Multiobjective Optimization of Functionally Graded Material Columns

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

Modular design refers to a design approach whereby customized modules or components are assembled to form the layout plan of a building. Previous researches have attempted to optimize the layout plan design of low-rise houses for maximizing the natural daylighting, ventilation performance, and energy efficiency. Engineers have also studied the modular design of high-rise residential buildings to meet site constraints and to optimize site development potentials. However, the previous studies on modular building design were based on empirical trial-and-error approaches, efficient methods for identifying the optimal combination of different modules and components were still lacking in literature. Therefore, this study attempts to develop an innovative approach for optimizing the modular design of high-rise residential buildings, with the aim of maximizing the building energy performance while fulfilling the site constraints and design code requirements. The design optimization problem, including the design variables and objective functions, is properly formulated to guarantee the quality of final optimized deign. Provided a set of well-defined modules and components, evolutionary genetic algorithm (GA) is then utilized for the wide-ranging exploration of the building layout plans, taking into consideration the site conditions and building design requirements. A computer program is developed, coupling the GA optimization and energy modeling, to systematically evaluate the candidate layout plans. The energy simulation results are subsequently used to guide the GA towards finding the optimal design solution. The proposed optimization method is utilized to generate the optimal layout design for a 40-story high-rise residential building, using a set of pre-defined modular flat units. The optimal design maximizes the use of natural ventilation and daylighting to save 30-40% of the energy consumption without compromising the site constraints and design requirements. The findings of this study serve as the decision support basis to enhance modular design of high-rise residential buildings (such as energy conservation in this study), thereby improving the sustainability and cost-effectiveness of the built environment.

This work presents a method to develop computational models for topology optimization of linear elastic structures, when we have more than one objective function, each of them with different individual optimal solution.The method is developed for multi-objective optimization problems. Its purpose is to evolve an evenly distributed group of solutions to determinate the optimum Pareto set for the given problem.The algorithm evaluates a set of solutions (population) sorting it by considering domination properties and using a definition of filter to retain Pareto solutions.To reduce computational effort, it is introduced, in the initial population, optimal solutions of each of the single-objective problems.The computational model is applied and tested in two numerical applications.

A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples.

An optimization procedure is developed for the design of structural components under crashworthiness requirements. The optimization procedure consists of first developing a system of parallel neural networks able to reproduce the structural behavior during the crash phenomena. Training and test sets are generated by finite element analyses. Then, to find the optimal configuration, both sequential quadratic programming and genetic algorithms are implemented to evaluate the objective and constraint functions using the response surfaces generated by the neural networks. The procedure is applied for the optimization of helicopter subfloor components. In this application, the objective function is taken equal to the sum of two terms: the crush force efficiency and the specific absorbed energy. The values of maximum and mean forces are constrained to meet crashworthiness requirements, whereas other constraints are applied to define the feasibility of the structural solution. The optimal configuration, obtained measuring orders of magnitude savings in the CPU time, allows an increase of the crush force efficiency equal to 18% and a decrease of the mass equal to 8%.

The mathematical model of thermomechanical coupling multi-objective topology optimization for anisotropic structures was established using the element-free Galerkin (EFG) method, and the weighted function of compliance and heat dissipation was defined as the objective function. The proposed model and procedure were verified by the topological results based on the finite element method. The multi-objective EFG optimal topological structures have clearer boundary profiles even without using the sensitivity filtering technique. The effects of the weight coefficient, thermal conductivity factor, Poisson's ratio factor, off-angle and volume fraction on the multi-objective EFG optimal topological structure and multi-objective function were evaluated in detail, and reasonable ranges of the above parameters were recommended to improve the heat dissipation and mechanical performance. The multi-objective optimal results of the anisotropic structure were 3D printed and compared with the isotropic material, and their temperature, displacement and stress were improved, which reflects the advantages of orthotropic structures.

An electric power supply is the backbone of development in advanced as well as in developing economies. An integral part of ensuring a secure power supply system is a power communication system. Due to the high and sustained performance requirements of power communication systems, electric companies prefer to construct their own communication networks privately rather than relying solely on a public communication system. The focus of this paper is on the optimal topological design of a power communication network. Based on advanced optimization models in public communication networks, and taking into account the specific Quality of Service, as demanded by various applications, such as protection, SCADA, voice, etc., an optimization model (PC/ISO) has been developed. The PC/ISO requires tedious numerical processing. Hence, a Genetic Algorithm (GA) is proposed to solve the optimization problem. In order to demonstrate the application of the proposed model for a power system communication network design and in order to evaluate GA solver results, a case study on designing the optimal communication network topology of one of the Iranian Regional Electric Companies has been conducted. The results suggest that the PC/ISO model and its GA solver are entirely viable and offer a simple, accurate, and cost effective solution.

Mechanical properties of TiO2-Kaolin Functionally Graded Materials (FGMs) that combined TiO2 and Korean kaolin (Al2Si2O5(OH)4) in a graded distribution were experimentally investigated. TiO2 is an excellent photocatalysis material, however, it does not have the mechanical strength sufficiently. Therefore, FGMs were used as the photocatalysis materials with mechanical strength. To improve the mechanical properties, Korean kaolin was selected as a binder. Bulk FGMs were produced by vacuum filtration and compression involving wet filtration, mechanical compression and sintering. By this process, it is easy to control the thickness of FGMs. The porosity in FGM depends on the content of TiO2. The porosity in FGM decreases with increasing pressure of the compressor. The shrinkage decreases with increasing compression pressure at all ratios of TiO2 and kaolin. The materials have almost no shrinkage at 10 MPa. The bending strength and the Young’ modulus depends on content of TiO2. The bending strength of material was found to be approximately 2.5 MPa for 10 MPa compression pressure at TiO2 side. The bending strength and the Young’ modulus increases with increasing compression pressure. These results indicate that kaolin particles are useful to improve the strength of FGM. These properties of FGM, such as porosity, shrinkage, mechanical strength, etc., can be controlled by content of TiO2 and compression pressure. Based on an optimal design of production conditions, FGMs were developed for the nitrogen oxides (NOx) removal. The NOx reduction increases with increasing compression pressure. NO of 11.7 mg/m2h was removed under present conditions. The sintering temperature ensured the optimal removal of NOx was 800 oC. After NOx removal test, the FGMs were found to be free from erosion due to photocatalysis. And kaolin particles do not interfere in photocatalysis effect of TiO2. It can be concluded that TiO2-Kaolin FGM have a possibility for application to the air purification.

This paper addresses single and multiobjective topology optimization of truss-like structures using genetic algorithms (GA's). In order to improve the performance of the GA's (despite the presence of binary topology variables) a novel approach based on kinematic stability repair (KSR) is proposed. The methodology consists of two parts, namely the creation of a number of kinematically stable individuals in the initial population (IP) and a chromosome repair procedure. The proposed method is developed for both 2D and 3D structures and is shown to produce (in the single-objective case) results which are better than, or equal to, those found in the literature, while significantly increasing the rate of convergence of the algorithm. In the multiobjective case, the proposed modifications produce superior results compared to the unmodified GA. Finally the algorithm is successfully applied to a cantilevered 3D structure.

—This article presents a novel optimal design for a permanent magnet excitation transverse flux linear motor with an inner mover using bacterial foraging optimization. The target is maximizing the motor thrust force, which is the most important quantity in linear electric drives. The stator pole length, air-gap length, winding window width, and stator pole width define the search space for the optimization problem. The response surface methodology is used to build the mathematical model of the motor thrust force in terms of the design variables. It can create an objective function easily, and great computational time is saved. Finite-element computations are used for numerical experiments on the geometrical design variables to determine the coefficients of a second-order analytical model for the response surface methodology. The bacterial foraging optimization technique is used as a searching tool under the constraints of design variables for design optimization of the transverse flux linear motor to improve the motor thrust force. The effectiveness of the proposed bacterial foraging optimization model is then compared with that of both genetic algorithm and particle swarm optimization models. With this proposed bacterial foraging optimization technique, the thrust force of the initially designed transverse flux linear motor can be increased.

A novel approach to solve inverse heat conduction problems: Coupling scaled boundary finite element method to a hybrid optimization algorithm

Robotic flat-end milling of complex surfaces offers advantages such as high flexibility and high machining efficiency. In the process of planning the toolpath based on the cutter contact path, the robot functional redundancy and the tool orientation need to be solved carefully. This paper presents a posture optimization method for robotic flat-end milling. Taking the weighted sum of the machining width and the toolpath smoothness performance criterion as the objective function, an optimization model considering the joint limits and gouging avoidance is established. An efficient algorithm based on sequential quadratic programming is proposed to solve this nonconvex problem. During the execution of the algorithm, the machining width is efficiently calculated by an iterative method based on conformal geometric algebra, while its derivatives are approximated analytically. Simulations and experiments demonstrate that the presented technique can resolve the tool axis direction and the robot redundancy effectively to increase the machining width and improve the toolpath smoothness, thus reducing the time for machining and improving the surface quality.

IntroductionIn recent years, SMPMSM is quietly famous compared with other conventional motors in industrial applications due to higher efficiency, higher reliability, low cost, and smooth torque [1]–[3]. In general, several objective optimizations need to be consider, which required an optimization technique for an electrical motor. This paper deals with an optimal design of a surface-mounted permanent magnet synchronous machine (SMPMSM) with an exact analytical subdomain model by using a genetic algorithm method. To analyze the characteristic of permanent magnet (PM) motors, the classical optimization method, such as the finite element method (FEM), is intensively used. However, FEM has several time problems that require a longer computational time to evaluate the performance of PM motors. This problem can be overcome by using a genetic algorithm (GA) method combined with a subdomain model (SD), which developed an improved performance of SMPMSM, for instance, total harmonic distortion (THDv) and phase back-EMF. In this design, a three-phase 12-slot/8-pole PM motor is established with an exact SD model with radial magnetization patterns. Then, the GA ensemble with SD model to search the optimality of SMPMSM machine design. In the final analysis, the optimal new design of SMPMSM demonstrated by comparing with the initial design that is investigated by FEM. The result of induced back-EMF, and magnetic flux density of optimal design is compared with the initial design to show the advantages of GA optimization method.Analytical Model, Genetic Algorithm and Parameter of optimizationThe purpose of this analysis is to investigate the optimization design of a three-phase 12-slot/8-pole SMPMSM with a radial magnetization pattern. This optimization problem has been solved by obtains the minimum THDv as a fitness function. In order to process the optimization design of SMPMSM, several parameters need to be optimized i.e magnet pole-pitch, αp and slot-opening angle, boa. The roulette method is used to select the objective function of optimization with 50 maximum generations per iteration. The cross and mutation probability need to be set which requires linear and uniform recombination which is 0.89 and 0.025 respectively. The parameters of 12-slot/8-pole SMPM motor as follows: radius of the rotor, Rr = 23mm, the radius of PM surface Rm = 26mm, the inner radius of the stator Rsb = 42.5mm, axial length, la = 50mm, air-gap length, lg = 1mm, remanence of the magnet, Br, 1.12T, relative coil permeability, µr = 1.05 with the number of pole pairs, Np is 8 and number of stator slots, Ns is 12.The result, Discussion and ConclusionThe phase back electromotive force has a significant relationship with flux-linkage because phase back electromotive force is derived from the rate of change of flux-linkage. In Fig. 1. show the waveform of phase back electromotive force against rotor position of initial and optimal design in radial magnetization patterns. The initial design of phase back electromotive force waveform shows more trapezoidal compare with the optimal design which has a sinusoidal waveform. The comparison of total harmonic distortion between the initial and optimal design of SMPMSM are demonstrated in Fig. 2 below. The result from Fig.2. shows the highest total harmonic distortion of 12-slot/8-pole motor is an initial design which is 11.34% compared with the optimal design where 1.3%. The magnitude of harmonic in phase back electromotive force |En| of initial design shows 22.24 V compare to optimal design which is 17.4 V. This shows a good agreement that the optimal motor design gives lowest total harmonic distortion compare with the initial design. The optimizes of SMPMSM motor with the following parameters are given in Table 1. **

An effective artificial neural network together with a genetic algorithm have been demonstrated for predicting the optimal thermal performance of plain plate-fin heat sinks in a ducted flow under multi-constraints such as pressure drop, mass, and space limitations. A series of constrained optimal designs can be efficiently performed. Comparisons of the optimal results between the artificial neural network with genetic algorithm (ANN-GA) and the response surface methodology with sequential quadratic programming (RSM-SQP) methods are made. Although more training patterns are needed for the ANN-GA method as compared to that for the RSM-SQP method, the ANN-GA method which has randomly uniform-distributed training patterns in the whole solving domain can be applied to the global region of interest, not just in the region of operability. Consequently, a globally precise optimal solution can be achieved with the ANN-GA method; while the solution obtained with the RSM-SQP method may cause a significant error if the optimal values of the design variables happen to be located beyond the region of operability.

Power electronic devices have been widely applied such as in consumer devices and electrical vehicles, and improvement of their efficiency is strongly required. One of the main factors of energy loss in the devices is the magnetic core loss in inductors and transformers. Therefore, simulation technology that realizes accurate energy loss estimation based on magnetic characteristics of the materials has been highly demanded. For this reason, we have been developing large-scale magnetic field simulation technology by combining micromagnetic models and the finite element method (FEM) [1]. One the other hand, structural design optimization for devices with complicated shapes requires huge man-hours, and it is difficult to judge whether the designed shape is sufficiently optimized. Genetic algorithm (GA) is widely used in various optimal design problems for its excellent global search capabilities. However, GA generally requires large numbers of simulations, and it takes a long time to search the optimal solution. To solve this problem, neural networks (NN) are applied as surrogate models instead of physics models to reduce computing time in some previous work [2]. In this work, we perform shape parameter optimization of an EI-shaped inductor using GA and NN surrogate models designed from magnetic simulation results. Magnetic loss and volume of the cores are chosen to be objective functions. Few previous works have been reported on optimization studies with magnetic core loss as an objective function [3]. Here we solve multi-objective optimization problems, and Pareto optimal fronts for various inductance values are obtained. We also show that experiment that employs one of the optimal design parameters presents good agreement within 10% with the simulation results.