Multi-objective Optimization Design Method Research Articles

Multi-objective optimization design of shaftless rim-driven thruster

This paper proposes a multi-objective optimization design method for shaftless rim-driven thruster (RDT) based on the ISIGHT platform. The pitch ratio, the blade area ratio and the advance coefficient of RDT were considered as the design optimization variables, the thrust and efficiency of the RDT were the optimization objectives. The multi-objective optimization design method was based on the surrogate module and the optimization module in the ISIGHT platform. Two analytical methods (response surface methodology (RSM) and radial basis function Model (RBF)) were used to build the surrogate model. The Muti-Island GA optimization algorithm was adopted in the optimization module. The paper indicates that both RSM model and RBF model are feasible to build the surrogate model, the RBF model has better accuracy and reliability than RSM model. The blade obtained by RBF method has larger thrust and smaller torque than that of the blade obtained by RSM method. For the large advance coefficient ( J > 0.6), the efficiency of the blade obtained by RBF method is slightly higher than that of the blade obtained by RSM method.

Reliability Design of Two-Stage Planetary Gear Wheel Hub Reducer based on Multi-Objective Optimization

The mining dump truck has a large load capacity, low running speed, and the characteristics of low speed and high torque. The planetary wheel reducer can meet this demand, which is widely used in such vehicles. According to the structural characteristics of a 170-ton vehicle two-stage planetary gear reducer, the reliability of planetary gear transmission at all levels was analysed, and the system parameters were optimized on this basis. The multi-objective optimization design method was used to transform the maximum reliability of the system into the maximum reliability of the gears at all levels, and the constraints are established based on the actual processing, operation, installation, assembly and other working conditions. The MATLAB multi-objective optimization module was used to solve the analysis, and the best gear design parameters were obtained after rounding. Under different operating conditions, the planetary reducer before and after optimization was compared and analysed to obtain the reliability and service life of the entire deceleration system after optimization. The analysis results show that: after the parameter optimization of the planetary reducer, the transmission efficiency is 0.946, and the transmission ratio of the system is 30.54, which meets the actual use requirements. The reliability coefficient of the contact strength of the tooth surface of the secondary sun gear is 2.52, the reliability coefficient of the bending fatigue strength of the root of the secondary inner ring gear is 2.59, and the reliability of the secondary gear is 0.989. The reliability is obviously improved. The safety factor of the main parts is high. The service life of each gear of the whole secondary reduction system meets the design requirements. The analysis content and results provide reference for the optimization design and reliability analysis of similar planetary gear systems.

A novel optimization design method for obtaining high-performance micro-hole aerostatic bearings with experimental validation

Micro-hole aerostatic bearings have received broadly attention due to their inherent high stability, large load capacity, and higher stiffness, etc. However, the performances of micro-hole aerostatic bearings are strictly influenced by the number, diameter, and location of the micro-holes. In particular, the number of micro-holes must be large enough for bearings achieving better performances, which determines that there are many design variables. So, it is very time-consuming to design the micro-hole aerostatic bearings with desired performances. Therefore, a novel multi-objective optimization design method is proposed for quickly and efficiently designing the ideal micro-hole aerostatic bearings which have the characteristics that both the maximum load capacity and stiffness are large. The proposed method couples the solving Reynolds equation, micro multi-objective genetic algorithm (μMOGA), and min-max method. The Reynolds equation included in the μMOGA is calculated to obtain the objective values. The design variables for Reynolds equation are confirmed by genetic operating the objective values. The Pareto optimal solutions are constructed by non-dominated ranking the objective values. Then, the ideal optimal bearings are obtained from the Pareto optimal solutions based on min-max method. Four optimal designed micro-hole aerostatic bearings are manufactured by laser technology. Meanwhile, the load capacity and stiffness of the bearings are tested. The effectiveness of the optimization design method is verified by comparing theoretical and experimental data.

Multi-objective optimization of an axial flow hydraulic turbine with a collection device to be installed in an open channel

In this study, a multi-objective optimization design method was developed by combining, among other methods, single-phase flow analysis and the optimization method to simultaneously optimize the runner and collection device of an axial-flow hydraulic turbine with a collection device, using the power coefficient and axial thrust coefficient as objective functions. To verify the effectiveness of this design method, the characteristics of the optimized turbine were investigated through verification experiments and multiphase flow analysis, and were compared with the results of single-phase flow analysis. The results of single-phase flow analysis showed that the axial thrust coefficient of the optimized turbine was equivalent to that of the original turbine, while the power coefficient improved dramatically. However, the results of the multiphase flow analysis showed that although the axial thrust coefficient of the optimized turbine was increased compared to that of the original turbine, the power coefficient was significantly higher than that of the results in the single-phase flow analysis, due to a significant increase in the efficiency of the turbine, as well as an increase in the loading coefficient and the inlet velocity ratio, unlike the single-phase flow analysis. This indicates that this design method is effective in terms of output improvement.

Design and Optimization of Linear Permanent Magnet Vernier Generator for Direct Drive Wave Energy Converter

A novel linear permanent magnet vernier generator (LPMVG) for small-power off-grid wave power generation systems is proposed in this paper. Firstly, in order to reduce the cogging force and the inherent edge effect of the linear generator, a staggered tooth modular structure is proposed. Secondly, in order to improve the output power and efficiency of the LPMVG and reduce the fluctuation coefficient of electromagnetic force, the relationship between the parameters of the generator is studied, and a method combining multi-objective optimization and single parameter scanning based on the response surface model and particle swarm optimization algorithm is proposed to obtain the optimal structural parameters of the generator. Thirdly, the output power and efficiency of the optimized generator are calculated and analyzed based on the two-dimensional finite element method, and the effectiveness of the multi-objective optimization design method based on the response surface model and particle swarm optimization algorithm is verified. Finally, a prototype is developed, and the calculated results and the measured results are shown to be in good agreement.

Design method for high-power high-frequency magnetic-resonance air-core transformer

PurposeThe purpose of this paper is to study the multi-objective optimization design method of high-power high-frequency magnetic-resonance air-core transformer (ACT).Design/methodology/approachFirst, this paper studies the interleaved winding technology, the process of modeling and simulation, the calculation method of high-frequency loss of Litz wire and the design of magnetic shielding in detail. Second, the multi-objective optimization design process of high-frequency magnetic-resonance ACT is established by parametric scanning method and orthogonal experiment method.FindingsAn ACT model of 2 kV/100 kW/81.34 kHz was designed. The efficiency, weight power density and volume power density are 99.61%, 21.6 kW/kg and 5.1 kW/kg, respectively. Finally, the multi-physical field coupling simulation method is used to calculate the port excitation voltages and currents and temperature field of ACT. The maximum temperature of the ACT is 95.5 °C, which meets the design requirements.Originality/valueThe above research provides guidance and basis for the optimization design of high-power high-frequency magnetic-resonance ACT.

Design and Optimization a New Spoke-Type Flux-Modulation Machine With Inverted T-Shape Permanent Magnets

This paper takes a new spoke-type flux-modulation (STFM) machine with inverted T-shape permanent magnets as the research object and proposes a multi-objective optimization design method based on air-gap flux density harmonics to improve the torque and torque ripple. The key of the proposed method is to optimize the overall torque performance by improving the contribution of main air-gap harmonics to torque and torque ripple. The working harmonic expression of the machine is firstly obtained based on the magnetomotive force (MMF) -permeance model due to the new rotor structure make the working harmonics are different from the existing flux-modulation PM machine. Then, the torques generated by the 11th and 31st air-gap harmonics and the torque ripple generated by the 29th air-gap harmonics are taken as sub-objectives. Furthermore, the response surface analysis (RSM) and the barebones multi-objective particle swarm optimization (BB_MOPSO) algorithm are combined to optimize three sub-objectives. The overall torque and torque ripple are improved due to the optimization of three sub-objectives. Moreover, the 20-slot/11-pole pair traditional model is used as a benchmark to verify the performance of the investigated machine. Finally, a prototype is manufactured and tested to verify the correctness of the theoretical analysis.

Research on high efficiency and high dynamic optimal matching of the electro-hydraulic servo pump control system based on NSGA-II

An electro-hydraulic servo pump control system (hereinafter referred to as EHSPCS) is a volume servo control unit that is highly integrated with servo motors, fixed-displacement pumps, hydraulic cylinders and functional valve groups. Because of its unique volume direct-drive control mode, the dynamic performance of the system is limited, and the thermal power loss is large, which seriously restricts the improvement of the working quality of the system. To improve the dynamic performance of the system and reduce the thermal power loss to the maximum extent, a multi-objective optimization design method for the EHSPCS is proposed by comprehensively considering the dynamic and efficient energy-saving characteristics of the system. The evaluation model of the dynamic period of the hydraulic cylinder and the thermal power loss of the servo motor are given. Parameters such as the electromagnetic torque of the servo motor, displacement of the hydraulic pump, and working area of the hydraulic cylinder are intelligently optimized by a non-dominated sorting genetic algorithm with elite strategy (NSGA-II). The Pareto front of multi-objective optimization and the corresponding Pareto solution set are obtained; thus, the optimal matching of the system characteristics is realized. Finally, the relevant theory of the multi-objective optimization algorithm is applied to optimize the performance parameters of the hydraulic servo motor, and the prototype is tested in engineering. The experimental results show that the dynamic period of the hydraulic servo motor is accelerated after optimization, and the thermal power loss is significantly reduced. The dynamic and efficient energy-saving characteristics of the system are improved, which further verifies the feasibility of the proposed theory.

Design and Multiobjective Optimization of a New Flux-Concentrating Rotor Combining Halbach PM Array and Spoke-Type IPM Machine

In this article, a new spoke-type interior permanent magnet (PM) with a flux-concentrating rotor is proposed. Based on the flux-concentrating principle, the fitting parameters between PMs and magnetic cores on the rotor make a significant impact on the flux concentration and saliency effect, thus resulting in the output torque and power capacity. Therefore, taking the average torque, cogging torque, peak power, and PM utilization as the optimization objectives, first, the sensitivity analysis is carried out that includes the different geometric variables of the rotor. Afterward, the response surface model based on the Box–Behnken method is established by selecting the reasonable optimization variables. Then, the optimal solution of the design parameters is verified by solving the response surface model. Meanwhile, a set of Pareto solutions is generated by adopting a multiobjective genetic algorithm. By two-dimensional finite-element analysis, the electromagnetic performance of a 72-slot/16-pole topology with the optimized flux-concentrating rotor is analyzed and compared with that of the initial design model. The results are demonstrated based on the response surface model. The effectiveness of the multiobjective optimization design method and multiobjective genetic algorithm is confirmed for the flux-concentrating rotor. Finally, a 30-kW prototype is developed and experimented with to verify the finite-element analysis results as well as the effectiveness of multiobjective optimization.

Multi-Objective Optimization Design Method for Whole-Aeroengine Coupling Vibration

With the increasing thrust-to-weight ratio of modern aeroengines and the widespread adoption of thin-walled casing, the impact of the coupling vibration effect between the rotor and stator on the critical speed, rotor–stator mode shape coordination, and response characteristics of the whole engine have become increasingly prominent. However, the vibrational design of the whole-engine coupling has thus far relied on human experience, revealing a need for the study of its intelligent optimization. In this study, to quantitatively analyze the vibration of the whole engine, three vibration evaluation indexes were defined, which were risk coefficients for the critical speed, rotor strain energy, and cross-section rotor–stator rubbing. Using these indexes as the optimization targets, a multi-objective intelligent optimization design method for aeroengine support stiffness was proposed. The design optimization of the support stiffness of a turbofan engine with a large bypass ratio was performed. The results showed that the vibration index of the whole machine can be reduced to different degrees and that the whole-engine coupling vibration is optimized.

Assessment of an Optimal Design Method for a High-Energy Ultrasonic Igniter Based on Multi-Objective Robustness Optimization

The current deterministic optimization design method ignores uncertainties in the material properties and potential machining error which could lead to unreliable or unstable designs. To improve the design efficiency and anti-jamming ability of a high-energy ultrasonic igniter, a Six Sigma multi-objective robustness optimization design method based on the response surface model and the design of the experiment has been proposed. In this paper, the initial structural dimensions of a high-energy ultrasonic igniter have been obtained by employing one-dimensional longitudinal vibration theory. The finite element simulation method of COMSOL Multiphysics software has been verified by the finite element simulation results of ANSYS Workbench software. The optimal igniter design has been achieved by using the proposed method, which is based on the finite element method, the Optimal Latin Hypercube Design method, Grey Relational Analysis, the response surface model, the non-dominated sorting genetic algorithm, and the mean value method. Considering the influence of manufacturing errors on the igniter’s performance, the Six Sigma method was used to optimize the robustness of the igniter. The Eigenfrequency analysis and the vibration velocity ratio calculation were conducted to verify the design’s effectiveness. The results reveal that the longitudinal resonant frequency of the deterministic optimization scheme and the robustness optimization scheme are closer to the design’s target frequency. The relative error is less than 0.1%. Compared with the deterministic optimization scheme, the vibration velocity ratio of the robustness optimization scheme is 2.8, which is about 15.7% higher than that of the deterministic optimization scheme, and the quality level of the design targets is raised to above Six Sigma. The proposed method can provide an efficient and accurate optimal design for developing a new special piezoelectric transducer.

Optimal Design Method of High Voltage DC Power Supply EMI Filter Considering Source Impedance of Motor Controller for Electric Vehicle

Passive filters are often used for electromagnetic interference (EMI) suppression on the high voltage (HV) DC side of motor drive systems due to their simple structure and large noise suppression. However, the traditional passive filter design method takes less consideration of the change of the system source impedance, which will lead to almost no insertion loss in some frequency bands or an over-design of the filter. Based on the onboard working conditions of high-voltage and high-current, this article adopts the dual current probe method to obtain the source impedance of the system when it is working, and proposes a filter multi-objective optimization design method based on the genetic algorithm (GA). This method automatically selects the optimal topology of the filter and related component parameters according to the source impedance and load impedance, avoiding the filter resonance phenomenon and over-design problems caused by not considering source impedance. The experimental results show that conducted interference voltage and current of motor drive system with filter designed by the proposed method can pass CISPR25-2016rd level 3.

Multiobjective Lightweight Optimization Design Method for a Dump Truck Carriage under Multiple Working Conditions

To reduce the transportation cost and improve the fuel economy of a dump truck in road transport, vehicle lightweight optimization with the objectives such as the mass, stiffness, and sixth-order frequency of the carriage is adopted in this study. First, the carriage is divided into finite element meshes, and the working conditions of the carriage are analyzed under the conditions of full-load and uniform transportation, 0° lift, and 30° lift. Then, a comprehensive model consisting of full-load uniform transport and 0° lifting dual conditions is established, and 18 plate thicknesses are defined as design variables. The samples derived from the design variables of the carriages via the optimal Latin hypercube method are employed to analyze, in which the design variable that critically impacts the optimization objective is screened out from the sample for research. In addition, the dual-case approximation model constructed by a variety of methods is executed for accuracy comparison. And a moving least squares method combining linear and specific numerical values with the highest accuracy is selected to build a dual-case approximation model for the carriage. Ultimately, on the basis of the constructed double-condition approximation model, a multiobjective genetic algorithm is utilized to optimize the mass, bending stiffness, and sixth-order frequency. Compared with other methods, the multiobjective genetic algorithm can maintain the optimal solution, and the stored optimal solution can also be introduced into other groups to obtain another optimal solution. The simulation results, obtained from the scenarios of the carriage under the conditions of full-load uniform transportation, 0° lift and 30° lift, reveal that, on the basis of keeping the shape and structure of the original carriage unchanged, the mass is reduced by 1.215 t, the overall bending stiffness of the carriage is increased by 16300 N·mm−1, and the sixth-order modal frequency is optimized.

Multiobjective Optimization Method of Solid Rocket Motor Finocyl Grain Based on Surrogate Model

To improve the performance of a solid rocket motor (SRM), a multiobjective optimal design method that can consider the structural integrity, internal ballistic performance, and loading performance of the SRM was proposed based on parametric modeling and surrogate modeling technology. Firstly, the parametric modeling technology was introduced into the field of structural integrity analysis for a high-loading SRM, based on which the influences of load and geometric parameters on the maximum von Mises strain of the SRM grain were analyzed, which effectively improved the sampling speed and prediction accuracy of the surrogate model. Combining the calculation models of the combustion surface area and volume loading fraction of the SRM, the Pareto optimal solution set was obtained based on the NSGA-II algorithm. Under the constraints of the optimization model, the maximum von Mises strain can be reduced by up to 26.72% and the volume loading fraction can be increased by up to 1.83% compared with the original. In addition, the optimal design method proposed in this paper is significantly superior in efficiency, capable of reducing both the single sampling time by more than 95% and the number of numerical simulations from 20,000 to 400, and the average prediction deviation is only 1.87%.

Optimization design method of pressure pentamode materials

Pentamode materials have broad application prospects in the control of underwater elastic waves. It is of great significance to design pentamode materials configuration with certain compressive resistance to promote the underwater application of pentamode materials. Based on the particle swarm optimization algorithm, a multi-objective optimization design method considering structural pressure resistance is proposed. The optimization objective consists of three parts: pentamode attribute matching degree, underwater compression ability test, and target density and target modulus matching degree. Aiming at the octagonal frame structure with a fan-shaped mass block in the inner corner, the multi-objective optimization design method is adopted to optimize the thickness of the frame wall t, the radius of the mass block R, and the limit lengths l2 and h2. After optimization, the pentamode attribute matching degree of the material is 0.998. When the safety factor is equal to 1.5, it can withstand the hydrostatic pressure of more than 200 m water depth. In the frequency domain of 3 K to 6 kHz, the average value of the total scattering cross-section of the material is 0.055, which is similar to the sound propagation in pure water. The research shows that the multi-objective optimization design method of pentamode materials can be used to design the configuration of pentamode materials considering both underwater pressure resistance and sound transmission performance. The research results are expected to provide a method reference for the configuration design of underwater pressure-resistant pentamode materials.

A New Multi-Objective Optimization Design Method for Directional Well Trajectory Based on Multi-Factor Constraints

The design of the wellbore trajectory directly affects the construction quality and efficiency of drilling. A good wellbore trajectory is conducive to guiding on-site construction, which can effectively reduce costs and increase productivity. Therefore, further optimization of the wellbore trajectory is inevitable and necessary. Based on this, aiming at the three-segment, five-segment, double-increase-profile extended reach wells, this paper considered the constraints of formation wellbore stability; formation strength; and the determination of the deviation angle, deviation point position, and target range by the work of deflecting tools. In addition, the optimization objective function of the shortest total length of the wellbore, minimum error of the second target, lowest cost, minimum friction of the lifting and lowering string, and minimum torque of rotary drilling were proposed and established. The objective function of the longest extension limit of the horizontal section of the extended reach well is established. Taking the 14-8 block of the Lufeng Oilfield in the eastern South China Sea as an example, the actual data of the field were modeled, and the independence of the objective function was verified by comparing the number of non-inferior solutions of the two objective functions. By normalizing simplified to double-, three-, and four-objective functions, using a genetic algorithm and particle swarm optimization results, it can be found that the new method of optimization design established in this paper has an obvious optimization effect compared with the original design.

Multi-Objective Optimal Design of SPMSM for Electric Compressor Using Analytical Method and NSGA-II Algorithm

In contrast to internal combustion engine vehicles, electric vehicles (EVs) obtain the power required for the compressor of air conditioning system from an electric source. Therefore, an optimal design for electric motor, the main component of an electric compressor, is essential for improving EV mileage. A multi-objective optimal design is required because the characteristics of the motor are in a trade-off relationship with each other. When the finite element method (FEM) is used, multi-objective optimal designs for the motor take a significant amount of time because of the diversity analyses required for the optimal-model search. To solve this problem, in this study, a multi-objective optimal design method of an SPMSM for an EVs air conditioner system compressor was proposed and applied using the NSGA-II and an analytical method. The validity of the proposed method was confirmed by comparing the characteristics of the optimal design model with those of the initially designed model.

A Novel Multi-Objective Optimal Design Method for Dry Iron Core Reactor by Incorporating NSGA-II, TOPSIS and Entropy Weight Method

Dry iron core reactors are widely used in various power quality applications. Manufacturers want to optimize the cost and loss simultaneously, which is normally achieved by the designers’ experience. This approach is highly subjective and can lead to a non-ideal product. Thus, an objective dry iron core reactor design approach to balance the cost and loss with a scientific basis is desired. In this paper, a multi-objective optimal design method is proposed to optimize both the cost and loss of the reactor, which provides an automatic and scientific design method. Specifically, a three-dimensional finite element model of dry iron core reactor is established, based on which the dependency of cost and loss upon the wire size of the reactor’s winding is studied by using joint Matlab-finite element method (FEM) simulation. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to search for the Pareto optimal solution set, out of which the optimal wire size of the reactor is determined by using the fusion of the technique for order preference by similarity to ideal solution (TOPSIS) method and the entropy weight method. TOPSIS helps the designer to balance the concern between cost and loss, while the entropy weight method can determine the weight information through the dispersion degree of cost and loss. This methodology can avoid personal random subjective opinion when selecting the design solution out of the Pareto set. The calculation shows that the cost and loss can be reduced by up to 17.85% and 19.45%, respectively, with the proposed method. Furthermore, the obtained optimal design is approved by experimental tests.

Analysis of End-Effect Torque and Multi-Objective Optimization for Multi-Port Spatial Permanent Magnet Synchronous Motor

Multi-port spatial permanent magnet synchronous motor (MSPMSM) combines the advantages of disk motor and permanent magnet (PM) planetary gear drive, which solves the problem of single output port on traditional PM synchronous motor (PMSM) and realizes multi-port outputs and direct drive. Due to the special structure of disk stator, the planetary gear rotors are affected by end-effect torque in rotation process. The end-effect torque will not only cause torque ripple but also cause vibration and noise. Aiming at the problem of end-effect torque, the generation mechanism of end-effect torque is analyzed. In order to analyze air-gap magnetic field distribution accurately, the arc slotless subdomain (SD) model of planetary gear rotor and disk stator is established in polar coordinate system. The end-effect torque is derived by the Maxwell stress tensor method. Based on Box–Behnken design (BBD) method, a response surface model (RSM) is constructed to reduce end-effect torque amplitude and increase electromagnetic torque. The influences of structural parameters on end-effect torque amplitude are analyzed, and a set of optimal structural parameters are obtained. The end-effect torque and electromagnetic torque of the optimized MSPMSM are analyzed by finite-element analysis method (FEM), and the effectiveness of multi-objective optimization design method is verified. These research results have a good effect on improving the output performance of MSPMSM.

Optimization and Performance Analysis of Francis Turbine Runner Based on Super-Transfer Approximate Method under Multi-Energy Complementary Conditions

Hydropower unit is the compensation power generation of the energy regulating unit in wind–solar–water multi-energy complementary systems that often require the turbine to operate in a partial working condition area, thereby resulting in problems of low hydraulic efficiency and severe vibration during operation. A multi-objective and multi-condition optimization design method for Francis turbine runner based on the super-transfer approximation approach was proposed in this study. The proposed method aims to improve the hydraulic performance of the turbine, enhance and suppress the vibration of the turbine, and expand the operation range of the turbine on the basis of the actual situation given that Francis turbine frequently operates in low- and ultralow-load areas under the condition of multi-energy complementarity and continuous adjustment of operating conditions. Different operating conditions from low load to full load were selected as performance evaluation conditions. The super-transfer approximation method was used to select the weight co-efficient of water turbine operating conditions, and a multi-objective optimization function with the efficiency and cavitation performance of the water turbine as optimization objectives was constructed to ensure that the optimized water turbine can achieve the optimal performance in the full working condition range. Results showed that the pressure distribution on the blade surface of the optimized runner was uniform and the working ability was enhanced under the condition of ensuring the performance stability of optimal and rated conditions when the original runner was optimized. The hydraulic efficiency of the turbine under the low-load conditions OP1 and OP2 increased by 4.61 and 3.17%, respectively. Hence, the optimized runner is suitable for hydraulic turbines under multi-energy complementary conditions. The results of this study can provide a reference for the optimal design and operation of the turbine runner.