Automated optimization of polymer extrusion dies using finite element analysis

An extrusion die is used to continuously produce parts with a constant cross section; such as sheets, pipes, tire components and more complex shapes such as window seals. The die is fed by a screw extruder when polymers are used. The extruder melts, mixes and pressures the material by the rotation of either a single or double screw. The polymer can then be continuously forced through the die producing a long part in the shape of the die outlet. The extruded section is then cut to the desired length. Generally, the primary target of a well designed die is to produce a uniform outlet velocity without excessively raising the pressure required to extrude the polymer through the die. Other properties such as temperature uniformity and residence time are also important but are not directly considered in this work. Designing dies for optimal outlet velocity variation using simple analytical equations are feasible for basic die geometries or simple channels. Due to the complexity of die geometry and of polymer material properties design of complex dies by analytical methods is difficult. For complex dies iterative methods must be used to optimize dies. An automated iterative method is desired for die optimization. To automate the design and optimization of an extrusion die two issues must be dealt with. The first is how to generate a new mesh for each iteration. In this work, this is approached by modifying a Parasolid file that describes a CAD part. This file is then used in a commercial meshing software. Skewing the initial mesh to produce a new geometry was also employed as a second option. The second issue is an optimization problem with the presence of noise stemming from variations in the mesh and cumulative truncation errors. In this work a simplex method and a modified trust region method were employed for automated optimization of die geometries. For the trust region a discreet derivative and a BFGS Hessian approximation were used. To deal with the noise in the function the trust region method was modified to automatically adjust the discreet derivative step size and the trust region based on changes in noise and function contour. Generally uniformity of velocity at exit of the extrusion die can be improved by increasing resistance across the die but this is limited by the pressure capabilities of the extruder. In optimization, a penalty factor that increases exponentially from the pressure limit is applied. This penalty can be applied in two different ways; the first only to the designs which exceed the pressure limit, the second to both designs above and below the pressure limit. Both of these methods were tested and compared in this work.

Automated design of self-stabilization

Self-stabilization is a property of a distributed system such that, regardless of the legitimacy of its current state, the system behavior shall eventually reach a legitimate state and shall remain legitimate thereafter. The elegance of self-stabilization stems from the fact that it distinguishes distributed systems by a strong fault tolerance property against arbitrary state perturbations. The difficulty of designing and reasoning about self-stabilization has been witnessed by many researchers; most of the existing techniques for the verification and design of self-stabilization are either brute-force, or adopt manual approaches non-amenable to automation. In this dissertation, we first investigate the possibility of automatically designing self-stabilization through global state space exploration. In particular, we develop a set of heuristics for automating the addition of recovery actions to distributed protocols on various network topologies. Our heuristics equally exploit the computational power of a single workstation and the available parallelism on computer clusters. We obtain existing and new stabilizing solutions for classical protocols like maximal matching, ring coloring, mutual exclusion, leader election and agreement. Second, we consider a foundation for local reasoning about self-stabilization; i.e., study the global behavior of the distributed system by exploring the state space of just one of its components. It turns out that local reasoning about deadlocks and livelocks is possible for an interesting class of protocols whose proof of stabilization is otherwise complex. In particular, we provide necessary and sufficient conditions – verifiable in the local state space of every process – for global deadlock- and livelock-freedom of protocols on ring topologies. Local reasoning potentially circumvents two fundamental problems that complicate the automated design and verification of distributed protocols: (1) state explosion and (2) partial state information. Moreover, local proofs of convergence are independent of the number of processes in the network, thereby enabling our assertions about deadlocks and livelocks to apply on rings of arbitrary sizes without worrying about state explosion.