Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport

Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates

Slotted Rotatable Target Assembley and Systematic Error Analysis for a Search for Long Range Spin Dependent Interactions from Exotic Vector Boson Exchange Using Neutron Spin Rotation

We discuss the design and construction of a novel target array of nonmagnetic test masses used in a neutron polarimetry measurement made in search for new possible exotic spin dependent neutron–atominteractions of Nature at sub-mm length scales. This target was designed to accept and efficiently transmit a transversely polarized slow neutron beam through a series of long open parallel slots bounded by flat rectangular plates. These openings possessed equal atom density gradients normal to the slots from the flat test masses with dimensions optimized to achieve maximum sensitivity to an exotic spin-dependent interaction from vector boson exchanges with ranges in the mm - μm regime. The parallel slots were oriented differently in four quadrants that can be rotated about the neutron beam axis in discrete 90°increments using a Geneva drive. The spin rotation signals from the 4 quadrants were measured using a segmented neutron ion chamber to suppress possible systematic errors from stray magnetic fields in the target region. We discuss the per-neutron sensitivity of the target to the exotic interaction, the design constraints, the potential sources of systematic errors which could be present in this design, and our estimate of the achievable sensitivity using this method

High performance interior point methods for three-dimensional finite element limit analysis

The ability to obtain rigorous upper and lower bounds on collapse loads of various structures makes finite element limit analysis an attractive design tool. The increasingly high cost of computing those bounds, however, has limited its application on problems in three dimensions. This work reports on a high-performance homogeneous self-dual primal-dual interior point method developed for three-dimensional finite element limit analysis. This implementation achieves convergence times over 4.5× faster than the leading commercial solver across a set of three-dimensional finite element limit analysis test problems, making investigation of three dimensional limit loads viable. A comparison between a range of iterative linear solvers and direct methods used to determine the search direction is also provided, demonstrating the superiority of direct methods for this application. The components of the interior point solver considered include the elimination of and options for handling remaining free variables, multifrontal and supernodal Cholesky comparison for computing the search direction, differences between approximate minimum degree [1] and nested dissection [13] orderings, dealing with dense columns and fixed variables, and accelerating the linear system solver through parallelization. Each of these areas resulted in an improvement on at least one of the problems in the test set, with many achieving gains across the whole set. The serial implementation achieved runtime performance 1.7× faster than the commercial solver Mosek [5]. Compared with the parallel version of Mosek, the use of parallel BLAS routines in the supernodal solver saw a 1.9× speedup, and with a modified version of the GPU-enabled CHOLMOD [11] and a single NVIDIA Tesla K20c this speedup increased to 4.65×

Constraints on a Brane-World from the Vanishing of the Cosmological Constant

We derive the analogue of the vanishing of the cosmological constant in 3+1 dimensions, T_0^0 = 0, in terms of an integral over components of the energy-momentum tensor of a 4+1 dimensional universe with parallel three-branes, and an additional constraint local to the branes. The basic ingredients are the existence of a static solution of the Einstein equations, and the compactness of the 5th dimension. The corresponding constraints are applied to a general action of scalar fields with arbitrary potentials in the bulk and on the branes. The equations of motion are solved in a linearized approximation in the 5th dimension, whereupon they require the search for extrema of an ``effective potential'', which depends nonlinearly on the action in the bulk and on the branes. The previous constraints then turn into the vanishing of this ``effective potential'' at the extremum.Comment: 14 pages (LaTeX2e), no figs, v2:Local constraint and references adde

The Ultimate Solution Approach to Intractable Problems

There is now strong belief that P ? NP. This means that some very common problems cannot be solved efficiently under current and so called Von Neumann type computer architectures including parallel configurations. And, this will remain the case even in relatively low dimensions. What one may hope to achieve is the best possible solution given the available facilities within the allowed time. This makes the current definition of the optimum redundant for practical purposes. Therefore, a new definition of the optimum is required as well as appropriate approaches to find it. This paper will put forward a definition for the practical or sensible optimum, the s-optimum, consider its consequences and suggest what can be the ultimate approach to finding it. Although this approach is generic and can be applied in any context, optimisation and search are the specific contexts we will be concerned with here

Study on problems in detecting plural cracks by alternating flux leakage testing using 3D nonlinear eddy current analysis

The alternating magnetic flux leakage testing is used for the detection of cracks in a steel plate. A new technique of how to detect plural cracks, which are located at a very short distance from each other, using the parallel (x-) component of the leakage flux density is proposed. The behavior of leakage flux is examined using a three-dimensional edge-based hexahedral finite-element method. The effects of dimensions of search coils and cracks on the detection accuracy are illustrated. </p