This thesis introduces a new optimization algorithm for simulation-based design of systems with multi-modal, nonlinear, black box objective functions. The algorithm extends the recently introduced adaptive multi-modal optimization by incorporating surrogate modeling features similar to response surface methods (RSM). The resulting optimization algorithm has reduced computational intensity and is therefore well-suited for optimization of expensive black box objective functions. The algorithm relies on an adaptive and multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed to represent the objective function and to generate additional trial points in the vicinity of local minima discovered. The steps of mesh refinement and surrogate modeling continue until convergence criteria are met. An important property of this algorithm is that it produces progressively accurate surrogate models around the local minima; these models can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This algorithm is suitable for optimal design of complex engineering systems and enhances the design cycle by enabling computationally affordable uncertainty analysis. The mathematical basis of the algorithm is explained in detail. The thesis also demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions. It also shows several practical applications of the algorithm in the design of complex power and power-electronic systems.

This thesis introduces a new optimization algorithm for simulation-based design of systems with multi-modal, nonlinear, black box objective functions. The algorithm extends the recently introduced adaptive multi-modal optimization by incorporating surrogate modeling features similar to response surface methods (RSM). The resulting optimization algorithm has reduced computational intensity and is therefore well-suited for optimization of expensive black box objective functions. The algorithm relies on an adaptive and multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed to represent the objective function and to generate additional trial points in the vicinity of local minima discovered. The steps of mesh refinement and surrogate modeling continue until convergence criteria are met. An important property of this algorithm is that it produces progressively accurate surrogate models around the local minima; these models can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This algorithm is suitable for optimal design of complex engineering systems and enhances the design cycle by enabling computationally affordable uncertainty analysis. The mathematical basis of the algorithm is explained in detail. The thesis also demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions. It also shows several practical applications of the algorithm in the design of complex power and power-electronic systems.

The objective of this study is to develop an accurate surrogate modeling method for construction of the surrogate model to represent the performance measures of the compute-intensive simulation model in reliability-based design optimization (RBDO). In addition, an assessment method for the confidence level of the surrogate model and a conservative surrogate model to account the uncertainty of the prediction on the untested design domain when the number of samples are limited, are developed and integrated into the RBDO process to ensure the confidence of satisfying the probabilistic constraints at the optimal design. The effort involves: (1) developing a new surrogate modeling method that can outperform the existing surrogate modeling methods in terms of accuracy for reliability analysis in RBDO; (2) developing a sampling method that efficiently and effectively inserts samples into the design domain for accurate surrogate modeling; (3) generating a surrogate model to approximate the probabilistic constraint and the sensitivity of the probabilistic constraint with respect to the design variables in most-probable-point-based RBDO; (4) using the sampling method with the surrogate model to approximate the performance function in sampling-based RBDO; (5) generating a conservative surrogate model to conservatively approximate the performance function in sampling-based RBDO and assure the obtained optimum satisfy the probabilistic constraints. In applying RBDO to a large-scale complex engineering application, the surrogate model is commonly used to represent the compute-intensive simulation model of the performance function. However, the accuracy of the surrogate model is still challenging for highly nonlinear and large dimension applications. In this work, a new method, the Dynamic Kriging (DKG) method is proposed to construct the surrogate model accurately. In this DKG method, a generalized pattern search algorithm is used to find the accurate optimum for the correlation parameter, and the optimal mean structure is set using the basis functions that are selected by a genetic algorithm from the candidate basis functions based on a new accuracy criterion. Plus, a sequential sampling strategy based on the confidence interval of the surrogate model from the DKG method, is proposed. By combining the sampling method with the DKG method, the efficiency and accuracy can be rapidly achieved. Using the accurate surrogate model, the most-probable-point (MPP)-based RBDO and the sampling-based RBDO can be carried out. In applying the surrogate models to MPP-based RBDO and sampling-based RBDO, several efficiency strategies, which include: (1) using local window for surrogate modeling; (2) adaptive window size for different design candidates; (3) reusing samples in the local window; (4) using violated constraints for surrogate model accuracy check; (3) adaptive initial point for correlation parameter estimation, are proposed. To assure the accuracy of the surrogate model when the number of samples is limited, and to assure the obtained optimum design can satisfy the probabilistic constraints, a conservative surrogate model, using the weighted Kriging variance, is developed, and implemented for sampling-based RBDO.

No description available.

This research details a procedure for the systematic design of custom foot orthotics based on simulation models and their validation through experimental and clinical studies. These models may ultimately be able to replace the use of empirical tables for designing custom foot orthotics and enable optimal design thicknesses based on the body weight and activities of end-users. Similarly, they may facilitate effortless simulation of various orthotic and loading conditions, changes in material properties, and foot deformities by simply altering model parameters. Finally, these models and the corresponding results may also form the basis for subsequent design of a new generation of custom foot orthotics. Two studies were carried out, the first involving a methodical approach to development of engineering analysis models using the FEA technique. Subsequently, for model verification and validation purposes, detailed investigations were executed through experimental and clinical studies. The results were within 15% difference for the experimental studies and 26% for the clinical studies, and most of the probability values were greater than α= 0.05 accepting our null hypothesis that the FEA model data versus clinical trial data are not significantly different. The accuracy of the FEA model was further enhanced when the uniform loading condition was replaced with a more realistic pressure distribution of 70% of the weight in the heel and the rest in the front portion of the orthotic. This alteration brought the values down to within 22% difference of the clinical studies, with the P-values once again showed no significant difference between the modified FEA model and the clinical studies for most of the scenarios. The second study dealt with the development of surrogate models from FEA results, which can then be used in lieu of the computationally intensive FEA-based analysis models in the engineering design of CFO. Four techniques were studied, including the second-order polynomial response surface, Kriging, non-parametric regression and neural networking. All four techniques were found to be computationally efficient with an average of over 200% savings in time, and the Kriging technique was found to be the most accurate with an average % difference of below 0.30 for each of the loading conditions (light, medium and heavy). The two studies clearly indicate that engineering modeling, analysis and design using FEA techniques coupled with surrogate modeling methods offer a consistent, accurate and reliable alternative to empirical clinical studies. This powerful alternative simulation-based design framework can be a viable and valuable tool in the custom design of orthotics based on an individual's unique needs and foot characteristics. With these capabilities, the CFO prescriber would be able to design and develop the best-fit CFO with the optimal design characteristics for each individual customer without relying upon extensive and expensive trial and error ad hoc approaches. Such a model could also facilitate the inspection of robustness of resulting designs, as well as enable visual inspection of the impact of even small changes on the overall performance of the CFO. By adding the results from these studies to the CFO community, the prescription process may become more efficient and therefore more affordable and accessible to all populations and groups.

A study was performed to compare two different methods for generating surrogate models for the analysis and design of airfoils. Initial research was performed to compare the accuracy of surrogate models for predicting the lift and drag of an airfoil with data collected from highidelity simulations using a modern CFD code along with lower-order models using a panel code. This was followed by an evaluation of the Class Shape Trans- formation (CST) method for parameterizing airfoil geometries as a prelude to the use of surrogate models for airfoil design optimization and the implementation of software to use CST to modify airfoil shapes as part of the airfoil design process. Optimization routines were coupled with surrogate modeling techniques to study the accuracy and efficiency of the surrogate models to produce optimal airfoil shapes. Finally, the results of the current research are summarized, and suggestions are made for future research.

No description available.

Tsunami and storm surge are two of the main destructive and costly natural hazards faced by coastal communities around the world. To enhance coastal resilience and to develop effective risk management strategies, accurate and efficient tsunami and storm surge prediction models are needed. However, existing physics-based numerical models have the disadvantage of being difficult to satisfy both accuracy and efficiency at the same time. In this dissertation, several surrogate models are developed using statistical and machine learning techniques that can rapidly predict a tsunami and storm surge without substantial loss of accuracy, with respect to high-fidelity physics-based models. First, a tsunami run-up response function (TRRF) model is developed that can rapidly predict a tsunami run-up distribution from earthquake fault parameters. This new surrogate modeling approach reduces the number of simulations required to build a surrogate model by separately modeling the leading order contribution and the residual part of the tsunami run-up distribution. Secondly, a TRRF-based inversion (TRRF-INV) model is developed that can infer a tsunami source and its impact from tsunami run-up records. Since this new tsunami inversion model is based on the TRRF model, it can perform a large number of tsunami forward simulations in tsunami inversion modeling, which is impossible with physics-based models. And lastly, a one-dimensional convolutional neural network combined with principal component analysis and k-means clustering (C1PKNet) model is developed that can rapidly predict the peak storm surge from tropical cyclone track time series. Because the C1PKNet model uses the tropical cyclone track time series, it has the advantage of being able to predict more diverse tropical cyclone scenarios than the existing surrogate models that rely on a tropical cyclone condition at one moment (usually at or near landfall). The surrogate models developed in this dissertation have the potential to save lives, mitigate coastal hazard damage, and promote resilient coastal communities. / Doctor of Philosophy / Tsunami and storm surge can cause extensive damage to coastal communities; to reduce this damage, accurate and fast computer models are needed that can predict the water level change caused by these coastal hazards. The problem is that existing physics-based computer models are either accurate but slow or less accurate but fast. In this dissertation, three new computer models are developed using statistical and machine learning techniques that can rapidly predict a tsunami and storm surge without substantial loss of accuracy compared to the accurate physics-based computer models. Three computer models are as follows: (1) A computer model that can rapidly predict the maximum ground elevation wetted by the tsunami along the coastline from earthquake information, (2) A computer model that can reversely predict a tsunami source and its impact from the observations of the maximum ground elevation wetted by the tsunami, (3) A computer model that can rapidly predict peak storm surges across a wide range of coastal areas from the tropical cyclone's track position over time. These new computer models have the potential to improve forecasting capabilities, advance understanding of historical tsunami and storm surge events, and lead to better preparedness plans for possible future tsunamis and storm surges.

<div>The numerical calculation of the electromagnetic fields within electric machines is sensitive to the magnetic characteristic of steel. However, the magnetic characteristic of steel is uncertain due to fluctuations in alloy composition, possible contamination, and other manufacturing process variations including punching. Previous attempts to quantify magnetic uncertainty due to punching are based on parametric analytical models of <i>B-H</i> curves, where the uncertainty is reflected by model parameters. In this work, we set forth a data-driven approach for quantifying the uncertainty due to punching in <i>B-H</i> curves. In addition to the magnetic characteristics of steel lamination, the remanent flux density (<i>B_r</i>) exhibited by the permanent magnets in a permanent magnet synchronous machine (PMSM) is also uncertain due to unpredictable variations in the manufacturing process. Previous studies consider the impact of uncertainties in <i>B-H</i> curves and <i>B_r</i> of the permanent magnets on the average torque, cogging torque, torque ripple and losses of a PMSM. However, studies pertaining to the impact of these uncertainties on the combined machine/drive system of a PMSM is scarce in the literature. Hence, the objective of this work is to study the effect of <i>B-H</i> and <i>B_r</i> uncertainties on the performance of a PMSM machine/drive system using a validated finite element simulator. </div><div>Our approach is as follows. First, we use principal component analysis to build a reduced-order stochastic model of <i>B-H</i> curves from a synthetic dataset containing <i>B-H</i> curves affected by punching. Second, we model the the uncertainty in <i>B_r</i> and other uncertainties in <i>B-H</i> characteristics e.g., due to unknown state of the material composition and unavailability of accurate data in deep saturation region. Third, to overcome the computational limitations of the finite element simulator, we replace it with surrogate models based on Gaussian process regression. Fourth, we perform propagation studies to assess the effect of <i>B-H</i> and <i>B_r</i> uncertainties on the average torque, torque ripple and the PMSM machine/drive system using the constructed surrogate models.</div>

Estimating the structural weight of a Hybrid Wing Body (HWB) aircraft during conceptual design has proven to be a significant challenge due to its unconventional configuration. Aircraft structural weight estimation is critical during the early phases of design because inaccurate estimations could result in costly design changes or jeopardize the mission requirements and thus degrade the concept's overall viability. The tools and methods typically employed for this task are inadequate since they are derived from historical data generated by decades of tube-and-wing style construction. In addition to the limited applicability of these empirical models, the conceptual design phase requires that any new tools and methods be flexible enough to enable design space exploration without consuming a significant amount of time and computational resources. This thesis addresses these challenges by developing a parametric and physics-based modeling and simulation (M&S) environment for the purpose of HWB structural weight estimation. The tools in the M&S environment are selected based on their ability to represent the unique HWB geometry and model the physical phenomena present in the centerbody section. The new M&S environment is used to identify key design parameters that significantly contribute to the variability of the HWB centerbody structural weight and also used to generate surrogate models. These surrogate models can augment traditional aircraft sizing routines and provide improved structural weight estimations.