Progressive Quadratic Response Surface Method Research Articles

Optimization for maximum specific energy density of a lithium-ion battery using progressive quadratic response surface method and design of experiments

The demand for high-capacity lithium-ion batteries (LIB) in electric vehicles has increased. In this study, optimization to maximize the specific energy density of a cell is conducted using the LIB electrochemical model and sequential approximate optimization (SAO). First, the design of experiments is performed to analyze the sensitivity of design factors important to the specific energy density, such as electrode and separator thicknesses, porosity, and particle size. Then, the design variables of the cell are optimized for maximum specific energy density using the progressive quadratic response surface method (PQRSM), which is one of the SAO techniques. As a result of optimization, the thickness ratio of the electrode was optimized and the porosity was reduced to keep the specific energy density high, while still maintaining the specific power density performance. This led to an increase in the specific energy density of 56.8% and a reduction in the polarization phenomenon of 11.5%. The specific energy density effectively improved through minimum computation despite the nonlinearity of the electrochemical model in PQRSM optimization.

Multi-objective optimization of a permanent magnet synchronous motor based on an automated design and analysis procedure

Since traction motors for electric vehicles require a variety of features to be used simultaneously, research on the design optimization of permanent magnet synchronous motors (PMSMs) has been increasing. To apply design optimization in the industrial field, it must be accurate, simple, and the design time should be minimized. This study proposes an automated design and analysis procedure to optimize the shape of a PMSM. ANSYS Maxwell and PIAnO were combined to implement automation, which are finite element analysis and design optimization software programs, respectively. The average torque and total harmonic distortion of the back electromotive force were set as a multi-objective function. In addition, the efficiency and torque ripple were set as constraints with five design variables to satisfy them. To verify the superiority of the proposed design optimization procedure, three optimization algorithms were reviewed and compared with metamodel-based design optimization. These algorithms include parallel algorithm discovery and orchestration, a progressive quadratic response surface method, and sequential two-point diagonal quadratic approximate optimization Moreover, because it is a design optimization problem with a multi-objective function, the changes in the design optimization results according to the changes in the weighting ratio were examined. Finally, the validity of the design results was verified through experiments. The research results demonstrate that the proposed design optimization procedure is more accurate, faster, and better than the conventional method.

Design study of impact performance of a DTH hammer using PQRSM and numerical simulation

This paper presents a simulation model to predict the percussive drilling performance of a down-the-hole (DTH) hammer. First, the pneumatic dynamic model of the DTH hammer is developed considering mass flow rate relations representing orifice opening areas of the air tube, the piston, and the bit flushing channels. Next, the performance of the DTH hammer is numerically simulated and evaluated by considering fluctuations of the upper and lower chamber pressure, impact frequency, and force. The simulation model is validated through a series of laboratory tests. Finally, design factors influencing the hammers impact performance are selected via screening design, and the progressive quadratic response surface method then optimizes the set of design factors to propose a design modification to increasing the impact performance of the DTH hammer.

Robust design optimization of an angular contact ball bearing under manufacturing tolerance

The performances of an angular contact ball bearing (ACBB) are influenced by its geometric dimensions that can have uncertainty due to manufacturing tolerances. Uncertainty of these geometric dimensions results in uncertainty of the performances. This study performed robust design optimization considering the uncertainty of the geometric dimensions which affect the performances of an ACBB, mounted on the main shaft of a grinder. Six geometric parameters and an axial preload were selected as design variables. Among these design variables, three geometric variables were regarded as random design variables that have significant uncertainty of geometric dimensions. To ensure manufacturing precision of the grinder, simultaneously maximizing means and minimizing standard deviations of both axial and radial stiffness values were defined as objective functions. Constraints were imposed to consider uncertainty of the performance functions. A quasi-static analysis was employed to evaluate the bearing performances. The means and standard deviations of the performances were evaluated by the enhanced dimensional reduction method. Robust design optimization was performed using the progressive quadratic response surface method. The robust optimum design revealed that the performance and robustness of both stiffness values were improved than the initial design of the ACBB while satisfying all constraints.

Shape Optimization to Minimize The Response Time of Direct-acting Solenoid Valve

Direct-acting solenoid valves are used in the automotive industry due to their simple structure and quick response in controlling the flow of fluid. We performed an optimization study of response time in order to improve the dynamic performance of a direct-acting solenoid valve. For the optimal design process, we used the commercial optimization software PIAnO, which provides various tools for efficient optimization including design of experiments (DOE), approximation techniques, and a design optimization algorithm. 35 sampling points of computational experiments are performed to find the optimum values of the design variables. In all cases, ANSYS Maxwell electromagnetic analysis software was used to model the electromagnetic dynamics. An approximate model generated from the electromagnetic analysis was estimated and used for the optimization. The best optimization model was selected using the verified approximation model called the Kriging model, and an optimization algorithm called the progressive quadratic response surface method (PQRSM).

Reduction in the moan noise by frequency-response-function-based substructuring and optimization techniques

‘Moan’ noise in a vehicle causes discomfort and anxiety to passengers. In the previous study, the causes of moan noise were identified, and a coherence analysis of the components was conducted. It was found that moan noise was generated by the attribution of resonance when the exciting force produced by the stick–slip motion in a brake system was transmitted to a coupled torsional beam axle module. The analysis involved calculation of the response of the coupled torsional beam axle module on a full suspension brake system reconstructed by consideration of the transfer functions and the joint conditions of the coupled torsional beam axle module and the brake system. Each transfer function is decomposed by a frequency-response-function-based substructuring technique. In this study, when using the sensitivity analysis and optimization techniques for moan-noise reduction, the frequency-response-function-based substructuring technique was performed to calculate the response of the modified coupled torsional beam axle module by considering the joint conditions and the transfer functions of the brake system. Highly sensitive design parameters regarding the response of the coupled torsional beam axle module were identified after the sensitivity analysis. The most sensitive design parameters were selected to enhance the efficiency and the robustness of optimization. The optimal values for the design variables were obtained by applying a progressive quadratic response surface method as a optimization algorithm. The application of an optimization technique was possible using the finite element model and the results of the finite element analysis from the previous study. After optimization, a prototype was re-designed, manufactured and tested. Finally, it was verified that the moan noise was reduced, as the natural frequency of 387 Hz for the coupled torsional beam axle module was moved to a higher frequency.

해석 및 설계 프로세스 통합을 통한 차량 후륜 현가장치 최적화

In this study, we perform the optimization of trailing arm bush in a vehicle rear suspension to improve the ride and handling performance. A design problem was formulated considering 2 objective functions and 7 constraints related to vehicle ride and handling performance. PIAnO, one of the PIDO (Process Integration and Design Optimization) tool, was used to automate analysis procedures and perform a design optimization. In order to assess relation between performances and design variables, we perform the DOE (Design of Experiments). To find the optimal solution, we used Progressive quadratic response surface method (PQRSM), one of the design optimization techniques equipped in PIAnO. As an optimization result, we got an optimal solution and could improve lateral force steer off-center by 43.0% while decreasing brake compliance at wheel center by 8.1%.

Optimization of the lower arm of a vehicle suspension system for road noise reduction by sensitivity analysis

This study analyzed characteristics of road noise using vehicle tests and identified the 200–230Hz range as the most important frequency for road noise reduction. Moreover, vibration sources in the vehicle suspension system were identified through transfer path analysis and coherence analysis. Using a finite element model of a vehicle suspension system, sensitivity analysis was performed to determine sensitive design factors. In order to achieve noise reduction using sensitivity analysis, the lower arm of the vehicle suspension system was found to be the most important design variable. For design optimization, we employed a robust and efficient sequential approximate optimization method, named PQRSM (Progressive Quadratic Response Surface Method) suitable for solving practical design optimization problems. The estimates based on a model proposed from optimization were in accord with the results of the experiment and road noise reduction was achieved by applying the optimally designed lower arm of the vehicle suspension system to a real vehicle.

Application of progressive quadratic response surface method for an oscillation problem optimization

PurposeThe purpose of this paper is to present an effective optimization strategy applied in a physical structure optimization of a semiconductor power metal oxide semiconductor field‐effect transistor (MOSFET), with an expensive integration constraint computation.Design/methodology/approachIn order to deal with inaccuracy due to inevitable numerical errors in the objective function calculation (the power losses of the power MOSFET) and in the constraint computation, the paper proposes to use the progressive quadratic response surface method (PQRSM).FindingsThe paper focuses on four aspects: the inevitable numerical errors in the power loss and the integration constraint computation; the response surface approximation (RSA) method; the PQRSM principle; and finally the comparisons of several optimization methods applied on this application problem.Originality/valueAn original optimization method, PQRSM, is proposed for reducing the oscillation problem of a semi‐analytical model. The optimization results of PQRSM have been compared with the evolution strategy (ES) algorithm, with similar results but faster computation.

Comparative study of optimization technique for the global performance indices of the robot manipulator based on an approximate model

This paper presents the procedure and results of the multi-objective design optimization of a seven-degrees-of-freedom (7DOF) robot manipulator for better global performance, which pertains to the Global Conditioning Index (GCI) and the Structural Length Index (SLI). The concepts of, and the calculation techniques for, GCI and SLI are introduced to allow their use as objective functions for optimization. The optimization techniques, which are Sequential Two-point Diagonal Quadratic Approximate Optimization (STDQAO), the Progressive Quadratic Response Surface Method (PQRSM), the micro genetic algorithm (μGA), and the evolutionary algorithm (EA), were explained briefly, and they are being used to optimize the global performance indices of the robot manipulator. Also, the results of the optimization and comparison of the four optimization methods are summarized in tables.

Design optimization of an injection mold for minimizing temperature deviation

The quality of an injection molded part is largely affected by the mold cooling. Consequently, this makes it necessary to optimize the mold cooling circuit when designing the part but prior to designing the mold. Various approaches of optimizing the mold cooling circuit have been proposed previously. In this work, optimization of the mold cooling circuit was automated by a commercial process integration and design optimization tool called Process Integration, Automation and Optimization (PIAnO), which is often used for large automotive parts such as bumpers and instrument panels. The cooling channels and baffle tubes were located on the offset profile equidistant from the part surface. The locations of the cooling channels and the baffle tubes were automatically generated and input into the mold cooling computer-aided engineering program, Autodesk Moldflow Insight 2010. The objective function was the deviation of the mold surface temperature from a given design temperature. Design variables in the optimization were the depths, distances and diameters of the cooling channels and the baffle tubes. For a more practical analysis, the pressure drop and temperature drop were considered the limited values. Optimization was performed using the progressive quadratic response surface method. The optimization resulted in a more uniform temperature distribution when compared to the initial design, and utilizing the proposed optimization method, a satisfactory solution could be made at a lower cost.

Optimal design of heat exchangers using the progressive quadratic response surface model

The optimal values of the design variables which minimize the pressure loss under the required temperature rise are obtained numerically in a plate-fin heat sink. In thermal/fluid systems, three fundamental difficulties such as a high computational cost for function evaluations (i.e., pressure drop and thermal resistance), the absence of design sensitivity information, and the occurrence of numerical noise are commonly confronted. Thus, sequential approximate optimization (SAO) algorithms have been used to overcome the above mentioned problems. In the present work, the progressive quadratic response surface method (PQRSM), which is one of the SAO algorithms, is proposed for constrained nonlinear optimization problems and is coupled with the computational fluid dynamics (CFD) for the optimization of heat sink. The optimal solutions obtained from the PQRSM are also compared with those of the sequential quadratic programming (SQP) method, which is one of the gradient-based optimization algorithms, to validate the efficiency and fidelity of the PQRSM.

Geometric and electrical optimization design of SR motor based on progressive quadratic response surface method

This paper presents an approximate optimization that is able to determine optimal geometric and electrical design variables of switched reluctance motor. In order to reduce torque ripple that causes noise and vibration, the approximate optimum design has been investigated by means of combining a progressive quadratic response surface method (PQRSM) and a time-stepping finite element method considering drive circuit. The PQRSM is more effective than conjugate gradient method in torque ripple minimization.