The use of Fixed Point Theory (FPT) to optimize the design of coupling beams in coupled core wall (CCW) systems is demonstrated. The basis for optimization is minimizing the transmissibility of horizontal ground motion by appropriately linking two coupled wall piers having different dynamic properties with beams having appropriate stiffness and damping characteristics. Using 21 example CCW structures illustrating a range of pier properties, it was shown that the resulting optimization of coupling stiffness is quite small and other design considerations will require stiffer, non-optimal coupling beams. Nonetheless, the potential to leverage the small amount of coupling available in a 'slab-coupled' series of wall piers in order to reduce transmissibility is suggested by the findings of this study.

Gases can migrate into the cemented annulus of a wellbore during early gelation when hydrostatic pressure within the cement slurry declines. Different means to describe hydrostatic pressure reduction have been proposed and reported in the literature. Among them, static gel strength (SGS) is the most-widely accepted concept in describing the strength development of hydrating cement. The classic shear stress theory proposed by Sabins et al. (1982) employs SGS to quantify the hydrostatic pressure reduction. API Standard 65-2 provides a standard for determining the transition time using the concept of SGS. Current industry practice is to reduce the transition time, thereby lowering the potential for invading gas introducing migration pathways in the cemented annulus. This approach, while certainly helpful in reducing the risk of gas migration, does not eliminate its occurrence. A better means to characterize cement matrix strength using fundamental concepts for replacing SGS is desired.

In this study, an enhanced wellbore simulation chamber (WSC) is developed to simulate hydrostatic pressure reduction in the cemented annulus and possible gas invasion under representative borehole conditions. In addition to the device itself, specific casting and testing protocols have been developed, which detail the procedures required for proper operation of the apparatus. The WSC makes adjustments to the existing cement hydration analyzers by providing representative wellbore conditions, which accounts for rock formation, real-scale wellbore section, and varying overburden pressure.

The results from the simulations ran using the WSC are quite revealing. The wellbore cross-sections from the WSC simulations show the porous cement that resulted in localized regions from pressurized fluids as well as gas channeling during cement gelation. The effects of different factors on hydrostatic pressure reduction are also investigated, including: formation permeability, initial overburden pressure, wellbore temperature, water-cement ratio, cement composition, and CaCl2-based accelerator. Experimental results verify that shortening transition time cannot change the occurrence of gas migration, as the microstructural development for the same slurry may be identical although the hydration occurs at different rate. The introduction of fundamental concepts in analysis provides the opportunity to parameterize slurry designs and other important factors associated with wellbore conditions.

Modern society is critically dependent on a network of complex systems for almost every social and economic function. While increasing complexity in large-scale engineered systems offer many advantages including high efficiency, performance and robustness, it inadvertently makes them vulnerable to unanticipated perturbations. A disruption affecting even one component may result in large cascading impacts on the entire system due to high interconnectedness. Large direct and indirect impacts across national and international boundaries of natural disasters like Hurricane Katrina, infrastructure failures like the Northeast blackout, epidemics like the H1N1 influenza, terrorist attacks like the 9/11, and social unrests like the Arab Spring are indicative of the vulnerability associated with growing complexity. There is an urgent need for a quantitative framework to understand resilience of complex systems with different system architectures. In this work, a novel framework is developed that integrates graph theory with statistical and modeling techniques for understanding interconnectedness, interdependencies, and resilience of distinct large-scale systems while remaining cognizant of domain specific details. The framework is applied to three diverse complex systems, 1) Critical Infrastructure Sectors (CIS) of the U.S economy, 2) the Kalundborg Industrial Symbiosis (KIS), Denmark and 3) the London metro-rail infrastructure. These three systems are strategically chosen as they represent complex systems of distinct sizes and span different spatial scales.

The framework is utilized for understanding the influence of both network structure level properties and local node and edge level properties on resilience of diverse complex systems. At the national scale, application of this framework on the U.S. economic network reveals that excessive interconnectedness and interdependencies among CIS significantly amplify impacts of targeted disruptions, and negatively influence its resilience. At the regional scale, analysis of KIS reveals that increasing diversity, redundancy, and multi-functionality is imperative for developing resilient and sustainable IS systems. At the urban scale, application of this framework on the London Metro system identifies stations and rail connections that are sources of functional and structural vulnerability, and must be secured for improving resilience. This framework provides a holistic perspective to understand and propose data-driven recommendations to strengthen resilience of large-scale complex engineered systems.

The in-situ measurement of thermal stress in civil and mechanical structures may prevent

structural anomalies such as unexpected buckling. In the first half of the dissertation, we present

a study where highly nonlinear solitary waves (HNSWs) were utilized to measure axial stress in

slender beams. HNSWs are compact non-dispersive waves that can form and travel in nonlinear

systems such as one-dimensional chains of particles. The effect of the axial stress acting in a

beam on the propagation of HNSWs was studied. We found that certain features of the solitary

waves enable the measurement of the stress.

In general, most guided ultrasonic waves (GUWs)-based health monitoring approaches

for structural waveguides are based on the comparison of testing data to baseline data. In the

second half of the dissertation, we present a study where some baseline-free signal processing

algorithms were presented and applied to numerical and experimental data for the structural

health monitoring (SHM) of underwater or dry structures. The algorithms are based on one or

more of the following: continuous wavelet transform, empirical mode decomposition, Hilbert

transform, competitive optimization algorithm, probabilistic methods. Moreover, experimental

data were also processed to extract some features from the time, frequency, and joint timefrequency

domains. These features were then fed to a supervised learning algorithm based on

artificial neural networks to classify the types of defect. The methods were validated using the

numerical model of a plate and a pipe, and the experimental study of a plate in water. In

experiment, the propagation of ultrasonic waves was induced by means of laser pulses or

transducer and detected with an array of immersion transducers. The results demonstrated that

the algorithms are effective, robust against noise, and able to localize and classify the damage.

The prediction of long-term deflection of large-span prestressed concrete bridges is a serious challenge to the current progress towards sustainable transportation system, which requires for a longer service lifetime. Although a number of concrete models and numerical formulations were proposed, the accuracy of prediction is not satisfactory and significant underestimate happens in structural analysis.

In order to overcome this obstacle, a unified viscoelasto-plastic damage model is proposed for the prediction of long-term performance of large-span prestressed concrete bridges carrying heavy traffic flow. In this unified concrete model, concrete cracking, plasticity and history-dependent behaviors (e.g. static creep, cyclic creep and shrinkage) are coupled. The isotropic damage model developed by Tao and Phillips enriched with the plastic yield surface is used in this study. For the static creep and shrinkage models, the rate-type formulation is applied so as to 1) save the computational cost and 2) make it admissible to couple memory-dependent and -independent processes. Cyclic creep, which is frequently ignored in structural analysis, is found to contribute substantially to the deflections of bridges with heavy traffic loads. The model is embedded in the general FEM program ABAQUS and a case study is carried out on the Humen Bridge Auxiliary Bridge. The simulation results are compared to the inspection reports, and the effectiveness of the proposed model is supported by the good agreement between the simulation and in-situ measurements.

The use of app-based, on-demand ride-sourcing services has spread rapidly and become more and more important in urban transport. Companies such as Uber and Lyft may provide better service with less waiting time and higher vehicle occupancy when compared to traditional transportation services such as private auto, public transit and taxis. This new type of transportation service is defined as ride-sourcing. This increase in the ride-sourcing availability, due to the introduction of Uber and Lyft, may impact travel habits and change the local, regional and national travel demand. The research compared the users’ differences in travel characteristics between traditional transportation services and new ride-sourcing services. This comparison was be done by conducting a survey in the Pittsburgh region to determine users’ attitude and travel habits when using ride-sourcing services. The results of the survey were used to compare to the travel characteristics of ride-source users to established travel behavior data and then determine how the impact of ride-sourcing on travel habits may be incorporated into the transportation planning process.

The findings indicate that ride-sourcing users are generally younger than the typical traveler, the service is used by a higher percentage of males and females. Social and recreational trips are the predominant type of trips used for ride-sourcing followed by work trips, trip lengths are shorter for all types of trips when compared to typical trip makers and vehicle occupancy rates are generally higher for ride-sourcing trips. Ride sourcing users generate more trips than typical traveler’s in the Pittsburgh region and the use of taxis and private autos are most impacted by ride sourcing where users’ shift away from these modes.

Currently, ride-sourcing is still a relatively small number of daily trips in an urban area. However as populations increase in urban areas and the demand for transportation facilities increases the new type of travel could increase to significant levels. It could be considered as a new transportation mode or categorized in as an auto mode in travel demand models.

Marcellus Shale is one of the world's largest unconventional gas resources. Recent developments in horizontal drilling and hydraulic fracturing enabled efficient and economical extraction of natural gas from unconventional (shale) resources and have led to rapid expansion of natural gas production in the United States. Hydrofracturing generates large volume of flowback and produced water that contains high concentrations of total dissolved solids (TDS), heavy metals, and naturally occurring radioactive materials (NORMs) resulting in significant environmental and public concerns and challenging waste management issues. Ra-226 is the dominant form of NORM and is one of the key challenges for sustainable management of Marcellus Shale wastewater.

This study is focused on the life cycle of NORMs during natural gas extraction from Marcellus Shale. A rapid method for Ra-226 analysis by inductively coupled plasma mass spectrometry (ICP-MS) was developed to overcome some of the shortcomings of current analytical techniques (e.g., long detection time). The fate of Ra-226 under different scenarios associated with the shale gas extraction, including origin of Ra-226, partitioning in flowback water storage and treatment facilities, and associated solid waste disposal issues were evaluated in this study. This study showed that radium mainly originates from relative rapid shale leaching. High concentration of radium in the Marcellus Shale wastewater can be managed by proper treatment (e.g., sulfate precipitation). However, solid waste generated from treatment facilities or impoundments containing elevated radium concentrations far exceed the limits for disposal in the Resource Conservation and Recovery Act Subtitle D (RCRA-D) landfills. Current practice in landfill management allows the disposal of this solid waste by controlling the Allowed Source Term Loading (ALST) on annual basis. However, if the landfill capacity to accept all the NORM generated from Marcellus Shale gas extraction becomes insufficient, other disposal or beneficial use options for solid waste should be developed. Reuse of radium enriched barite as weighting agent in drilling mud might be a sustainable strategy to reduce the mass of NORM that has to be disposed in the landfills.

Health risks associated with NORMs were evaluated for several typical scenarios associated with Marcellus Shale gas extraction. Total effective dose equivalent (TEDE) at drilling pads, storage impoundments and landfills are well below the Nuclear Regulatory Commission (NRC) limit for the general public of 100 mrem/yr even under the worst-case scenario assumptions. Workers in the centralized waste treatment facilities might receive excessive TEDE and appropriate measures recommended by NRC should be applied. For example, a safe distance of 5 m is recommended to reduce TEDE to acceptable level. Hence, the key environmental and public health risks associated with NORM brought to the surface by natural gas extraction from Marcellus Shale are from the spills that may contaminate surface and groundwater.

Overall, this study contributes to the understanding of the fate of NORMs associated with Marcellus Shale gas wastewater management and expands the ability to resolve the environmental concerns associate with NORMs. A novel rapid analytical for Ra-226 measurement by ICP-MS offers an alternative for researchers to quickly analyze environmental samples. The fate of Ra-226 in centralized treatment facilities and storage facilities is important for operators to choose proper management strategy for liquid and solid waste disposal/reuse. The health risk associated with NORM that is assessed in this study will help to resolve the public concern stemming from the high NORM extracted from Marcellus Shale play and provides several options to further reduced its risks.

This research investigates the development of life cycle assessment (LCA) in the building and healthcare industries. The ultimate goal is to advance necessary contributions and provide strategic recommendations on the development of LCA in both industries. Because the building industry has progressed farther in terms of environmental and economic assessments than the healthcare industry, the lessons learned from past implementation and market adoption of building LCAs is essential for the future of healthcare LCAs. To achieve the goal of this dissertation, the evolution of LCA in each industry was studied, followed by recommendations and strategies for future sustainable development.

To understand the building industry, three different studies are presented. The first building LCA study focused on building materials, comparing green building materials to traditional building materials and concluding that there is a quantitative need for LCA integration in the zero-energy building definition. The second LCA study integrated LCA with life cycle cost assessment (LCCA) as a complimentary tool for building owner decision-making. The last LCA study builds on the LCA/LCCA study and developed an integrated pathway linking LCA with a host of other environmental and economic tools that broaden the scope of building projects.

To understand the healthcare industry, three different studies are presented. The use of LCA in the healthcare industry is relatively new; therefore the first study compared two different birth procedures to determine the high-impact areas within healthcare. The second LCA study focused on disposable products discussing streamlining efforts and strategies that could be applied universally across the healthcare industry. The last healthcare LCA study is a set of organizational techniques that can be applied to any healthcare institution attempting to reduce their environmental impacts; the more advanced green teams integrating LCA for quantitative information.

The final study presented connects the building and healthcare industries, quantifying design decisions of evidence-based design and green building design through a host of metrics such as quality of care, utilities, and staff satisfaction. Both the building and healthcare industries have a tremendous amount of potential to enhance sustainable development utilizing life cycle assessment.

Adaptive Traffic Control Systems (ATCS) have recently been implemented across the world and are considered as a new tool to reduce traffic delays and stops in coordinated traffic signal systems, which are urgent problems regarding not only traffic flow efficiency, but also environmental issues. Excessive fuel consumption and vehicular emissions on urban streets can be reduced by maintaining optimal signal timings which reflect changes in traffic demand and distribution. It is hypothesized that there are environmental benefits to implementing ATCS as compared to traditional Time of Day (TOD) plans. This research develops a methodology to quantify these benefits and tests the methodology to establish the reduction in emissions for a signalized roadway corridor as a line source of emissions. The research also considers the linking between microsimulation models, emission models and dispersion models to estimate air quality benefits in a corridor at specific receptors.

This testing of the methodology was conducted by using a high-fidelity SYNCHRO microsimulation model of an 8-intersection corridor on Route 19 in Pittsburgh Pennsylvania. This signal system was recently converted from a traditional TOD timing plan operation to an ATCS operation, using the InSync system. The simulation results comparison showed significant reductions in all emission categories estimated by SYNCHRO. This first step in showing the benefits in a corridor can then be used to determine actual emission reductions at specific locations. Using simulation results from SimTraffic for an optimized TOD timing plan and the InSync system actual operations, a methodology was then hypothesized to integrate simulation emission results of the ATCS benefits with emission and dispersion models to indicate emission benefits at specific receptors.

The importance of bridge aerodynamic investigations was immediately realized after the Tacoma Narrows Bridge collapsed in 1940. Since then the aerodynamic control system that using moveable flaps to increase the aerodynamic stability of bridge has been an important aspect in bridge aerodynamic designs. In last two decades, the record of longest bridge in the world is refreshed frequently, which means the size of current bridges is much bigger than previous bridge. Basically, aerodynamic control system is an indispensable part of a super long bridge, and the active control system seems the only solution to improve the aerodynamic stability when the main span exceeds 3000 m. The purpose of this thesis is to study the effect of active aerodynamic control system with two sharp shape control devices installed on the edges of deck by FEM simulation. Here, the Tatara Bridge is analyzed via FEM software ABAQUS and SOLIDWORKS. This study consists of FEM modal analysis of the bridge, wind tunnel test simulation and wind effect test modeling for the entire bridge under the wind from different directions. In the bridge modal analysis, first 400 vibration mode shapes and their corresponding frequencies are calculated through Lanczos method solver in ABAQUS and the first order mode shape is found to be lateral bending of the deck. Therefore, the target is to optimize the deck shape to reduce the lateral aerodynamic force. To achieve this goal, 9 deck shapes are designed and tested under wind load from 15 different directions in the wind tunnel test simulation through SOLIDWORKS. The result of this test shows the optimized deck shapes can significantly reduce the lateral aerodynamic force. Then the wind effect tests of the entire bridge before and after optimization are performed in ABAQUS. As shown in the results, the displacement of midspan is decreased, especially in lateral direction. The results of this study indicate that this actively transformable sharp control surface can significantly reduce the response of the bridge under lateral aerodynamic force.

H-piles are widely used to support bridge piers and foundations, particularly those founded on relatively weak subsoil layers. The piles are forcefully driven to stronger layers to transfer the load of the entire structure to the bearing strata. Driven steel H-piles are designed to effectively interact with their surrounding environment in and out of the ground without failure. Standard practices such as AASHTO/LRFD and state codes regulate the load bearing capacity and drivability of H-piles to ensure safe performance during their service life.

This thesis investigates the feasibility of installing H-piles considering the limitations on the driving stress to achieve the design capacity (αASFy). Effects of parameters related to the soil-pile-hammer system have been studied. The gradual development of standard practices regulating the properties of H-piles related to material type, cross section geometry, pile length, and driving stress is discussed focusing on AASHTO/LRFD and PennDOT revisions to AASHTO. The results of a comprehensive parametric study carried out on the soil-pile-hammer system for 50 ksi driven H-piles are presented. 126 base scenarios, and 15 sensitivity analyses were constructed and analyzed using computer program GRLWEAP. In addition, 11 benchmark scenarios were considered to validate the study methodology approach using field data provided by PennDOT. An additional application of H-piles as driven ‘extended piles’ under combined axial and lateral load is briefly discussed and the effects of soil-pile interaction on the performance of pile is investigated.

The production and maintenance of Portland cement concrete pavements creates a considerable amount of waste water, usually with a high pH and high levels of dissolved and suspended solids and the safe disposal of this material can be costly. The ability to reuse this waste water as mixing water into new concrete production would be a more cost efficient option, which would greatly reduce waste. Due to the presence of existing cement particles and elevated pH, waste water with both hydrated and unhydrated cement particles used as mixing water affects the performance of the concrete. These effects can potentially be beneficial, even if the water has a percent solids higher than recommended in current mix water specifications. Therefore, a method of quantifying the characteristics of the waste water is necessary to predict the performance of the concrete based on measurable properties of the waste water. This study quantifies the characteristics of the waste water, including pH, conductivity, and index of refraction. Models are then developed using a regression analysis. This is accomplished by characterizing waste water produced using multiple different sources of both grinding and wash out fines. Then, mortar properties are tested from mortar batches made with the characterized waste water, including compressive strength and set time. The laboratory data is then used for the development of regression equations for predicting the performance (set time and compressive strength) of the concrete, as a function of the waste water characteristics that are easily measured using in-line sensors. These relationships makes it possible to use waste water from a variety of sources in the production of new concrete while, being able to predict the effects of the inclusion of the waste water on the concrete performance a priori. Finally, a mock set up of a plant water circulation system was constructed using in-line sensors for measuring the waste water properties. Concrete is then cast using water pulled from the lab-scale water circulation system to provide insight into the adequacy of the final models.

The Ucayali River, one of the largest rivers in the Peruvian Amazon, is one of the most dynamic rivers in the region. The Upper Ucayali River is a single-thread, meandering river, while the Lower Ucayali has multiple threads. Before being able to answer complex questions such as if the planform characteristics of Ucayali River are affected by climate change or land use change, the river itself needs to be characterized. The river can be characterized both in terms of the planform and morphometrics. I have developed a toolbox to facilitate the calculation of static planform statistics on meandering rivers, and have calculated some basic parameters of a reach of the Ucayali, including wavelength, amplitude, and orientation of bends. In order to understand the morphodynamic processes on the Lower Ucayali River, which has multiple threads, I have conducted a case study of one reach where two cutoffs have occurred in recent years, and where a third may soon happen. The study includes a temporal analysis using satellite imagery, hydrodynamic and morphodynamic field measurements and a two-dimensional Reynolds Average Navier Stokes (RANS) model, in order to predict how and when the cutoff may occur.

The formation of biofilm-electrodes is crucial for microbial fuel cell current production because optimal performance is often associated with thick biofilms. However, the influence of the electrode structure and morphology on biofilm formation is only beginning to be investigated. This study provides insight on how changing the electrode morphology affects current production of a pure culture of anode-respiring bacteria. Specifically, an analysis of the effects of carbon fiber electrodes with drastically different morphologies on biofilm formation and anode respiration by a pure culture (Shewanella oneidensis MR-1) were examined. Results showed that carbon nanofiber mats had -10 fold higher current than plain carbon microfiber paper and that the increase was not due to an increase in electrode surface area, conductivity, or the size of the constituent material. Cyclic voltammograms reveal that electron transfer from the carbon nanofiber mats was biofilm-based suggesting that decreasing the diameter of the constituent carbon material from a few microns to a few hundred nanometers is beneficial for electricity production solely because the electrode surface creates a more relevant mesh for biofilm formation by Shewanella oneidensis MR-1.

There is significant ongoing interest to develop smart structure technologies, such as those that can automatically detect their condition and/or actively change their geometry or material behaviors to adapt to adverse conditions or otherwise improve operational efficiency. Of the structural materials under development for smart structure applications, active smart materials are attracting increasing attentions due to their abilities to exhibit controlled variable stiffness through activation (e.g., thermal, electrical, or light activation) and experience extremely large deformations and shape changes without damage. Active smart materials, such as shape memory polymers, are currently being explored and show promise as morphing skins, replacements to mechanical hinges, and other structural components. Moreover, in a general sense any structure or structural component that is fully composed of active smart materials could have limitless shape-changing functionality if provided sufficient activation and actuation. Towards the design or control of smart structures to utilize such functionality, it is of paramount importance to develop strategies to efficiently solve the coupled multi-physics inverse problems of identifying the optimal activation stimulus and mechanical actuation to achieve desired morphing processes.

The objective of the present work is to develop and investigate a computational strategy for computationally efficient estimation of the parameters relating to the distribution and sequencing of activation and actuation for a morphing smart material structure or structural component to efficiently and effectively achieve a desired morphing function. This strategy combines a numerical representation of the morphing process with an optimization algorithm to estimate the activation and actuation parameters that best address cost functions and constraints relating to energy consumption, target shape change(s), morphing time, and/or damage prevention. In particular, the strategy is presented in the context of morphing structures or structural components composed of thermally responsive smart materials, and with specific properties based on thermally responsive shape memory polymers.

First, as a proof of concept, an initial computational framework is presented which combines a numerical representation of linear thermo-mechanical behavior of conceptual smart material structures with a non-gradient based optimization technique to identify the activation and actuation parameters to achieve the desired morphing process. The computational inverse mechanics approach is shown through numerical tests to provide a generalized and flexible means to facilitate the use of smart material structures to achieve desired morphing processes with controllable localized activation and actuation. Towards improving the computational efficiency, a variation of the computational framework based on a gradient-based optimization algorithm using the adjoint method is then presented. Numerical examples are shown to verify and test the computational approach, in which the synchronization of multiple activation and actuation parameters is optimized with respect to the energy cost and target shape changes in morphing skeletal structural components. The computational design approach with the adjoint method is shown to provide the capability to efficiently identify activation and actuation parameters to achieve desired morphing capabilities. Moreover, the computational approach is shown to be capable of determining energy-efficient design solutions for a diverse set of target shape changes with fixed instrumentation, providing the potential for substantial functionality beyond what could be expected through traditional empirical design strategies. Finally, to establish the theories and implementation aspects that would be applicable to a variety of structural behaviors, material types and morphing concepts, the efficient computational framework using the adjoint method is generalized to be applicable to various thermally-responsive smart materials. Numerical tests are shown to verify the generalized computational framework, in which the synchronization of multiple activation and actuation parameters is optimized with respect to energy cost and target shape changes in morphing structures with nonlinear thermo-mechanical behaviors (rather than the purely linear behaviors considered previously). In addition, the significant influence of the nonlinearity in the thermal modeling on the morphing processes, and ultimately the design solutions is explored.

Computational inverse characterization approaches that combine computational physical modeling and nonlinear optimization minimizing the difference between measurements from experimental testing and the responses from the computational model are uniquely well-suited for quantitative characterization of structures and systems for a variety of engineering applications. Potential applications that are suited for computational inverse characterization range from damage identification of civil structures to elastography of biological tissue. However, certain challenges, primarily relating to accuracy, efficiency, and stability, come along with any computational inverse characterization approach. As such, proper application-specific formulation of the inverse problem, including parameterization of the field to be inversely determined and selection/implementation of the optimization approach are critical to ensuring an accurate solution can be estimated with minimal (i.e. practically applicable) computational expense.

The present work investigates strategies to optimally utilize the available measurement data in combination with a priori information about the nature of the unknown properties to maximize the efficiency and accuracy of the solution procedure for applications in inverse characterization of localized material property variations. First, a strategy using multi-objective optimization for inverse characterization of material loss (i.e., cracks or erosion) in structural components is presented. For this first component, the assumption is made that sufficient a priori information is available to restrict the parameterization of the unknown field to a known number and shape of material loss regions (i.e., the inverse problem is only required to identify size and location of these regions). Since this type of parameterization would typically be relatively compact (i.e., low number of parameters), the inverse problem is well suited for non-gradient-based optimization approaches, which can provide accuracy through global search capabilities. The multi-objective inverse solution approach shown divides the available measurement data into multiple competing objectives for the optimization process (rather than the typical single objective for all measurement data) and uses a stochastic multi-objective optimization technique to identify a Pareto front of potential solutions, and then select one "best" inverse solution estimate. Through simulated test problems of damage characterization, the multi-objective optimization approach is shown to provide increased solution estimate diversity during the search process, which results in a substantial improvement in the capabilities to traverse the optimization search space to minimize the measurement error and produce accurate damage size and location estimates in comparison with analogous single objective optimization approaches. An extension of this multi-objective approach is then presented that addresses problems for which the quantity of localized changes in properties is unknown. Thus, a self-evolving parameterization algorithm is presented that utilizes the substantial diversity in the Pareto front of potential solutions provided by the multi-objective optimization approach to build up the parameterization iteratively with an ad hoc clustering algorithm, and thereby determine the quantity, size, and location of localized changes in properties with minimal computational expense. Similarly as before, through simulated test problems based on characterization of damage within plates, the solution strategy with self-evolving parameterization is shown to provide an accurate and efficient process for the solution of inverse characterization of localized property changes.

For the second half of the present work, a substantial change in the inverse problem assumptions is made, in that the nature (i.e., shape) of the property variation is no longer assumed to be known as precisely a priori Thus, a more general (e.g., mesh-based) parameterization of the unknown field is needed, which would typically come at a cost of significantly increased computational expense and/or loss of solution uniqueness. To balance the generalization of the approach and still utilize some amount of the knowledge that the solution is localized in nature, while maintaining efficiency, a hybrid compact-generalized parameterization approach is presented. The initial incarnation of this hybrid approach combines a machine learning data reconstruction strategy known as gappy proper orthogonal decomposition (POD) with a least-squares direct inversion approach to estimate material stiffness distribution in solids (i.e., to solve elastography problems). The direct inversion approach uses a generalized mesh-based parameterization of the unknown field, but full-field response measurements (i.e., measurements everywhere in the solid) are required, which are not available for most practical inverse characterization problems. Therefore, the gappy POD technique first identifies the pattern of potential response fields of the solid through a collection of a priori forward numerical analyses of the solid response with a specified compact parameterization and a corresponding collection of arbitrarily generated parameter sets. Once the pattern is identified, the gappy POD technique is able to use the available partial-field measurement data to estimate the full-field response of the solid to be used by the direct inversion. Thus, the computational cost of the inverse characterization is negligible once the gappy POD process has been completed. Through simulated test problems relating to characterization of inclusions in solids, the direct inversion approach with gappy POD is shown to provide highly efficient and relatively accurate inverse characterization results for the prediction of Young's modulus distributions from partial-field measurement data. This direct inversion approach is further validated through an example problem regarding characterization of the layered stiffness properties of an engineered vessel from ultrasound measurements. Lastly, an extension of this hybrid approach is presented that uses the characterization results provided by the previous direct inversion approach as the initial estimate for a gradient-based optimization process to further refine/improve the inverse solution estimate. In addition, the adjoint method is used to calculate the gradient for the optimization process with minimal computational expense to maintain the overall computational efficiency of the inverse solution process. Again, through simulated test problems based on the characterization of localized, but arbitrarily shaped, inclusions within solids, the three-step (gappy POD - direct inversion - gradient-based optimization) inverse characterization approach is shown to efficiently provide accurate and relatively unique inverse characterization estimates for various types of inclusions regardless of inclusion geometry and quantity.

Computational approaches to solve inverse problems can provide generalized frameworks for treating and distinguishing between the various contributions to a system response, while providing physically meaningful solutions that can be applied to predict future behaviors. However, there are several common challenges when using any computational inverse mechanics technique for applications such as material characterization. These challenges are typically connected to the inherent ill-posedness of the inverse problems, which can lead to a nonexistent solution, non-unique solutions, and/or prohibitive computational expense.

Toward reducing the effects of inverse problem ill-posedness and improving the capability to accurately and efficiently estimate inverse problem solutions, a suite of computational tools was developed and evaluated. First, an approach to NDT design to maximize the capabilities to use computational inverse solution techniques for material characterization and damage identification in structural components, and more generally in solid continua, is presented. The approach combines a novel set of objective functions to maximize test sensitivity and simultaneously minimize test information redundancy to determine optimal NDT parameters. The NDT design approach is shown to provide measurement data that leads to consistent and significant improvement in the ability to accurately inversely characterize variations in the Young's modulus distributions for simulated test cases in comparison to alternate NDT designs. Next, an extension of the NDT design approach is presented, which includes a technique to address potential system uncertainty and add robustness to the resulting NDT design, again in the context of material characterization. The robust NDT design approach uses collocation techniques to approximate the modified objective functionals that not only maximize the test sensitivity and minimize the test information redundancy, but now also maximize the test robustness to system uncertainty. The capability of this probabilistic NDT design method to provide consistent improvement in the ability to accurately inversely characterize variations in the Young's modulus distributions for cases where systems have uncertain parameters, such as uncertain boundary condition features, is again shown with numerically simulated examples. Lastly, an approach is presented to more directly address the computational expense of solving an inverse problem, particularly for those problems with significant system uncertainties. The sparse grid method is used as the foundation of this solution approach to create a computationally efficient polynomial approximation (i.e., surrogate model) of the system response with respect to both deterministic and uncertain parameters to be used in the inverse problem solution process. More importantly, a novel generally applicable algorithm is integrated for adaptive generation of a data ensemble, which is then used to create a reduced-order model (ROM) to estimate the desired system response. In particular, the approach builds the ROM to accurately estimate the system response within the expected range of the deterministic and uncertain parameters, to then be used in place of the traditional full order modeling (i.e., standard finite element analysis) in constructing the surrogate model for the inverse solution procedure. This computationally efficient approach is shown through simulated examples involving both solid mechanics and heat transfer to provide accurate solution estimates to inverse problems for systems represented by stochastic partial differential equations with a fraction of the typical computational cost.

Inverse problem solution methods have been widely used for nondestructive material characterization problems in a variety of fields, including structural engineering, material science, aerospace engineering and medicine. A traditional inverse problem solution approach for material characterization is to create a numerical representation of the system, such as a finite element model, combined with nonlinear optimization techniques to minimize the difference between the experimental response and the numerical representation. Unfortunately, due to the high computational cost of analyzing the numerical representation of many systems, it can often be impractical to solve a given inverse problem by this traditional method.\par

A strategy for using reduced-order modeling, in particular the proper orthogonal decomposition (POD) model reduction approach in inverse material characterization problems is presented in this work. POD is used to derive a low-dimensional basis from a finite set of full-order numerical analyses of the system. The governing equations of the system are projected onto the obtained POD basis to construct a reduced-order model (ROM). The ROM is then used to replace the full-order modeling to reduce the high computational cost, while still keeping the accuracy of the response close to that of the full-order model. After that, the ROM is combined with a global optimization algorithm to identify an estimation of the material properties in the system. A case study of a damaged aluminum plate, which is subjected to a time-dependent harmonic sinusoidal excitation, is chosen to demonstrate that the ROM strategy is capable of accurately identifying material parameters of a system with minimal computational cost.

One of the important hurdles in horizontal-well stimulation is the generation of hydraulic fractures (HFs) from all perforation clusters within a given stage, despite the challenges posed by stress shadowing and reservoir variability. In this paper, we use a newly developed, fully coupled, parallel-planar 3D HF model to investigate the potential to minimize the negative impact of stress shadowing and thereby to promote more-uniform fracture growth across an array of HFs by adjusting the location of the perforation clusters. In this model, the HFs are assumed to evolve in an array of parallel planes with full 3D stress coupling while the constant fluid influx into the wellbore is dynamically partitioned to each fracture so that the wellbore pressure is the same throughout the array. The model confirms the phenomenon of inner-fracture suppression because of stress shadowing when the perforation clusters are uniformly distributed. Indeed, the localization of the fracture growth to the outer fractures is so dominant that the total fractured area generated by uniform arrays is largely independent of the number of perforation clusters. However, numerical experiments indicate that certain nonuniform cluster spacings promote a profound improvement in the even development of fracture growth. Identifying this effect relies on this new model's ability to capture the full hydrodynamical coupling between the simultaneously evolving HFs in their transition from radial to Perkins-Kern-Nordgren (PKN)-like geometries (Perkins and Kern 1961; Nordgren 1972).