Multiobjective Optimization

Transcription

1 Multiobjective Optimization MOO Applications Professores: Eduardo G. Carrano Frederico G. Guimarães Lucas S. Batista lusoba Universidade Federal de Minas Gerais Programa de Pós-Graduação em Engenharia Elétrica, Brasil

2 Topological Design of IPM Machine Sumário 1 IPM Machine Desing Topological Design of IPM Machine 2 Magnetic Actuator Design Design of a C-core Magnetic Actuator 3 Microwave Design Design of a Microwave Heating Device 4 Research Team Optimization Research Team 2 / 34

3 Topological Design of IPM Machine Reference Ant colony optimization for the topological design of interior permanent magnet (IPM) machines L. Batista, M. Li, F. Campelo, F. Guimarães, D. Lowther, and J. Ramírez Compel, v. 33, p , / 34

4 Topological Design of IPM Machine Motivation Optimization of Interior Permanent Magnet (IPM) machines High efficiency (compared to induction machines); High torque density (compared to conventional AC synchronous machines); Better demagnetization withstand (compared to surface mount PM machines). 4 / 34

5 Topological Design of IPM Machine The Topology Optimization Problem Each element of the discretized design space represents a discrete variable capable of assuming different material properties. 5 / 34

6 Topological Design of IPM Machine The Topology Optimization Problem The problem of topology optimization is essentially a problem of finding the optimal distribution of an arbitrary finite number of materials within a bounded subspace of R d : Find: ξ(ω) = arg max f (ξ(ω)) ξ { ξ(ω) S Ω Subject to: Problem constraints 6 / 34

7 Topological Design of IPM Machine The Nature-Inspired Method The inspiring source is the foraging behavior of real ants; Indirect communication among ants via pheromone trails enables them to find shortest paths between their nest and food sources; This characteristic of real ant colonies has inspired the definition and use of artificial ant colonies to search for approximate solutions to hard combinatorial optimization problems. 7 / 34

8 Topological Design of IPM Machine Artificial Ant System The basic idea behind the ACO approach consists in solving an optimization problem by repeating the following steps: Candidate solutions are constructed using a pheromone model (pheromone intensity distribution), i.e., a parametrized probability distribution over the solution space; Candidate solutions are evaluated and then used to modify the pheromone values in a way that is deemed to bias future sampling toward high quality solutions. 8 / 34

9 Topological Design of IPM Machine Graph Representation of the Design Region Each connection e u among nodes corresponds to a specific material property that can be assumed by the cell c ij : 9 / 34

10 Topological Design of IPM Machine Graph Representation of the Design Region Each candidate solution (ant) will represent a path, i.e., a valid topology, which is equivalent to a given distribution of materials. 10 / 34

11 Topological Design of IPM Machine Problem Definition The objective is to maximize the torque from the device: Find: ξ(ω) = arg max Torque ξ { Physical constraint on the Subject to: volume of the PM material. Three materials are distributed within the design region: air, iron, and permanent magnet. The design domain is discretized into a 8 8 square grid. 11 / 34

12 Topological Design of IPM Machine Results The final rotor topology obtained from the ACO system. This configuration generates a torque of Nm. 12 / 34

13 Topological Design of IPM Machine Results A different design objective function was also considered. Maximize the smoothness of the design topology: Find: ξ(ω) = arg max Smoothness ξ { Minimun torque constraint; Subject to: Maximum PM volume constraint. The design domain is discretized into a 9 18 square grid. 13 / 34

14 Topological Design of IPM Machine Results This configuration generates a torque of Nm. The results show the potential of the approach as a useful tool for applied topology optimization. 14 / 34

15 Design of a C-core Magnetic Actuator Sumário 1 IPM Machine Desing Topological Design of IPM Machine 2 Magnetic Actuator Design Design of a C-core Magnetic Actuator 3 Microwave Design Design of a Microwave Heating Device 4 Research Team Optimization Research Team 15 / 34

16 Design of a C-core Magnetic Actuator Reference Multi-domain Topology Optimization with Ant Colony Systems L. Batista, F. Campelo, F. Guimarães and J. Ramírez Compel, v. 30, p , / 34

17 Design of a C-core Magnetic Actuator Problem Definition Three materials are distributed within the design region: iron, permanent magnet, and air. The objective is to maximize the armature torque in the x-direction: Find: ξ(ω) = arg max T x (Armature) ξ 17 / 34

18 Design of a C-core Magnetic Actuator Problem Definition The armature and the yoke are solid blocks of ferromagnetic material (in our case, pure iron); The design domain is discretized into a 16 8 square grid: Each cell within the design domain can assume three states: air, pure iron, or a magnetic material (NdFeB magnets); We have considered magnetization direction pointing to the top in the figure (y-direction). 18 / 34

19 Design of a C-core Magnetic Actuator Results This configuration was able to generate an armature torque of N.m in the x-direction; This result is consistent with results reported in the literature for the particular configuration used in this work. 19 / 34

20 Design of a C-core Magnetic Actuator Results This problem was also solved considering 6 possible materials: air, iron, and magnet (up / down / right / left); The configuration obtained generated an armature torque of N.m. 20 / 34

21 Design of a Microwave Heating Device Sumário 1 IPM Machine Desing Topological Design of IPM Machine 2 Magnetic Actuator Design Design of a C-core Magnetic Actuator 3 Microwave Design Design of a Microwave Heating Device 4 Research Team Optimization Research Team 21 / 34

22 Design of a Microwave Heating Device Reference Dynamic Multiobjective Clonal Selection Algorithm for Engineering Design Lucas Batista, Diogo Oliveira, Frederico Guimarães, Elson Silva, and Jaime Ramírez IEEE Transactions on Magnetics, v. 46, p , / 34

23 Design of a Microwave Heating Device Problem Definition It is used to heat a water layer (sterilization processes); Its structure consists of six dielectric layers (l 1,...,l 6 ); Glass layers must support high pressures, air layers perform thermal insulation, and teflon layer provides mechanical resistance; The device receives microwave power from both sides. 23 / 34

24 Design of a Microwave Heating Device Problem Definition The width of each layer must be carefully specified in order to ensure as minimal power reflection as possible. The relative position between the power sources is also important due to constructive and destructive interferences. The pressurization process requires the temperature measured in the water layer to be maintained between 100 o C and 121 o C. The electric field computation is done by a recursive closed-form expression, and the thermal problem is solved by using the finite element method (FEM) in the time domain. 24 / 34

25 Design of a Microwave Heating Device Problem Definition The optimization problem consists of the maximization of the quantity of water and the minimization of the energy consumption, subject to the temperature constraints: min F {f 1, f 2 } f 1 ( x) = l 3 f 2 { ( x) = (P 1 + P 2 ) t h g1 ( x) T subject to o C 0 g 2 ( x) T 121 o C 0 25 / 34

26 Design of a Microwave Heating Device Results Estimated Pareto front: f 2 [GJ/1.44GJ] MCSA f 1 = l 3 [m] (a) Pareto front. 26 / 34

27 Design of a Microwave Heating Device Results For the decision-making process, we have selected the solution which corresponds to the most efficient device. W/cm b c d e interfaces (b) Power density. o C a b c d e interfaces f g (c) Temperature. 27 / 34

28 Optimization Research Team Sumário 1 IPM Machine Desing Topological Design of IPM Machine 2 Magnetic Actuator Design Design of a C-core Magnetic Actuator 3 Microwave Design Design of a Microwave Heating Device 4 Research Team Optimization Research Team 28 / 34

29 Optimization Research Team ORCS Lab. Eduardo Carrano, Felipe Campelo and Lucas Batista Development and application of optimization methods to complex systems; Data science and statistical modeling; Applications of computational intelligence to large-scale power and energy systems. 29 / 34

30 Optimization Research Team ORCS Lab. Optimization Evolutionary Computation and Other Metaheuristics Multi- and Many-Objective Optimization Multicriteria Decision Making Matheuristics Statistical Modeling and Inference Experimental Analysis and Comparison of Algorithms Reliability Modeling and Applications Applications Power and Energy Systems Aeronautical Systems Transportation Systems 30 / 34

31 Optimization Research Team Ricardo H. C. Takahashi CV: Main research areas: control theory; optimization theory (multiobjective optimization and evolutionary computation); applications in power and energy systems. 31 / 34

32 Optimization Research Team Rodney R. Saldanha CV: Main research areas: finite element methods; electromagnetic field calculation; mathematical programming methods; numerical methods; applications in power and energy systems. 32 / 34

33 Optimization Research Team João A. Vasconcelos CV: Main research areas: evolutionary computation tools; artificial intelligence; data mining; computational electromagnetics; applications in power and energy systems. 33 / 34

34 Optimization Research Team Petr I. Ekel CV: Main research areas: modeling, optimization and control of complex systems; uncertainty modeling and optimization; mathematical programming; multicriteria decision making. 34 / 34