Browsing by Subject "Stochastic Modeling"

Storage systems play a vital part in modern IT systems. As the volume of data grows explosively and greater requirement on storage performance and reliability is put forward, effective and efficient design and operation of storage systems become increasingly complicated.

Such efforts would benefit significantly from the availability of quantitative analysis techniques that facilitate comparison of different system designs and configurations and provide projection of system behavior under potential operational scenarios. The techniques should be able to capture the system details that are relevant to the system measures of interest with adequate accuracy, and they should allow efficient solution so that they can be employed for multiple scenarios and for dynamic system reconfiguration.

This dissertation develops a set of quantitative analysis methods for modern storage systems using stochastic modeling techniques. The presented models cover several of the most prevalent storage technologies, including RAID, cloud storage and replicated storage, and investigate some major issues in modern storage systems, such as storage capacity planning, provisioning and backup planning. Quantitative investigation on important system measures such as reliability, availability and performance is conducted, and for this purpose a variety of modeling formalisms and solution methods are employed based on the matching of the underlying model assumptions and nature of the system aspects being studied. One of the primary focuses of the model development is on solution efficiency and scalability of the models to large systems. The accuracy of the developed models are validated through extensive simulation.

The proper modeling of uncertainties in constitutive models is a central concern in mechanics of materials and uncertainty quantification. Within the framework of probability theory, this entails the construction of suitable probabilistic models amenable to forward simulations and inverse identification based on limited data. The development of new manufacturing technologies, such as additive manufacturing, and the availability of data at unprecedented levels of resolution raise new challenges related to the integration of geometrical complexity and material inhomogeneity — both aspects being intertwined through processing.

In this dissertation, we address the construction, identification, and validation of stochastic models for spatially-dependent material parameters on nonregular (i.e., nonconvex) domains. We focus on metal additive additive manufacturing, with the aim of closely integrating experimental measurements obtained by collaborators, and consider the randomization of anisotropic linear elastic and plasticity constitutive models. We first present a stochastic modeling framework enabling the definition and sampling of non-Gaussian models on complex domains. The proposed methodology combines a stochastic partial differential approach, which is used to account for geometrical features on the fly, with an information-theoretic construction, which ensures well-posedness in the associated stochastic boundary value problems through the derivation of ad hoc transport maps.

We then present three case studies where the framework is deployed to model uncertainties in location-dependent anisotropic elasticity tensors and reduced Hill’s plasticity coefficients (for 3D printed stainless steel 316L). Experimental observations at various scales are integrated for calibration (either through direct estimators or by solving statistical inverse problems by means of the maximum likelihood method) and validation (whenever possible), including structural responses and multiscale predictions based on microstructure samples. The role of material symmetries is specifically investigated, and it is shown that preserving symmetries is, indeed, key to appropriately capturing statistical fluctuations. Results pertaining to the correlation structure indicate strong anisotropy for both types of behaviors, in accordance with fine-scale observations.