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Inverse problems can be applied to aircraft in many areas. One of the disciplines within the aerospace industry with the most openly published data is in the area of aircraft performance. Many aircraft manufacturers publish performance claims, flight manuals and Standard Aircraft Characteristics (SAC) charts without any mention of the more fundamental technical information of the drag and engine data. With accurate tools, generalized aircraft models and a few curve-fitting techniques, it is possible to evaluate vehicle performance and estimate the drag, thrust and fuel consumption (TSFC) with some accuracy. This thesis is intended to research the use of aircraft performance information to deduce these aircraft--specific drag and engine models. The proposed method incorporates models for each performance metric, modeling options for drag, thrust and TSFC, and an inverse method to match the predicted performance to the actual performance. Each of the aircraft models is parametric in nature, allowing for individual parameters to be varied to determine the optimal result. The method discussed in this work shows both the benefits and pitfalls of using performance data to deduce engine and drag characteristics. The results of this method, applied to the McDonnell Douglas DC-10 and Northrop F-5, highlight many of these benefits and pitfalls, and show varied levels of success. A groundwork has been laid to show that this concept is viable, and extension of this work to additional aircraft is possible with recommendations on how to improve this technique.

This thesis concerns the approximation of optimally controlled partial differential equations for applications in optimal design and reconstruction. Such optimal control problems are often ill-posed and need to be regularized to obtain good approximations. We here use the theory of the corresponding Hamilton-Jacobi-Bellman equations to construct regularizations and derive error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method where the first, analytical, step is to regularize the Hamiltonian. Next its stationary Hamiltonian system, a nonlinear partial differential equation, is computed efficiently with the Newton method using a sparse Jacobian. An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its L2 projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems. In the thesis we present solutions to applications such as optimal design and reconstruction of conducting materials and elastic structures. / QC 20101110

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<p dir="ltr">Characterizing unknown space objects is an important component of robust space situational awareness. Estimating the shape of an object allows analysts to perform more accurate orbit propagation, probability of collision, and inference analysis about the object’s origin. Due to the sheer distance from the camera combined with diffraction and atmospheric ef- fects, most resident space objects of interest are unresolved when observed from the ground with electro-optical sensors. State of the art techniques for object characterization often rely on light curves — the time history of the object’s observed brightness. The brightness of the object is a function of the object’s shape, material properties, attitude profile, as well as the observation geometry. The process of measuring real light curves is complex, involv- ing the physics of the object, the sensor, and the background environment. The process of recovering shape information from brightness measurements is known as the light curve shape inversion problem. This problem is ill-posed without further assumptions: modern direct shape inversion methods require that the attitude profile and material properties of the object is known, or at least can be hypothesized. This work describes improvements to light curve simulation that faithfully model the environmental and sensor effects present in true light curves, yielding synthetic measurements with more accurate noise characteris- tics. Having access to more accurate light curves is important for developing and validating light curve inversion methods. This work also presents new methods for direct shape inver- sion for convex and nonconvex objects with realistic measurement noise. In particular, this work finds that improvements to the convex shape inversion process produce more accurate, sparser geometry in less time. The proposed nonconvex shape inversion method is effective at resolving singular large concave feature.</p>

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A class of immersed finite element (IFE) spaces is developed for solving elliptic boundary value problems that have interfaces. IFE spaces are finite element approximation spaces which are based upon meshes that can be independent of interfaces in the domain. Three different quadratic IFE spaces and their related biquadratic IFE spaces are introduced here for the purposes of solving both forward and inverse elliptic interface problems in 1D and 2D. These different spaces are constructed by (i) using a hierarchical approach, (ii) imposing extra continuity requirements or (iii) using a local refinement technique. The interpolation properties of each space are tested against appropriate testing functions in 1D and 2D. The IFE spaces are also used to approximate the solution of a forward elliptic interface problem using the Galerkin finite element method and the mixed least squares finite element method. Finally, one appropriate space is selected to solve an inverse interface problem using either an output least squares approach or the least squares with mixed equation error method. / Ph. D.

A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This method includes a unique solution algorithm and a design tangency boundary condition which directly relates the target pressure to shape modification. The new design method was evaluated with an upwind, cell-centered finite-volume formulation of the two-dimensional Euler equations. Controlled inverse design tests were conducted with a symmetric channel where the initial and target geometries were known. The geometric design variable was a channel-wall ramp angle, 0, which is nominally five degrees. Target geometries were defined with ramp angle perturbations of J10 = 2 %, 10%, and 20 %. The new design method was demonstrated to accurately predict the target geometries for subsonic, transonic, and supersonic test cases; M=0.30, 0.85, and 2.00. The supersonic test case efficiently solved the design tests and required very few iterations. A stable and convergent solution process was also demonstrated for the lower speed test cases using an under-relaxed geometry update procedure. The development and demonstration of the consistent direct-iterative method herein represent the important first steps required for a new research area for the advancement of aerodynamic inverse design methods. / Ph. D.