**Author details**

212 Simulated Annealing – Single and Multiple Objective Problems

SA GA DE PS

problem.

4.35

4.4

4.45

Objective Function

4.5

4.55

**7. Conclusions** 

the mathematical model of the system.

for design and identification of mechanical systems.

Simulated Annealing and Simulated Quenching algorithms.

**Figure 6.** Boxplots showing the influence of different optimizaion strategies to solve the inverse

(a) Noiseless data. (b) Noisy data.

7

7.1

7.2

Objective Function

7.3

7.4

7.5

SA GA DE PS

In the present contribution, the mono and multi-objective algorithms based on Simulated Annealing were used in the design and identification of rotor bearing systems. For illustration purposes, two simple test-cases were studied by using the proposed methodology. The goal for the first application was to increase the difference between two critical speeds of the rotor-bearing system through the formulation of a multi-objective problem, where the radii of bar elements were taken as design variables. To solve this multiobjective problem the Multi-objective Optimization Simulated Annealing (MOSA) algorithm was proposed. This evolutionary strategy is based on the Simulated Annealing algorithm associated with the non-dominated sorting and crowding distance operators. The second application consists in the identification of unknown parameters of flexible rotor-bearing systems. The objective function was defined as the difference between the unbalance experimental responses of the rotor and the simulated unbalance responses so that the parameters of damping and stiffness are obtained by an inverse problem approach. The *experimental* (synthetic) data used were generated by using the solution of the direct problem and adding artificial noise. In all applications, the finite element method was used to obtain

It is important to emphasize that the results obtained in both test-cases are considered satisfactory as compared with those obtained by other evolutionary strategies. In addition, it is possible to conclude that the proposed methodology represents an interesting alternative

Further research work will be focused on the influence of the optimization parameter values on the solution of the optimization problem. Also, strategies to dynamically update the SA parameters will be evaluated. Finally, the authors will study the performance of the Simulated Quenching algorithm aiming at proposing a hybrid approach involving the Fran Sérgio Lobato, Elaine Gomes Assis and Valder Steffen Jr *Universidade Federal de Uberlândia, Brazil* 

Antônio José da Silva Neto *Universidade do Estado do Rio de Janeiro, Brazil* 
