Multi-objective Optimization Design Method Research Articles

A multi-objective optimization design method in zero energy building study: A case study concerning small mass buildings in cold district of China

This study aims to develop a new global multi-objective optimization design for zero energy buildings (ZEBs), integrating the multi-objective optimization technique with the comprehensive evaluation method technique. The study is conducted by adopting two design optimization methods for renewable energy systems in the building, including the multi-objective optimization using NSGA-II(Non-dominated Sorting Genetic Algorithm II)on the original design in terms of both costs and energy optimal designs, and then the mixture of grey correlation multi-level comprehensive evaluation method is applied to optimal design including the solar energy utilization efficiency, economy, energy conservation and social aspects. According to the selected determination based on global optimal design, the “best” solution, which can be guiding the scheme of practical engineering construction, is presented. In the end, a multi-objective design about a case study located in Tianjin of China is presented. Practice is proved that this method is beneficial to making effective scientific decisions.

Multi-objective aerodynamic optimization design of high-speed train head shape

To improve the aerodynamic performance of high-speed trains (HSTs) running in the open air, a multi-objective aerodynamic optimization design method for the head shape of a HST is proposed in this paper. A parametric model of the HST was established and seven design variables of the head shape were extracted. Sample points and their exact values of optimization objectives were obtained by an optimal Latin hypercube sampling (opt. LHS) plan and computational fluid dynamic (CFD) simulations, respectively. A Kriging surrogate model was constructed based on the sample points and their optimization objectives. Taking the total aerodynamic drag force and the aerodynamic lift force of the tail coach as the optimization objectives, the multi-objective aerodynamic optimization design was performed based on a non-dominated sorting genetic algorithm-II (NSGA-II) and the Kriging model. After optimization, a series of Pareto-optimal head shapes were obtained. An optimal head shape was selected from the Pareto-optimal head shapes, and the aerodynamic performance of the HST with the optimal head shape was compared with that of the original train in conditions with and without crosswinds. Compared with the original train, the total aerodynamic drag force is reduced by 2.61% and the lift force of the tail coach is reduced by 9.90% in conditions without crosswind. Moreover, the optimal train benefits from lower fluctuations in aerodynamic loads in crosswind conditions.

Optimal design and experiment of propellers for high altitude airship

The multi-objective optimization design method and experimental validation of the propeller for high altitude airships are presented in this paper. The method of predicting the propeller’s aerodynamic characteristics is based on the vortex theory. The non-dominated sorting genetic algorithm II is introduced and applied to solve the optimization problem. Then the optimization model which aims to design an efficient and lightweight propeller for high altitude airships is established based on the conditions of high altitude airships propulsion system. In addition, the effects of various design variables including pitch angle, chord length, diameter, rotational speed, and the number of blades on high altitude propeller performance are presented and discussed in a gradual manner. The optimization results indicate that the desirable tradeoff between the efficiency and weight of high altitude propeller is associated with the absorbed power, structural strength, and even the manufacturing and installation conditions. In order to evaluate the mathematical model and performance of the optimized propeller, wind tunnel experiments of scaled model on the basis of scaling laws and the full-scale propeller test using mobile testing system were carried out. It is shown that results obtained from the experiments agree well with those of the numerical calculation, which verifies that the designed propeller can satisfy the requirements of the high altitude airships’ propulsion system.

An improved multi-objective optimization method based on adaptive mutation particle swarm optimization and fuzzy statistics algorithm

ABSTRACTThis paper proposes an adaptive mutation particle swarm optimization (AMPSO) to realize multi-objective optimization design method through scale-based product platform theory model. The Pareto-optimal solution was obtained via AMPSO, then the fuzzy statistics algorithm is presented to extract the optimal solution of multi-objective optimization problem. The Multi-objective Optimization Method was carried out in two stages. In the first stage, each product is optimized independently via AMPSO and the product platform constant parameter and its value is obtained according to the change ratio of design variables; In the second stage, the scaling variables of each product are solved via AMPSO based on the optimization objectives improving the performance in constraint of restrictions and the best compromise solution is extracted based on fuzzy statistics algorithm.

A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun–Earth and the Earth–Moon systems

This paper considers the emergency trajectory design mission of libration point orbit transfer between the Sun–Earth system and the Earth–Moon system. In order to balance the two indexes of transfer time and fuel consumption, Halo orbits and their invariant manifolds in the circular restricted three body problem (CRTBP) are combined with low thrust in the bicircular restricted four body problem (BRFBP) to design the transfer trajectories. A fast multi-objective optimization method based on surrogate model which is greatly needed especially for emergency transfer missions is proposed to overcome the low-efficacy of original evolutionary multi-objective optimization methods. The advantages of the Sun–Earth manifolds, the Earth–Moon manifolds and the optimal control method are fully considered. In the part of numerical simulations, several simple problems with analytical solutions are first employed to validate the proposed fast optimization algorithm, then the proposed method is compared with NSGA-II for the same multi-objective transfer problem. Numerical results show that the fast optimization method chooses the expected samples and has a much higher efficiency than direct multi-objective optimization. The significance of the Sun–Earth manifolds and the Earth–Moon manifolds are considered. Several cases show the complicated relationship between transfer time and fuel consumption.

Muti-objective Topology Optimization of an Electric Vehicle's Traction Battery Enclosure

The traction battery enclosure is one of the most significant parts of an electric vehicle. Better structural performance and lightweight design of battery enclosure are extremely important in current situation. This paper introduces a multi-objective topology optimization design method for the traction battery enclosure, in which both the static stiffness and dynamic frequencies are taken into consideration. The optimization is utilized to achieve a new battery enclosure structure with better static and dynamic performances. The results illustrate that the structural topology optimization approach can be a feasible and efficient design methodology for the traction battery enclosure structural design and can provide the designer with detailed guidance in conceptual design phase.

Prototype and test of a novel rotary magnetorheological damper based on helical flow

To increase the output damping torque of a rotary magnetorheological (MR) damper with limited geometrical space, a novel rotary MR damper based on helical flow is proposed. A new working mode, helical flow mode, is discussed and applied to enlarge the flow path of MR fluids. The helical flow can improve the performance of the rotary damper by enlarging the length of the active region. Based on the idea, a rotary MR damper is designed. The rotary MR damper contains a spiral piston, dual-coil core, a rotating cylinder and a stator cylinder. Based on the Bingham model, the output damping torque of the damper is analytically derived. The finite element method (FEM) is applied to calculate the magnetic field of the active region. The multi-objective optimal design method is adopted to obtain the optimal geometric parameters. A prototype is fabricated based on the optimal results. To validate the proposed rotary MR damper, two types of experiments including the low rotation speed and the high rotation speed are investigated. The results show that the proposed rotary MR damper has high torque density and compact structure. The helical flow mode can increase the output damping torque with limited space.

Multiobjective Optimal Control of Longitudinal Seismic Response of a Multitower Cable-Stayed Bridge

The dynamic behavior of a multitower cable-stayed bridge with the application of partially longitudinal constraint system using viscous fluid dampers under real earthquake ground motions is presented. The study is based on the dynamic finite element model of the Jiashao Bridge, a six-tower cable-stayed bridge in China. The prime aim of the study is to investigate the effectiveness of viscous fluid dampers on the longitudinal seismic responses of the bridge and put forth a multiobjective optimization design method to determine the optimized parameters of the viscous fluid dampers. The results of the investigations show that the control objective of the multitower cable-stayed bridge with the partially longitudinal constraint system is to yield maximum reductions in the base forces of bridge towers longitudinally restricted with the bridge deck, with slight increases in the base forces of bridge towers longitudinally unrestricted with the bridge deck. To this end, a multiobjective optimization design method that uses a nondominating sort genetic algorithm II (NSGA-II) is used to optimize parameters of the viscous fluid dampers. The effectiveness of the proposed optimization design method is demonstrated for the multitower cable-stayed bridge with the partially longitudinal constraint system, which reveals that a design engineer can choose a set of proper parameters of the viscous fluid dampers from Pareto optimal fronts that can satisfy the desired performance requirements.

Passive Control System for Mitigation of Longitudinal Buffeting Responses of a Six-Tower Cable-Stayed Bridge

This paper presents an investigation of mitigation of longitudinal buffeting responses of the Jiashao Bridge, the longest multispan cable-stayed bridge in the world. A time-domain procedure for analyzing buffeting responses of the bridge is implemented in ANSYS with the aeroelastic effect included. The characteristics of longitudinal buffeting responses of the six-tower cable-stayed bridge are studied in some detail, focusing on the effects of insufficient longitudinal stiffness of central towers and partially longitudinal constraints between the bridge deck and part of bridge towers. The effectiveness of viscous fluid dampers on the mitigation of longitudinal buffeting responses of the bridge is further investigated and a multiobjective optimization design method that uses a nondominating sort genetic algorithm II (NSGA-II) is used to optimize parameters of the viscous fluid dampers. The results of the parametric investigations show that, by appropriate use of viscous fluid dampers, the top displacements of central towers and base forces of bridge towers longitudinally restricted with the bridge deck can be reduced significantly, with hampering the significant gain achieved in the base forces of bridge towers longitudinally unrestricted with the bridge deck. And the optimized parameters for the viscous fluid dampers can be determined from Pareto-optimal fronts using the NSGA-II that can satisfy the desired performance requirements.

Rotor Design of IPMSM Traction Motor Based on Multi- Objective Optimization using BFGS Method and Train Motion Equations

In this paper a multi-objective optimal design method of Interior Permanent Magnet Synchronous Motor (IPMSM) for traction applications so as to maximize average torque and to minimize torque ripple has been presented. Based on train motion equations and physical properties of train, desired specifications such as steady state speed, rated output power, acceleration time and rated speed of traction motor are related to each other. By considering the same output power, steady state speed, rated voltage, rated current and different acceleration time for a specified train, multi-objective optimal design has been performed by Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and Finite Element Method (FEM) has been chosen as an analysis tool. BFGS method is one of Quasi Newton methods and is counted in classic approaches. Classic optimization methods are appropriate when FEM is applied as an analysis tool and objective function isn’t expressed in closed form in terms of optimization variables.

Multi-objective optimization design method for the machine tool’s structural parts based on computer-aided engineering

In order to improve the static and dynamic performance of the machine tool’s structural parts and achieve lightweight design at the same time, a multi-objective optimization design method is proposed. The orthogonal experimental design method and response surface method are adapted to establish the optimization model, while a modified particle swarm optimization algorithm and grey relational analysis method are adapted to solve the model. The proposed method was used to conduct multi-objective optimization design for a gantry machine tool’s slide-seat. Based on the computer-aided engineering analysis, the response surface optimization model was established. After verifying the accuracy of response surface optimization model, five groups of non-inferior solutions are obtained by using the particle swarm optimization algorithm. The optimal design scheme was selected from the non-inferior solution set through using the grey relational analysis method, which reduces slide-seat’s mass and improves its static and dynamic performance considerably. After conducting static and dynamic experimental study on the slide-seats before and after multi-objective optimization design, the rationality and feasibility of the multi-objective optimization design method for the machine tool’s structural parts were verified.

Multi-Objective Optimization Design of a Magnetic Planetary Geared Permanent Magnet Brushless Machine by Combined Design of Experiments and Response Surface Methods

This paper proposes a new magnetic planetary geared permanent magnet brushless (MPG-PMBL) machine for hybrid electric vehicles. According to the dynamic performances in hybrid electric vehicles, the proposed machine needs to offer the advantages of high power density, high efficiency, and low torque ripple. To realize these goals, a multi-objective optimization design method based on the combined design of experiments approach and response surface method is presented, where three key optimization objectives of the efficiency, total loss, and cogging torque are selected. After the optimization, some reasonable key design variables are determined and the proposed MPG-PMBL machine is newly designed and built for evaluation. Both theoretical analysis and experimental results verify the validity of the proposed optimization method.

Low-carbon product multi-objective optimization design for meeting requirements of enterprise, user and government

In order to achieve government's supervision on enterprise's carbon emissions, it should be considered how to introduce carbon tax of carbon tax system into product design and how to handle resulting chain reaction and impact. Thus, it needs to handle not only the coupling or conflict among the design objectives of performance, cost, and carbon tax of enterprise product, but also the coupling or conflict of requirements among enterprise, user, and government. For handling this problem, this paper develops a low-carbon product multi-objective optimization design method for meeting triple win requirements of enterprise, user, and government, which is called L-CPMOD for short. This method successively builds trilateral requirement model, enterprise, user, and government their own requirement submodel, a three-level coupled systematic multi-objective optimization problem that is very difficult to solve. Thus, this paper proposes a solving approach that uses Non-dominated Sorting Genetic Algorithm II (NSGA-II) with a simplified solving strategy (NSGA with strategy way for short), which employs system decomposition, coupling relationship among variables and transformations among models in every layer. Finally, a case study shows that the proposed method is feasible.

NSGA-II를 이용한 마이크로 프로펠러 수차 블레이드 최적화

In addition to the development of micro hydro turbine, the challenge in micro hydro turbine design as sustainable hydro devices is focused on the optimization of turbine runner blade which have decisive effect on the turbine performance to reach higher efficiency. A multi-objective optimization method to optimize the performance of runner blade of propeller turbine for micro turbine has been studied. For the initial design of planar blade cascade, singularity distribution method and the combination of the Bezier curve parametric technology is used. A non-dominated sorting genetic algorithm Ⅱ(NSGA Ⅱ) is developed based on the multi-objective optimization design method. The comparision with model test show that the blade charachteristics is optimized by NSGA-II has a good efficiency and load distribution. From model test and scale up calculation, the maximum prototype efficiency of the runner blade reaches as high as 90.87%.

Integrated Multiobjective Optimal Design for Active Control System Based on Genetic Algorithm

The integrated multiobjective optimal design method for structural active control system is put forward based on improved Pareto multiobjective genetic algorithm, through which the position of actuator is synchronously optimized with active controller. External excitation is simulated by stationary filtered white noise. The root-mean-square (RMS) of structural response and active control force can be achieved by solving Lyapunov equation in the state space. The design of active controller adopts linear quadratic regulator (LQR) control algorithm. Minimum ratio of the maximum RMS of controlled structural displacement divided by the maximum RMS of uncontrolled structural displacement and minimum ratio of the maximum RMS of controlled structural shear divided by the maximum RMS of uncontrolled structural shear, together with minimization of the sum of RMS of active control force, are used as the three objective functions of multiobjective optimization. The optimization process takes the impact of structure and excitation parameter on the optimized results. An eight-storey six-span plane steel frame was used as an emulational example to demonstrate the validity of this optimization method. Results show that the proposed integrated multiobjective optimal design method is simple, efficient, and practical with good universality.

Multiobjective Design Optimization of Ironless Permanent Magnet Linear Synchronous Motors for Improved Thrust and Reduced Thrust Ripple

In order to achieve high thrust density and low thrust ripple simultaneously, a multiobjective optimization design method is applied to ironless permanent magnet linear synchronous motor with non-overlapping windings. On the basis of the magnetic field analysis model, the analytical formulae of key parameters such as No-load back EMF, thrust per copper quality and thrust ripple was deduced. Further, a multiobjective optimization is carried out by genetic algorithm to search for the optimal design variables. The design optimization is verified by 2-D Finite Element analysis and experimental results of the prototype.

Multi-objective optimization design method of the high-speed train head

With the continuous improvement of the train speed, the dynamic environment of trains turns out to be aerodynamic domination. Solving the aerodynamic problems has become one of the key factors of the high-speed train head design. Given that the aerodynamic drag is a significant factor that restrains train speed and energy conservation, reducing the aerodynamic drag is thus an important consideration of the high-speed train head design. However, the reduction of the aerodynamic drag may increase other aerodynamic forces (moments), possibly deteriorating the operational safety of the train. The multi-objective optimization design method of the high-speed train head was proposed in this paper, and the aerodynamic drag and load reduction factor were set to be optimization objectives. The automatic multi-objective optimization design of the high-speed train head can be achieved by integrating a series of procedures into the multi-objective optimization algorithm, such as the establishment of 3D parametric model, the aerodynamic mesh generation, the calculation of the flow field around the train, and the vehicle system dynamics. The correlation between the optimization objectives and optimization variables was analyzed to obtain the most important optimization variables, and a further analysis of the nonlinear relationship between the key optimization variables and the optimization objectives was obtained. After optimization, the aerodynamic drag of optimized train was reduced by up to 4.15%, and the load reduction factor was reduced by up to 1.72%.

Adaptive Multi-Objective Optimum Design of Journal Bearing Based on a Back-Stepping Approach

This article describes an adaptive multi-objective optimization journal bearing design method based on a back-stepping approach. Thermohydrodynamic lubrication analysis was used for accurate prediction of lubricant flow and power loss. The multi-objective optimization design method based on a back-stepping method was used to search for the optimum journal bearing design that can adaptively identify the equilibrium position of journal bearings and avoid iteration for the calculation of the equilibrium position of journal bearings. In the optimum journal bearing design, design variables such as radius, bearing length, radial clearance, journal eccentricity ratio, and attitude angle are used to simultaneously minimize oil flow and power loss. Comparisons between the adaptive optimization method and the conventional iteration method show that the proposed method can reduce the computational time of the optimization procedure, and the ability to find a diverse set of solutions was improved with the adaptive optimization methodology.

A Novel Method for Multiobjective Design and Optimization of Three Phase Induction Machines

A fast and efficient multiobjective optimization design method is developed for induction machines, which requires much fewer design iterations than the traditional design methods. In this new method, the number of prime variables that define the optimization is reduced to only six. A canonical particle swarm optimization (PSO) method with penalty function for design constraints is developed to find the optimal solution for a user-defined objective function. After several trial solutions with the PSO, the optimal regions for both the design variables and the performance indexes can be estimated. The results will provide useful information for both a drive system designer and a machine designer at an early stage of the design process. A comparison study of PSO and genetic algorithm (GA) is also performed in this paper, and the comparison shows that PSO is more successful in finding the global optima and also has better computational efficiency than GA. The original contributions of this paper are a novel induction machine design method, consideration of winding turn selection limitation, and a machine-design-focused comparison.

Multi-point and multi-objective optimization design method for industrial axial compressor cascades

Modern aerodynamic optimization design methods for the industrial axial compressor cascade mainly aim at improving both design point and off-design point performance. In this study, a multi-point and multi-objective optimization design method is established for the cascade, particularly aiming at widening the operating range while maintaining good performance at the acceptable expense of computational load. The design objectives are to maximize the static pressure ratio and minimize the total pressure loss coefficient at the design point, and to maximize the operating range for the positive and negative incidences. To alleviate the computational load, a design of experiment (DOE)-based GA–BP-ANN model is constructed to rapidly approximate the cascade aerodynamic performance in the optimization process. The artificial neural network (ANN) is trained by the genetic algorithm (GA) technique and back propagation (BP) algorithm, where the training cascades are sampled by the DOE method and analysed by the computational fluid dynamics method. The multi-objective genetic algorithm is used to search for a series of Pareto-optimum solutions, from which an optimal cascade is found out whose objectives are all better than (ABT) those of the original design. The ABT cascade is characterized by the lower camber and higher turning angle, leading to better aerodynamic performance in a widened operating range. Compared with the original design, the ABT cascade decreases the total pressure loss coefficient by 1.54 per cent, 23.4 per cent, and 7.87 per cent at the incidences of 5°, −9°, and 13°, respectively. The established optimization design method can be extended to the three-dimensional aerodynamic design of axial compressor blade.