Multi-objective Design Optimization Method Research Articles

Optimization and experimental study of stationary endwall of stator labyrinth cavity in a low-speed research compressor

Controlling the leakage flow of the labyrinth seal cavity is very important for the efficiency and aerodynamic matching design of aero-engine high-pressure compressor. However, due to the complexity of the geometry and internal flow of the labyrinth seal cavity, the design optimization of the labyrinth seal cavity is rarely studied. In this paper, a multi-objective design optimization method was used to optimize the stationary endwall of the shrouded stator labyrinth cavity, and the optimal endwall shape was obtained. Based on the optimal geometry, the 3D printing and aerodynamic testing of experimental parts were carried out, and the aerodynamic performance and flow field details of the optimal geometry were analyzed by unsteady numerical simulation. The experimental results show that for the optimal geometry, it has a little effect on the total pressure ratio, but the efficiency at the design point is increased by 1.4 %. The numerical results show that the optimal cavity shape reduces low-energy fluid, thus reduces the total pressure loss of S3. At the near stall point, the optimal S3 still has a better performance, which means that the optimal shape is not limited to the design point. From the result, an engineering design criterion can be concluded. It is suggested that the labyrinth seal cavity should be designed to match the velocity components of the leakage flow with the mainstream of the stator properly to make the leakage flow go evenly in the blade passage instead of gathering to the suction side.

Multi-Objective Aerodynamic and Aeroelastic Coupled Design Optimization Using a Full Viscosity Discrete Adjoint Harmonic Balance Method

Abstract With increasing requirements for high-loading and high-efficiency turbomachines, blades become thinner and thinner and thus design optimizations considering both aerodynamic performances and aeroelastic stability become more and more necessary. In this study, a full viscosity discrete adjoint harmonic balance solver has been developed using algorithmic differentiation (AD), verified by a discrete linear solver based upon duality property, and then adopted to perform multi-disciplinary coupled design optimizations. To this end, a framework of multi-objective adjoint design optimizations has been developed to improve both aerodynamic performances and the aeroelastic stability of turbomachinery blades. This framework is divided into two steps: aeroelastic design initialization and aerodynamic Pareto front determination. First, the blade profiles are optimized to improve the aeroelastic stability only and constrain the variations of aerodynamic performances. Second, the optimized blade profiles in the first step are used as the initial ones and then further optimized with the objective function of aerodynamic parameters and the constraints of aeroelastic parameters. The effectiveness of the multi-objective design optimization method is demonstrated by comparing the optimization results with those from a single-objective aerodynamic and aeroelastic coupled design optimization method. The results from the transonic NASA Rotor 67 subjected to a hypothetical vibration mode show that the multi-objective coupled design optimization method is capable of improving performances in both disciplines.

Multiobjective Design Optimization of a Novel Switched Reluctance Motor With Unequal Alternating Stator Yoke Segments

Switched reluctance motors (SRMs) have attracted considerable attention for energy conversion within industrial applications. To realize the high-quality operation status, optimization for SRMs is one of the most essential steps in the design stage. In this article, a multiobjective design optimization method is proposed for a novel SRM with unequal alternating stator yoke segments. First, the asymmetric flux distribution and the inconsistent current phenomenon of the conventional six-phase SRM are introduced. The unequal yoke SRM (UYSRM) is developed to improve the current profiles and reduce the unnecessary stator mass. Then, an optimization method considering the slot fill factor is proposed and performed on the proposed UYSRM. In the optimization process, the sensitivity analysis is conducted based on the orthogonal array, and the sensitive degrees of different variables are calculated. To take the full advantage of the stator slot area, the number of parallel strands of phase windings is adjusted according to the number of turns and the variables of the stator. The performances of the UYSRM are evaluated to validate the proposed SRM and optimization method. Finally, a prototype motor is manufactured and tested. Both the simulation and test results verify the effectiveness and reasonability of the proposed design optimization method for the UYSRM. In addition, the proposed method offers a new research orientation for electric machines.

Normal Force Elimination in Single-Sided Linear Induction Motor Using Design Parameters

In this article, the normal force acting on the primary of single-sided linear induction motors (SLIMs) is analytically derived. Considering all phenomena involved, the effects of different design variables on the normal force are investigated. In some applications such as transportation systems, the normal force elimination may be required or strongly beneficial, and, in this article, a multi-objective design optimization method based on genetic algorithm is introduced for this purpose, both with and without consideration of primary weight effect. All significant design variables are considered in the optimization. The results show that the motor performance is improved and the normal force is eliminated by an appropriate selection of design variables. To evaluate optimization effectiveness, a laboratory prototype has been constructed, tested, and numerically simulated by finite element analysis (FEA). Comparing the experimental and FEA results with analytical predictions confirms the accuracy and usefulness of the proposed design methodology.

Multi-objective design optimization using hybrid search algorithms with interval uncertainty for thin-walled structures

Thin-walled structures have been widely used in vehicle components due to their lightweight characteristics. To design structural parameters that are more in line with actual requirements, it is often necessary to consider the influence of uncertainty in design parameters. An effective multi-objective design optimization method using hybrid search algorithms under interval uncertainty (MDOHSA) is proposed in this study. The MDOHSA mainly consists of the modified gray​ wolf optimization (mGWO) and the pattern search (PS) algorithms. The mGWO algorithm is applied to derive a new solution set and the PS algorithm is used to quickly search the lower and upper bounds of interval responses in MDOHSA. The non-dominated strategy considering uncertainty is designed by the possibility degree of interval value. The mGWO is designed by improving the initialization population and the updating mechanism. Some standard test functions are implemented to analyze the proposed method, and the result shows that the mGWO algorithm is superior to the other analogous algorithms. In this study, the car subframe, the hexagonal fractal structure, and the bracket of an intelligent sanitation vehicle are optimized by MDOHSA. The above results show that the optimization method proposed in this study is effective. The feasible solution of the multi-objective design optimization method can be selected according to the interval deviation degree of design variables and performance requirements. This study develops an effective multi-objective design optimization method for thin-walled structures under interval uncertainty and can continue to be used for the uncertain optimization of other engineering problems.

Multi-Objective Design Optimization of a Tubular Permanent Magnet Linear Generator With 120° Phase Belt Toroidal Windings

The utilization of 120° phase belt toroidal windings (120°-TWs) can bring power density improvement in a tubular permanent magnet linear generator (TPMLG). Unfortunately, the TPMLG with 120°-TWs (120°-TPMLG) usually involve multiple structural parameters, and the interaction or even conflict among those structural parameters would have strong impact on generator performances in the design optimization process. To alleviate this problem, a multi-objective design optimization method is proposed to conduct a multi-objectives optimization, which aims to obtain the high-power density and low-detent force. First, the comprehensive sensitivity analysis method, namely global sensitivity analysis, is adopted to evaluate the sensitivities of the structural parameters on the performances of the 120°-TPMLG. According to the evaluation results, the structural parameters are divided into three levels: non-sensitive level, mild-sensitive level, and strong-sensitive level. Then, to improve the whole design optimization efficiency, the direct-screening method, the surface method, and the genetic algorithm is implemented in the three levels, respectively. And the optimal structural parameters of the 120°-TPMLG are finally determined. To verify the feasibility of the 120°-TPMLG and the effectiveness of the proposed design optimization method, the performances of the optimal 120°-TPMLG are analyzed and compared with the initial one and the same dimensions TPMLG with traditional toroidal windings (T-TPMLG) in detail. It shows that the performances of the optimal 120°-TPMLG meet the design requirements. Moreover, the detent force is largely decreased and the power density is notably improved. The results prove that the proposed multi-objective design optimization method is available for the 120°-TPMLG.

Multi-Objective Design of Single-Phase Differential Buck Inverters With Active Power Decoupling

The design of single-phase differential buck inverters has two important considerations, including reducing second-order ripple power using decoupling capacitors and increasing inverter performances. Using larger decoupling capacitors will improve the performance of ripple power reduction and efficiency while reducing power density. Such trade-off has not been fully modeled and investigated, leading to the sub-optimal design of inverters. To address that, in this paper, the trade-off among decoupling capacitance, inverter efficiency and power density are investigated through detailed mathematical modeling and sensitivity study. The trade-off of the volume and power loss of essential inverter components, including power switches, inductors and heatsinks, are also studied to facilitate the inverter design. A fast multi-objective design optimization method based on geometric programming is presented to optimize the inverter efficiency and power density. A 1 kW prototype of a Gallium Nitride (GaN) based inverter has been designed based on the proposed method. A hardware prototype of the inverter has been built and tested, which has an efficiency of 98.02% and power density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ {4.54\;\mathrm{{kW/dm^{3}}}}$</tex-math></inline-formula> and matches 99% to the presented multi-objective design method. This validates the accuracy and effectiveness of the presented design approach considering detailed trade-off analysis.

Exergy optimization of a multi‐stage solar micro‐cogeneration system

This paper proposes a dynamic model of a solar-based micro-cogeneration system called photovoltaic-thermal (PVT) collector to perform a design optimization of the multi-stage PVT system. The parametric study reveals the most important design parameters influencing the water-based flat-plate PVT system performance. The analysis also shows an existing trade-off between thermal and electrical efficiencies during the PVT operation. A novel exergy-based multi-objective design optimization method is demonstrated to find a trade-off design solution of the multi-stage PVT collector which compromises between the electrical and thermal exergy efficiencies under different weather conditions. The electrical and thermal exergy efficiencies are defined to be the objective functions of the Matlab gamultiobj-function, which is a multi-objective evolutionary algorithm using non-dominated sorting genetic algorithm-II (NSGA-II). As a result of the algorithm, the Pareto optimal sets were derived that revealed the optimal solutions taking into account the trade-off nature of the optimization problem. The decision-making method called an ideal point method was used in the decision-making process to find the final optimal solutions for different weather conditions. The results revealed that the optimal number of the PVT collectors in series depended on the weather conditions and decreased from 3 to 2 if the conditions got cooler.

Torque ripple reduction of synchronous reluctance machine by using asymmetrical barriers and hybrid magnetic core

As there is no need of permanent magnet (PM) material and only silicon steel sheet required on the rotor, synchronous reluctance machine (SynRM) can be used for many applications and draws a great research interest. For the SynRM, the torque ripple is a big issue and a great of work could been done on reducing it. In this paper, asymmetrical magnetic flux barriers in the SynRM rotor were studied comprehensively, including angle and width of each layer and each side of the magnetic barrier. The SynRMb with asymmetrical and parallel magnetic flux barrier was found as the best way to design SynRM based on the multi-objective design optimization method. Moreover, each parameter was studied to show the design rule of the asymmetrical magnetic flux barrier. As the average torque will be reduced with the asymmetrical barrier is used, the grain-oriented silicon steel is used on stator teeth of the SynRMb (SynRMbG) was proposed and studied. The analysis results show that the proposed new method can make the SynRM have better performance.

Optimization of process parameters in plastic injection molding for minimizing the volumetric shrinkage and warpage using radial basis function (RBF) coupled with the k-fold cross validation technique

Abstract In this study, a multi-objective design optimization method based on a radial basis function (RBF) model was applied to minimize the volumetric shrinkage and warpage of hip liners as an injection-molded biomedical part. The hip liners included an ultrahigh molecular weight polyethylene (UHMWPE) liner and UHMWPE reinforced with a nano-hydroxyapatite (nHA) liner. The shrinkage and warpage values of the hip liners were generated by simulation of the injection molding process using Autodesk Moldflow. The RBF model was used to build an approximate function relationship between the objectives and the process parameters. The process parameters, including mold temperature, melt temperature, injection time, packing time, packing pressure, coolant temperature, and type of liner, were surveyed to find the interaction effects of them on the shrinkage and warpage of the liners. The results indicated that the addition of nHA helps the liners to obtain more dimensional stability. The model was validated by the k-fold cross validation technique. Finally, the model revealed the optimal process conditions to achieve the minimized shrinkage and warpage simultaneously for various weights.

An Efficient Multiobjective Design Optimization Method for a PMSLM Based on an Extreme Learning Machine

This paper focuses on the multiobjective design optimization of the permanent magnet synchronous linear motors (PMSLMs), which are applied to a high-precision laser engraving machine. A novel efficient multiobjective design optimization method for a PMSLM is proposed to achieve optimal performances as indicated by high average thrust, low thrust ripple, and low total harmonic distortion at different running speeds. First, based on the finite-element analysis (FEA) data, a regression machine learning algorithm, called an extreme learning machine (ELM), is introduced to solve the calculation modeling problem by mapping out the nonlinear and complex relationship between input structural factors and output motor performances. Comparative simulation experiments conducted using the traditional analytical modeling method and another machine learning modeling method, i.e., support vector machine, confirm the superiority of the ELM. Then, a new bionic intelligent optimization algorithm, called the gray wolf optimizer algorithm, is used to search the best optimization performances and structural parameters by performing iteration optimization calculation for multiobjective functions. Finally, FEA and prototype motor experiments prove the effectiveness and validity of the proposed method.

Optimal design for the support structure of a cavity mirror in a chemical oxygen iodine laser resonator.

The dynamic characteristics of the cavity mirror support structure strongly influence the quality of the output beam. However, the contradiction between excellent dynamic performance and light weight make the design process challenging. To cope with the problems encountered in the original design of a chemical oxygen iodine laser system, this paper presents a two-dimensional adjustable support structure based on spherical constraints with large specific stiffness in the initial design phase. Subsequently, a two-level optimization strategy containing a macro design and a detailed design is adopted to optimize the initial structure. At the macro design stage, a two-step topology optimization procedure is introduced, in which the scale of the optimization model is dramatically reduced using the independent continuous mapping algorithm to improve the calculation speed in the first step, and the gray elements are eliminated using the bi-directional evolutionary structural optimization method to clearly obtain the optimal topology in the second step. This method is verified to overcome the defect of low efficiency, while still eliminating gray elements. At the detailed design stage, an adaptive surrogate model and the multi-objective design optimization method are employed to seek the best compromise between the lower weight and higher dynamic performance. The results from the application to the example of the cavity mirror support structure show that the mass is reduced by 41.8%, and the dynamic performance requirement is fulfilled.

Design Optimization of ESD (Emergency ShutDown) System for Offshore Process Based on Reliability Analysis

Hydrocarbon leaks have a major accident potential and it could give significant damages to human, property and environment.To prevent these risks from the leak in design aspects, installation of ESD system is representative. Because the ESD system should be operated properly at any time, It needs high reliability and much cost. To make ESD system with high reliability and reasonable cost, it is a need to find specific design method.In this study, we proposed the multi-objective design optimization method and performed the optimization of the ESD system for 1st separation system to satisfy high reliability and cost-effective.‘NSGA-II (Non-dominated Sorting Genetic Algorithm-II)’ was applied and two objective functions of ‘Reliability’ and ‘Cost’ of system were defined. Six design variables were set to related variables for system configuration. To verify the result of the optimization, the results of existing design and optimum design were compared in aspects of reliability and cost. With the optimization method proposed from this study, it was possible to derive the reliable and economical design of the ESD system.

Establishing the Relative Merits of Interior and Spoke-Type Permanent-Magnet Machines With Ferrite or &lt;roman&gt;NdFeB&lt;/roman&gt; Through Systematic Design Optimization

In this paper, a multiobjective design optimization method combining design-of-experiments techniques and differential-evolution algorithms is presented. The method was implemented and utilized in order to provide practical engineering insights for the optimal design of interior and spoke-type permanent-magnet machines. Two combinations with 12 slots and 8 poles and 12 slots and 10 poles, respectively, have been studied in conjunction with rare-earth neodymium-iron-boron (NdFeB) and ferrites. As part of the optimization process, a computationally efficient finite-element electromagnetic analysis was employed for estimating the performance of thousands of candidate designs. Three optimization objectives were concurrently considered for minimum total material cost, power losses, and torque ripple, respectively. Independent variables were considered for both the stator and rotor geometries. A discussion based on a systematic comparison is included, showing, among other things and despite common misconception, that comparable cost versus loss Paretos can be achieved with any of the rotor topologies studied.

Multi-objective design optimization of the transverse gaseous jet in supersonic flows

The mixing process between the injectant and the supersonic crossflow is one of the important issues for the design of the scramjet engine, and the efficiency mixing has a great impact on the improvement of the combustion efficiency. A hovering vortex is formed between the separation region and the barrel shock wave, and this may be induced by the large negative density gradient. The separation region provides a good mixing area for the injectant and the subsonic boundary layer. In the current study, the transverse injection flow field with a freestream Mach number of 3.5 has been optimized by the non-dominated sorting genetic algorithm (NSGA II) coupled with the Kriging surrogate model; and the variance analysis method and the extreme difference analysis method have been employed to evaluate the values of the objective functions. The obtained results show that the jet-to-crossflow pressure ratio is the most important design variable for the transverse injection flow field, and the injectant molecular weight and the slot width should be considered for the mixing process between the injectant and the supersonic crossflow. There exists an optimal penetration height for the mixing efficiency, and its value is about 14.3mm in the range considered in the current study. The larger penetration height provides a larger total pressure loss, and there must be a tradeoff between these two objection functions. In addition, this study demonstrates that the multi-objective design optimization method with the data mining technique can be used efficiently to explore the relationship between the design variables and the objective functions.

Multiobjective Optimization of Rocket Engine Pumps Using Evolutionary Algorithm

A design optimization method for turbopumps of cryogenic rocket engines has been developed. Multiobjective evolutionary algorithm is used for multiobjective pump design optimizations. Performances of design candidates areevaluated by using the meanline pump flow-modeling method based on the Euler turbine equation coupled with empirical correlations for rotor efficiency. To demonstrate feasibility of the present approach, single-stage centrifugal pump and multistage pump design optimizations are performed. The number of pump performance evaluations necessary to obtain a reasonable pareto-optimal set for the conceptual rocket engine pump design will be investigated using the single-stage centrifugal pump design optimization. In both design optimizations the present method obtains hundreds of reasonable and uniformly distributed pareto-optimal solutions that include some designs outperforming the original design in total head while reducing input power by 1%. Detailed observation of the design results also reveals some important design criteria for turbopumps in cryogenic rocket engines. These results demonstrate the feasibility of the evolutionary algorithm-based multiobjective design optimization method in this field.