Backward erosion piping (BEP) is one of the major causes of seepage failures in levees. Seepage fields dictate the BEP behaviors and are influenced by the heterogeneity of soil properties. To investigate the effects of the heterogeneity on the seepage failures, we develop a numerical algorithm and conduct simulations to study BEP progressions in geologic media with spatially stochastic parameters. Specifically, the void ratio e, the hydraulic conductivity k, and the ratio of the particle contents r of the media are represented as the stochastic variables. They are characterized by means and variances, the spatial correlation structures, and the cross correlation between variables. Results of the simulations reveal that the heterogeneity accelerates the development of preferential flow paths, which profoundly increase the likelihood of seepage failures. To account for unknown heterogeneity, we define the probability of the seepage instability (PI) to evaluate the failure potential of a given site. Using Monte-Carlo simulation (MCS), we demonstrate that the PI value is significantly influenced by the mean and the variance of ln k and its spatial correlation scales. But the other parameters, such as means and variances of e and r, and their cross correlation, have minor impacts. Based on PI analyses, we introduce a risk rating system to classify the field into different regions according to risk levels. This rating system is useful for seepage failures prevention and assists decision making when BEP occurs.

Developing machine learning enabled smart manufacturing is promising for composite structures assembly process. It requires accurate predictive analysis on deformation of the composite structures to improve production quality and efficiency of composite structures assembly. The novel composite structures assembly involves two challenges: (i) the highly nonlinear and anisotropic properties of composite materials; and (ii) inevitable uncertainty in the assembly process. To overcome those problems, we propose a neural network Gaussian process model considering input uncertainty for composite structures assembly. Deep architecture of our model allows us to approximate a complex system better, and consideration of input uncertainty enables robust modeling with complete incorporation of the process uncertainty. Our case study shows that the proposed method performs better than benchmark methods for highly nonlinear systems. / Master of Science / Composite materials are becoming more popular in many areas due to its nice properties, yet computational modeling of them is not an easy task due to their complex structures. More-over, the real-world problems are generally subject to uncertainty that cannot be observed,and it makes the problem more difficult to solve. Therefore, a successful predictive modeling of composite material for a product is subject to consideration of various uncertainties in the problem.The neural network Gaussian process (NNGP) is one of statistical techniques that has been developed recently and can be applied to machine learning. The most interesting property of NNGP is that it is derived from the equivalent relation between deep neural networks and Gaussian process that have drawn much attention in machine learning fields. However,related work have ignored uncertainty in the input data so far, which may be an inappropriate assumption in real problems.In this paper, we derive the NNGP considering input uncertainty (NNGPIU) based on the unique characteristics of composite materials. Although our motivation is come from the manipulation of composite material, NNGPIU can be applied to any problem where the input data is corrupted by unknown noise. Our work provides how NNGPIU can be derived theoretically; and shows that the proposed method performs better than benchmark methods for highly nonlinear systems.

Surface water and groundwater systems consist of interconnected reservoirs, rivers, and confined and unconfined aquifers. The integrated management of such resources faces several challenges: High dimensionality refers to the requirement of the large number of variables that need to be considered in the description of surface water and groundwater systems. As the number of these variables increases, the computational requirements quickly saturate the capabilities of the existing management methods. Uncertainty relates to the imprecise nature of many system inputs and parameters, including reservoir and tributary inflows, precipitation, evaporation, aquifer parameters (e.g., hydraulic conductivity and storage coefficient), and various boundary and initial conditions. Uncertainty complicates very significantly the development and application of efficient management models. Nonlinearity is intrinsic to some physical processes and also enters through various facility and operational constraints on reservoir storages, releases, and aquifer drawdown and pumping. Nonlinearities compound the previous difficulties. Multiple objectives pertain to the process of optimizing the use of the integrated surface and groundwater resources to meet various water demands, generate sufficient energy, maintain adequate instream flows, and protect the environment and the ecosystems. Multi-objective decision models and processes continue to challenge professional practice. This research draws on several disciplines including groundwater flow modeling, hydrology and water resources systems, uncertainty analysis, estimation theory, stochastic optimization of dynamical systems, and policy assessment. A summary of the research contributions made in this work follows: 1.High dimensionality issues related to groundwater aquifers system have been mitigated by the use of transfer functions and their representation by state space approximations. 2.Aquifer response under uncertainty of inputs and aquifer parameters is addressed by a new statistical procedure that is applicable to regions of relatively few measurements and incorporates management reliability considerations. 3.The conjunctive management problem is formulated in a generally applicable way, taking into consideration all relevant uncertainties and system objectives. This problem is solved via an efficient stochastic optimization method that overcomes dimensionality limitations. 4.The methods developed in this Thesis are applied to the Jordanian water resources system, demonstrating their value for operational planning and management.