Multi-objective Design Optimization Research Articles

Multi-Objective Optimization Design of Cycloid-Pin Gears Based on RV Reducer Precision Transmission Performance

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke’s law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer.

Surrogate-Based Multi-Objective Optimization of Flux-Focusing Halbach Coaxial Magnetic Gear

Due to their contact-free and low-maintenance features, magnetic gears (MGs) have been increasingly investigated to amplify the torque of electric motors in electric vehicles (EVs). In order to meet the requirements of propelling EVs, it is essential to design an MG with a high torque density. In this paper, a novel flux-focusing Halbach coaxial MG (FFH-CMG) is proposed, which combines the advantages of flux focusing and Halbach permanent magnet (PM) arrays. The proposed structure has a higher torque performance and greater efficiency than conventional structures. A multi-objective design optimization based on a surrogate model is implemented to achieve the maximum volumetric torque density (VTD), torque-per-PM volume (TPMV), and efficiency, as well as the minimum torque ripple, in the proposed FFH-CMG. The employed optimization approach has a higher accuracy and is less time-consuming compared to the conventional optimization methods based on direct finite-element analysis (FEA). The performance of the proposed FFH-CMG is then investigated through 2D-FEA. According to the simulation results, the optimized FFH-CMG can achieve a VTD of 411 kNm/m3, and a TPMV of 830 kNm/m3, which are significantly larger than those of the existing MGs and make the proposed FFH-CMG very suitable for EV applications.

Multi-objective optimization for composition design of civil materials based on data-driven method

The performance of civil materials depends on their compositions. The material design is an important, challenging, and time-consuming work during the construction due to the complex relationship among different compositions and the conflict between properties and economic cost. This study developed a data-driven multi-objective optimization design framework to determine the reasonable material compositions based on laboratory experiment, reduced order model (ROM), and multi-objective optimization (MOO). The ROM was used to capture the complex relationship between the material compositions and the corresponding material performance. The MOO was utilized to determine the pareto optimal solution of compositions in the global space. Taking examples of cement grouts and modified asphalt binders, the develop framework was demonstrated and verified. The developed framework provides an excellent tool for composition design of civil materials.

Optimization Design of Surface-mounted Permanent Magnet Synchronous Motors Using Genetic Algorithms

The permanent magnet synchronous motor (PMSM) has gained widespread popularity in various industrial applications due to its simple structure, reliable performance, compact size, high efficiency, and adaptability to different shapes and sizes. Its exceptional characteristics have made it a focal point in industrial settings. The PMSM can be categorized into two primary types based on the arrangement of the permanent magnets (PM): interior permanent magnet (IPM) and surface-mounted permanent magnet (SPM). In the IPM, the magnets are embedded into the rotor, while in SPM, they are mounted on the rotor's surface. The utilization of PMs eliminates the need for excitation currents due to their high flux density and significant coercive force. This absence of excitation losses contributes to a notable increase in efficiency. In this study, a multi-objective optimal design approach is introduced for a surface mounted PMSM, aiming to achieve maximum efficiency while minimizing material costs. The optimization task is accomplished using a genetic algorithm. Furthermore, the motor designs are simulated using the finite element method (FEM) to assess and compare designs before and after the optimization process.

Multi-objective design optimization of an in-pipe inspection robot

In addition to inspection, In-Pipe Inspection Robots (IPIRs) could be enabled to perform other tasks, such as object retrieval and blockage clearing. In this study, a new IPIR is proposed with a design aimed at expanding its range of potential applications beyond inspection. The design methodology followed to facilitate the aforementioned application expansion commences with the development of a parametric preliminary design of an IPIR, in which the sizing of the robot parts are determined based on an optimization problem formulated in this work. The multi-objective optimization problem maximizes two contradictory objective functions, namely, its payload capacity, and the range of pipe diameters in which it can fit (radial range). The problem's Pareto front is solved using the NSGA-II implemented by Matlab's gamultiobj(.). The robot's final design is selected based on one of the Pareto-optimal solutions obtained from the Pareto front with a theoretical payload capacity of 11 kg and a radial range of 33 mm. The robot was manufactured and tested to validate such theoretical results.

A Multi-Objective Optimal Design Method for Gravity Compensators With Consideration of Minimizing Joint Reaction Forces

Abstract This paper presents a multi-objective optimal design method for gravity compensators with consideration of minimizing the joint reaction forces. High performance of the gravity compensation is achieved while the joint reaction forces are kept to a minimum. In this method, the ratio of the compensated torque to the uncompensated torque and the maximum value of the joint reaction forces are formulated as cost functions in the optimization problem, which is solved by adopting the Pareto front of multiple fitness functions with a genetic algorithm. This work takes a spring four-bar mechanism as a gravity compensator for a case study. The theoretical models of a gravity compensator and a robot manipulator show that the proposed multi-objective optimal design allows for the achievement of smaller joint reaction forces than the original single-objective optimal design, while their gravity compensation performances are relatively the same. Moreover, a prototype of a 0.2-kg gravity compensator realized from the proposed method was also built. An experimental study with this prototype showed that the measured motor torque was reduced by up to 93% within a range of 3π/4.

Optimization design of load-sharing and light weight of the twin rotors concentric face gear power-split transmission system based on gear tooth matching condition

To improve the dynamic load-sharing performance and achieve lightweight, the twin rotors concentric face gear power-split transmission system (TRFGPSTS) was optimized. The gear tooth matching conditions of the system based on the design characteristics of power flow closed-loop and virtual constraint configuration of the system are established, and the basic parameters of each gear meet the requirements of the system load-sharing layout and synchronous meshing of each branch movement are calculated. Based on the lumped mass parameter method, combined with the calculation results of gear tooth matching, the 45-DOF bending torsional coupling dynamic model of the system was established considering time-varying meshing stiffness, support stiffness, manufacturing and installation errors, and other factors, and the influence of each factor on the dynamic load-sharing performance of the system was analyzed. Combined with the influence law of various factors, a multi-objective dynamic load-sharing optimization design model was established with the best dynamic load-sharing performance and the minimum system quality as the objective function. Through the weighted combination method, the global optimal solution of the system optimization design was determined, and the influence of each parameter on the optimization objective function was analyzed. The correctness of the results was verified by using the genetic algorithm based on Pareto frontier distribution. The results show that the dynamic load-sharing characteristics of the system become worse with the increase of error and torsional stiffness, and are more sensitive to the influence of various error parameters. The optimization process focuses on the geometric parameters such as the Module, the teeth Number, the Pressure angle, and the Tooth width of each gear, which can reflect the degree of influence on the dynamic load-sharing and lightweight of the system. After optimization, the dynamic load sharing coefficient (DLSC) was reduced to 1.017, and the overall geometric volume was reduced to 1.473 × 108 mm3. It provides a theoretical basis for the design and research of a new type of helicopter power transmission system with a compact structure, good maneuverability, and high reliability.

Multi-objective optimization design of a cobweb-like–channel heat sink using particle swarm algorithm

Abstract The cobweb-like microchannel heat sink is acknowledged for its exceptional heat transfer capabilities in comparison to other biomimetic microchannel heat sinks. The objective of this paper is to improve the performance of the cobweb-like microchannel heat sink by optimizing its geometric structure parameters through a multi-objective approach. The Box-Behnken design method was utilized to conduct response surface analysis on the design variables, and the Pareto solution set was obtained by applying the multi-objective particle swarm optimization algorithm to the fitted functions of pressure and temperature. The TOPSIS method was used to select the most appropriate solution from the Pareto solution set. The performance of a microchannel heat sink was evaluated using the computational fluid dynamics (CFD) analysis. The optimized structure of the cobweb-like microchannel heat sink led to a decrease in the average temperature by 3K and a reduction in pressure drop by 1514Pa, as compared to the original design. This significant improvement in the overall performance highlights the importance of a well-designed channel structure in further enhancing the comprehensive performance of the microchannel heat sink.

Multi-objective design optimization of five-phase fractional-slot concentrated-winding surface-mounted permanent-magnet machine

Multi-objective design optimization of five-phase fractional-slot concentrated-winding surface-mounted permanent-magnet machine

Reliability based design optimization of a two-stage wind turbine gearbox

This paper describes a multi-objective reliability-based design optimization (MORBDO) of a two-stage wind turbine gearbox. The optimization process incorporates the gear's reliability of accounting for the uncertainty of its internal geometric parameters. It also ensures that constraints relating to the gear's reliability index and efficiency are respected. The objective functions are to minimize both the total volume and the center distance. A specific reliability target is established, and to address the multi-objective reliability-based design optimization (MORBDO), the hybrid method (HM) in conjunction with the constrained non-dominated sorting genetic algorithm (C-NSGA-II) is employed. The outcomes demonstrate that applying C-NSGA-II to solve the multi-objective reliability-based design optimization problem yields dependable Pareto solutions that are well-distributed in relation to the desired reliability level. The optimization using C-NSGA-II with a population size of 300 particles and 1000 generations produced the most favorable outcomes. This research significantly contributes to the multi-objective design optimization of wind turbine gear while simultaneously considering their reliability.

Multi-Objective Bayesian Optimization for Design of Pareto-Optimal Current Drive Profiles in STEP

Multi-Objective Bayesian Optimization for Design of Pareto-Optimal Current Drive Profiles in STEP

Multiobjective Design Optimization of Hybrid-Powered Multirotors for Enhanced Endurance and Payload Capacity

Multiobjective Design Optimization of Hybrid-Powered Multirotors for Enhanced Endurance and Payload Capacity

Multiobjective Optimization Design of Microstrip Directional Coupler With Generalized Coupling Slots

Multiobjective Optimization Design of Microstrip Directional Coupler With Generalized Coupling Slots

Influence of quality factor on operating mode of TM<sub>02</sub> mode relativistic backwave oscillator

<sec>The mode competition in an overmoded relativistic backward wave oscillator is studied through theoretical analysis and three-dimensional particle-in-cell simulation in this work. Based on the quality factor and coupling impedance, the mode selection for a TM<sub>02</sub> mode backward wave oscillator is achieved, and its output power and magnetic field strength are optimized in the simulation.</sec><sec>The quality factor is related to the group velocity and end reflection of each mode. The dispersion curves of some non-axisymmetric modes are very close, and the group velocities are basically equal. Therefore, the end reflection needs considering to distinguish between the quality factors of different modes. In frequency domain simulation, analyzing the quality factor of each mode by using the <i>S</i><sub>11</sub> parameter curve can avoid calculating the end reflection.</sec><sec>The three-dimensional simulation results show that the coupling impedance and quality factor jointly affect the operating mode. When the coupling impedance advantage of the working mode is not obvious, changing the resonant frequency of the high-frequency structure can affect the beam-wave interaction process, thereby changing the excitation mode. When the advantage is obvious, the beam-wave interaction of the excitation mode will not be destroyed by the resonant mode, and other modes of microwave output mainly come from the conversion of the same frequency modes. Due to the constant dispersion curve, the effect of resonance on the mode is essentially the effect of the quality factor on the mode dominated by the end reflection.</sec><sec>The insensitive parameters and the electron beam radius obtained from the simulation are used as the optimal parameters, and the automatic optimization algorithm is used in combination with the two-dimensional simulation to perform multi-objective optimization design in the above device. The final output power of the backward wave oscillator reaches 534 MW, with an efficiency of 23.64%, an increase of 221.7% compared with the efficiency of the original device. The device operating mode remains stable, with a power ratio of TM<sub>02</sub> mode reaching 94.95%.</sec>

Multi-objective Optimization Design of PMa-BSynRM Rotor Structure Based on Macroscopic Parameters and DPCA

Multi-objective Optimization Design of PMa-BSynRM Rotor Structure Based on Macroscopic Parameters and DPCA

A Semi-Analytic Model for Temperature Distribution Prediction and Hotspot Tracking in SPMSM and Its Application for Improved Multiphysics Multiobjective Optimization Design

A Semi-Analytic Model for Temperature Distribution Prediction and Hotspot Tracking in SPMSM and Its Application for Improved Multiphysics Multiobjective Optimization Design

Multi-Objective Optimization Design of Dual-Band Reflective Linear-to-Circular Polarizer Based on Equivalent Circuit and Surrogate Model

Multi-Objective Optimization Design of Dual-Band Reflective Linear-to-Circular Polarizer Based on Equivalent Circuit and Surrogate Model

A Novel Lightweight Multi-Objective Optimization Design System for Vehicle Chassis Frames Based on ANFIS-SHAMODE-IWOA Model

A Novel Lightweight Multi-Objective Optimization Design System for Vehicle Chassis Frames Based on ANFIS-SHAMODE-IWOA Model

Multiobjective Robust PI Synthesis in Plants with Uncertain Poles

The use of multiobjective optimization procedures for control tuning has been constantly explored, presenting satisfactory results, and generating significant contributions to control engineering. In this way, the field of robust control can benefit significantly from the integration of multiobjective optimization design procedures for robust Proportional-Integral-Derivative (RPID) controller synthesis, enabling innovative solutions to complex control challenges. Due to this fact, this paper explores an approach to utilize multiobjective optimization algorithms in a simplified procedure, considering uncertain systems in the form of interval plants with uncertain poles, the Kharitonov theorem is used to obtain a region of stability as search space for the multiobjective algorithm, being the optimization process performed over a nominal system model. Two numerical cases and a flexible actuator model were used to demonstrate the procedure for RPI synthesis, resulting in robustly stable controllers with optimized performance over error and control signal effort measures.

Multi-objective optimisation design of cross-shaft based on Kriging response surface optimisation model

Multi-objective optimisation design of cross-shaft based on Kriging response surface optimisation model