Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Structural optimization of lattice materials

Lattice materials are characterized at the microscopic level by a regular pattern of voids confined by walls. Recent rapid prototyping techniques allow their manufacturing from a wide range of solid materials, ensuring high degrees of accuracy and limited costs. The microstructure of lattice material permits to obtain macroscopic properties and structural performance, such as very high stiffness to weight ratios, highly anisotropy, high specific energy dissipation capability and an extended elastic range, which cannot be attained by uniform materials. Among several applications, lattice materials are of special interest for the design of morphing structures, energy absorbing components and hard tissue scaffold for biomedical prostheses. Their macroscopic mechanical properties can be finely tuned by properly selecting the lattice topology and the material of the walls. Nevertheless, since the number of the design parameters involved is very high, and their correlation to the final macroscopic properties of the material is quite complex, reliable and robust multiscale mechanics analysis and design optimization tools are a necessary aid for their practical application. In this paper, the optimization of lattice materials parameters is illustrated with reference to the design of a bracket subjected to a point load. Given the geometric shape and the boundary conditions of the component, the parameters of four selected topologies have been optimized to concurrently maximize the component stiffness and minimize its mass. Copyright © 2011 by ASME.

A method for VVER-1000 fuel rearrangement optimization taking into account both fuel cladding durability and burnup

A method for VVER-1000 fuel rearrangement optimization that takes into account both cladding durability and fuel burnup and which is suitable for any regime of normal reactor operation has been established. The main stages involved in solving the problem of fuel rearrangement optimization are discussed in detail. Using the proposed fuel rearrangement efficiency criterion, a simple example VVER-1000 fuel rearrangement optimization problem is solved under deterministic and uncertain conditions. It is shown that the deterministic and robust (in the face of uncertainty) solutions of the rearrangement optimization problem are similar in principle, but the robust solution is, as might be anticipated, more conservative. © 2013 Elsevier B.V.

Multi-objective optimization for multiphase orbital rendezvous missions

A multi-objective optimization approach was proposed for multiphase orbital rendezvous missions and validated by application to a representative numerical problem. By comparing the Pareto fronts obtained using the proposed method, the relationships between the three objectives considered are revealed, and the influences of other mission parameters, such as the sensors' field of view, can also be analyzed effectively. For multiphase orbital rendezvous missions, the tradeoff relationships between the total velocity increment and the trajectory robustness index as well as between the total velocity increment and the time of flight are obvious and clear. However, the tradeoff relationship between the time of flight and the trajectory robustness index is weak, especially for the four- and five-phase missions examined. The proposed approach could be used to reorganize a stable rendezvous profile for an engineering rendezvous mission, when there is a failure that prevents the completion of the nominal mission.

Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

From subspace learning to distance learning: A geometrical optimization approach

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continuously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. © 2009 IEEE.