure configurations. A comprehensive statistical cause-effect analysis approach is presented for determining critical microstructure parameters.
Statistical upscaling methods are then proposed to quantify uncertainty propagated from a fine scale to a coarse scale in a multiscale context. To quantify the uncertainty propagated from material microstructure to material property, a statistical calibration process is employed to calibrate probabilistic material constitutive models based on the simulations of random microstructure configurations. An efficient random field uncertainty propagation technique is proposed to estimate the uncertainty in product performances using advanced dimension reduction techniques for both uncertainty representation and propagation. Design methodologies and strategies are finally developed for designing multiscale systems under uncertainty. Based on the generalized hierarchical multiscale decomposition pattern in multiscale modeling, a set of computational techniques are developed to manage the complexity of multiscale design under uncertainty. Novel design of experiments and metamodeling strategies are proposed to manage the complexity of propagating random field uncertainty through three generalized levels of transformation: the material microstructure random field, the material property random field, and the probabilistic product performance. Multilevel optimization techniques are employed to find optimal design solutions at individual scales. The benefits of the proposed techniques are illustrated through a variety of mathematical examples and multiscale design problems. It is shown that the research developments in this dissertation are generally applicable to multiscale design under uncertainty with high effectiveness and efficiency, and thus provide intelligent computational techniques for designing innovative, multiscale engineered systems.