In the design of mechanical components and systems, nature has often been the source of inspiration. It is easy to point out solutions in nature that are optimal in some sense. One example is the structure of the surface of a shark's skin. This is designed by nature to minimize the resistance when the shark swims in the water. Another example is the shape of an egg shell. This is an optimal load carrying structure that often is found in engineering design applications. An even more fascinating question is how nature has found these optimal solutions? The answer to this question is evolution. Instead of just analyzing and copy optimal structures invented by nature it seems reasonable to mimic the process how nature has come up with these solutions. Research on how these ideas can be interpreted and used in engineering design started in the early seventies and has now become a large field known as Evolutionary Algorithms (EAs). During the past decade these methods have emerged as potent tools for engineering design optimization. Some of these methods are especially suited for problems that involve multiple objectives such as almost all real engineering design problems. Just until recently, these methods have seldom been used in the area of rotordynamical design. This thesis deals with the question how these methods can be adapted and applied in order to improve the design and design process of large rotor-bearing system. A hypothesis for this work is that EAs are suitable to use in the late design process of these systems. The aim of this work is to evaluate this hypothesis by studying real applications found in industry. This thesis comprises an introductory part and four appended papers. The introductory part is divided into three different sections. In the first section the concept of engineering design optimization is introduced. In the second part Genetic Algorithms (GAs) is presented. Finally, the analysis and design of rotor-bearing systems is discussed in more general terms. The purpose with the introductory part is to introduce and prepare the reader to the concepts discussed in the papers. The introductory part may serve as a survey or start point for newcomers interested in these areas. This overview is also the most important contribution of the introductory part of the thesis. The appended papers cover selected problems of constrained rotor- bearing system optimizations. In the papers A the multiobjective optimization of a generator is presented and discussed. Paper B introduces a constraint handling technique based on concepts found in multiobjective GAs. In paper C and D this techniques is used for two different rotor-bearing system optimization problems where the actual geometry parameters of the bearings are used as design variables.

In engineering design, nature has often been the source of inspiration. It is easy to point out solutions in nature that are optimal in some sense. One example is the roughness of the surface of a shark's skin. This is designed by nature to minimize the resistance when the shark swims in the water. Another example is the shape of an egg shell. This is an optimal load carrying structure which often is found in engineering design applications. An even more fascinating question is how nature has found these optimal solutions? The answer to this question is evolution. Instead of just analyzing and copying optimal structures invented by nature it seems reasonable to mimic the process how nature has came up with these solutions. Research on how these ideas can be interpreted and used in engineering design started in the early seventies and has now become a large field known as Evolutionary Algorithms (EAs). During the past decade these methods have emerged as potent tools for engineering design optimization. Some of these methods are especially suited for problems which involve multiple objectives such as almost all real engineering design problems. Just until recently, these methods have seldom been used in the area of rotordynamical design. This thesis deals with the question how these methods can be adapted and applied in order to improve the design and design process of large rotor-bearing system. A hypothesis for this work is that EAs are suitable to use in the late design process of these systems. The aim of this work is to evaluate this hypothesis by studying real applications found in industry. This thesis comprises an introductory part and five appended papers. The introductory part is divided into four different chapters. In the second chapter the concept of engineering design optimization is introduced. In the third chapter Genetic Algorithms (GAs) is presented. Finally, the analysis and design of rotor-bearing systems are introduced and discussed. The purpose with the introductory part is to introduce and prepare the reader to the concepts presented in the papers. The introductory part may serve as a start point for newcomers interested in these areas. The appended papers deal with different rotor-bearing system optimization problems and how these can be formulated and solved with GAs. Paper A introduces a constraint handling technique based on concepts found in multiobjective GAs. In Paper B the multiobjective optimization of a generator is presented and discussed. In Paper C and Paper D the constraint handling technique introduced in Paper A is used for two different rotor- bearing system where the actual bearing geometry parameters are used as design variables in the optimizations. In Paper E the feasibility of site balancing rewinded turbo generators is investigated by the use of a multiobjective GA.

The detailed design of a turbo generator rotor system is highly constrained by feasible regions for the damped natural frequencies of the system. A major problem for the designer is to find a solution that fulfills the design criterion for the damped natural frequencies. The bearings and some geometrical variables of the rotor are used as the primary design variables in order to achieve a feasible design. This paper presents an alternative approach to search for feasible designs. The design problem is formulated as an optimization problem and a genetic algorithm (GA) is used to search for feasible designs. Then, the problem is extended to include another objective (i.e., multiobjective optimization) to show the potential of using the optimization formulation and a Pareto-based GA in this rotordynamic application. The results show that the presented approach is promising as an engineering design tool

This paper presents the constrained optimization of the tilting pad bearing design on a gas turbine rotor system. A real coded genetic algorithm with a robust constraint handling technique is used as the optimization method. The objective is to develop a formulation of the optimization problem for the late bearing design of a complex rotor-bearing system. Furthermore, the usefulness of the search method is evaluated on a difficult problem. The effects considered are power loss and limiting temperatures in the bearings as well as the dynamics at the system level, i.e., stability and unbalance responses. The design variables are the bearing widths and radial clearances. A nominal design is the basis for comparison of the optimal solution found. An initial numerical experiment shows that finding a solution that fulfills all the constraints for the system design is likely impossible. Still, the optimization shows the possibility of finding a solution resulting in a reduced power loss while not violating any of the constraints more than the nominal design. Furthermore, the result also shows that the used search method and constraint handling technique works on this difficult problem.

Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Material- och solidmekanik.

Optimization of a rotor-bearing system with an evolutionary algorithm2004Ingår i: 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery: ISROMAC-2004 / [ed] Dieter Bohn, Aachen: Inst. of steam and gas turbines, RWTH , 2004Konferensbidrag (Refereegranskat)

6. Angantyr, Anders

et al.

Andersson, Johan

Linköping University.

Aidanpää, Jan-Olov

Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Material- och solidmekanik.

A criticism of Evolutionary Algorithms (EAs) might be the lack of efficient and robust generic might be the lack of officient and robust generic methods to handle constraints. The most widespread approach for constrained search problems is to use penalty methods. EAs have received increased interest during the last decade due to the ease of handling multiple objectives., A constrained Optimization problem or an unconstrained multiobjective problem may in principle be two different ways to pose the same underlying I problem. In this paper an alternative approach for the constrained optimization problem is presented. The method is a variant of a multiobjective real coded Genetic Algorithm (CA) inspired by the penalty approach. It is evaluated on six different constrained single objective problems found in the literature. The results show that the proposed method performs well in terms of efficiency, and that it is rohust for a majority of the test problems.