Mathias Stolpe

Bivium as a Mixed-Integer Linear Programming Problem

Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations over GF (2) into a combinatorial optimization problem. We convert the Boolean equation system into an equation system over *** and formulate the problem of finding a 0-1-valued solution for the system as a mixed-integer programming problem. This enables us to make use of several algorithms in the field of combinatorial optimization in order to find a solution for the problem and recover the initial state of Bivium. In particular this gives us an attack on Bivium B in estimated time complexity of 263.7 seconds. But this kind of attack is also applicable to other cryptographic algorithms.

Design of planar articulated mechanisms using branch and bound

Abstract.This paper considers an optimization model and a solution method for the design of two-dimensional mechanical mechanisms. The mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously. The underlying mechanical analysis model is based on a truss representation allowing for large displacements. For mechanisms undergoing large displacements elastic stability is of major concern. We derive conditions, modeled by nonlinear matrix inequalities, which guarantee that a stable equilibrium is found and that buckling is prevented. The feasible set of the design problem is described by nonlinear differentiable and non-differentiable constraints as well as nonlinear matrix inequalities.To solve the mechanism design problem a branch and bound method based on convex relaxations is developed. To guarantee convergence of the method, two different types of convex relaxations are derived. The relaxations are strengthened by adding valid inequalities to the feasible set and by solving bound contraction sub-problems. Encouraging computational results indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality.

Design optimization of jacket structures for mass production

We present an approach for sizing optimization of jacket structures, and apply it to investigate the conceptual design of jackets for offshore wind turbines. Conceptual design is an input to early structural and financial models, and is not based on integrated load analysis. A four-legged jacket for the DTU 10 MW wind turbine in 50 meter water depth is modelled by Timoshenko beam finite elements, and the structural dimensions of the beam cross sections are considered as continuous design variables. A structural optimization problem is formulated to minimize the jacket mass, with constraints on fatigue and ultimate limit states. The optimal design problem is then used to investigate how the optimized mass depends on the jacket leg distance, the number of sections, and the number of independent design variables. Results show that reinforcing joints with stubs and cans can reduce the jacket mass with 22 percent. The conceptual design investigation also shows that the legs should be almost vertical, and with at least four levels of X-braces. We conclude that structural optimization can provide useful insights in the conceptual design phase and lead to a better starting point for the further design and planning processes. Copyright c

A Concept for Global Optimization of Topology Design Problems

We present a concept for solving topology design problems to proven global optimality. We propose that the problems are modeled using the approach of simultaneous analysis and design with discrete design variables and solved with convergent branch and bound type methods. This concept is illustrated on two applications. The first application is the design of stiff truss structures where the bar areas are chosen from a finite set of available areas. The second considered application is simultaneous topology and geometry design of planar articulated mechanisms. For each application we outline a convergent nonlinear branch and bound method and present a numerical example.

Discrete Material Optimization of Laminated Composites: SIMP vs. Global Optimization

Design of laminated composites structures is becoming increasingly important as the use of composite materials steadily increases. This development is driven by the aerospace, automotive and wind turbine industries who need still lighter and stiffer/stronger structures. This presents a very challenging design task that calls upon structural optimization tools for providing basic design ideas. However, existing methods for handling laminated composites suffer from problems with local optima when optimizing the fiber orientation, which is the key to efficient design with laminated composites. To counter this problem Discrete Material Optimization (DMO) was suggested in [1] where an alternative parametrization of the optimization problem is used, inspired by the procedures in topology optimization. The idea is to discretize the problem by using only a limited number of pre-defined candidate fiber orientations, each described by a constitutive matrix, Ci. The optimization problem is then parameterized on the element level by expressing the constitutive matrix for lamina j as \( C_j = \sum _i x_{ij} C_i \) where \( \forall x_{ij} \in \left\{ {0,1} \right\} \) are the design variables for material i in lamina j. The objective of the optimization is then to choose one distinct material from the set of candidates, i.e. \( \sum _i x_{ij} = 1,\forall j \). The design variables, xij, may be associated with a specific lamina/element or a patch consisting of several laminae/elements, thereby significantly reducing the total number of design variables. The constitutive matrices,Ci, may represent any type of material, allowing for simultaneously optimization for fiber orientation and material choice.

Fracture mechanics approach to optimize inspection planning of offshore welds for wind turbines

In the present work, fracture mechanics-based concepts are introduced into a fatigue life prediction framework used to optimise inspection planning of offshore welds for wind turbines. Offshore welds are typically subject to fatigue loading conditions in corrosive environments which can lead to accelerated crack growth, detrimentally affecting the structural integrity. The offshore wind industry commonly applies inspection/repair procedures in conjunction with corrosion protection systems in order to prolong the lifetime of offshore welds. The research conducted through this work addresses three important issues in the offshore wind industry, namely, the optimal inspection interval, cost of maintenance as well as the impact of protection system failure on the maintenance planning. This thesis is grossly divided into three different studies which encompass a stress-based fatigue approach, a fracture mechanics-based fatigue approach and a probability theory-based approach. Aforementioned fields are incorporated into inspection planning simulations, all of which are shown to provide meaningful predictions for the industry. Furthermore, the current research entails innovative approaches and methods used to simulate fatigue crack propagation in welded steel components with the following common characteristics: the Multiple-Site Damage and Residual Stresses. The research results presented herein show a strong dependency of the maintenance planning on the prevailing environmental conditions. Moreover, the parametric studies conducted suggest that the total maintenance costs can significantly vary depending on the adopted inspection planning strategy. The research results presented in this thesis can aid the development of cost effective solutions in the off-shore maintenance framework.

Optimal Design of Galvanic Corrosion Protection Systems for Offshore Wind Turbine Support Structures

The current work addresses a mass/cost-optimization procedure for galvanic anode cathodic protection systems based on both cathodic protection (CP) standards and numerical simulation. An approach i...