Response Surface Approximation Research Articles

Multi-objective optimization design of NPR protection shell for hydrogen storage tank

In order to improve the safety of on-board hydrogen storage tanks during collision, a protective shell based on a negative Poisson’s ratio (NPR) core is designed in this paper. After analyzing and comparing the crashworthiness of three typical honeycomb structures, the concave hexagonal negative Poisson’s ratio honeycomb is selected as the energy-absorbing inner core of the hydrogen storage tank protection structure. The sensitivity analysis of the structural parameters of the NPR shell is conducted through orthogonal tests to identify parameters with a significant impact on crash performance. These parameters are then used as experimental variables for subsequent optimization design. Subsequently, a response surface approximation model between the optimization objective and the structural parameters is established based on the response surface method. Finally, the adaptive simulated annealing algorithm (ASA), neighborhood cultivation genetic algorithm (NCGA), and non-dominated sorting genetic algorithm-II (NSGA-II) are used to optimize the structural parameters, and the optimization results are verified by the whole-vehicle crash simulation. The simulation results demonstrate that all three algorithms achieve better optimization results, among which NCGA is more advantageous in improving the overall performance of the protective shell. After NCGA optimization, the specific energy absorption of the protective shell increases by 19.75%, the maximum collision force of the rigid wall decreases by 23.63%, and the maximum stress of the hydrogen storage tank body decreases by 22.77%. These findings indicate that the designed protection shell effectively improves the crashworthiness of the hydrogen storage tank during collisions.

Effect of parameter optimization on the flow characteristics of venturi-self-excited oscillation mixer based on response surface model and multi-island genetic algorithm

Effect of parameter optimization on the flow characteristics of venturi-self-excited oscillation mixer based on response surface model and multi-island genetic algorithm

Optimization design and experimental research on cooling performance of U-shaped latticework cooling structure with perforations used for gas turbine blade

Latticework cooling structure provides great structural strength and well heat transfer enhancement commonly used for internal cooling of turbine blades. However, traditional rectangle latticework cooling structure raises friction loss badly and reduces cooling efficiency of turbine blades due to the increase of wetted surface area. A new latticework cooling structure with U-shaped sub-channel and perforations on raffles was proposed, aiming to promote heat transfer and reduce friction loss for latticework cooling structure. Numerical simulation, optimization method and experimental test are conducted to investigate heat transfer and fluid flow characteristics of this new latticework cooling structure. Optimization design based on response surface approximation model and non-dominated sorting genetic algorithms-Ⅱ was conducted and objectives were to maximize heat transfer and minimize friction loss. The optimal U-shaped latticework cooling structure with perforations was obtained and experimental research was conducted. Characteristics of heat transfer and friction loss between the optimal U-shaped latticework cooling structure with perforations and the rectangle latticework cooling structure were compared and analyzed. The experiment results showed that the overall heat transfer and thermal–hydraulic performances of the optimal U-shaped latticework cooling structure with perforations are 21.6–37.0% and 27.9–46.7% respectively higher than those of the rectangle latticework cooling structure while friction loss performance of the former is 16.3–29.2% lower than that of the latter as Reynolds number increases from 5000 to 50000. Moreover, empirical formulas for the optimal U-shaped latticework cooling structure with perforations and the rectangle latticework cooling structure are obtained. The present study indicates that the U-shaped latticework cooling structure with perforations not only maintains the superior heat transfer performance, but also reduces friction loss, which is mainly due to the perforation ribs reduce flow distance for part of coolant and also provide an impingement effect for the heated wall and enhance flow interactions and flow mixing.

Surrogate methods for determining profiles of material properties of planar test objects with accumulation of apriori information about them

New methods for identifying the material properties of planar objects as a result of measurements by the eddy current method are proposed. The methods are based on the latest surrogate strategies and advanced optimization techniques that improve efficiency and reduce resource consumption of problem solutions, and balance computational complexity with the accuracy of the results. High-performance metamodels for global surrogate optimization are based on deep truly meaningful fully connected neural networks, serving as an additional function of accumulating apriori information about objects. High accuracy of the approximation of the multidimensional response surface, which is determined by the “exact” electrodynamic model of the testing process, is ensured by performing calculations according to the computer design of a homogeneous experiment with a low weighted symmetric centered discrepancy. The results of numerical experiments performed for full and reduced dimensional search spaces, which can be obtained by linear transformations using the principal component method, are presented. The verification of the methods proved their sufficiently high accuracy and computational performance.

Structural analysis and optimal design of a spherical thin-walled stainless steel water tank without reinforced tie ribs

A spherical thin-walled stainless steel water tank without reinforced tie ribs has been designed to address the issues of easy fracture and corrosion of the ribs, difficulty in maintenance and cleaning, and short service life exposed during the use of thin-walled stainless steel water tanks with reinforced tie ribs. Firstly, an analytical model of a flat steel thin-walled water tank without reinforced tie ribs was established and subjected to static analysis under water pressure. The deformation and stress distribution patterns of the side molded plate of the flat box were obtained. Secondly, a spherical non ribbed thin-walled stainless steel water tank structure was designed with circular cross-section under different box bulge parameters, and its mechanical response characteristics under water pressure load were analyzed. A strengthening scheme was designed for the bottom box molded plate. Once again, optimize the combination design of the box scheme and the reinforcement scheme, and analyze their static, thermodynamic, and thermal solid coupling performance. Finally, the Latin Hypercube Sampling method was used to generate experimental design samples, and a response surface approximation model of a spherical thin-walled stainless steel water tank without reinforced tie ribs was constructed. The wall thickness of the box molded plate, skeleton, and reinforcement were used as design variables, and the maximum deformation and maximum equivalent stress were used as constraints. The lightweight design was carried out with the goal of minimizing mass. The research results indicate that the design program and parameter selection method for spherical thin-walled stainless steel water tanks without reinforced tie ribs proposed in the article are efficient and feasible, and can provide technical reference and theoretical support for the layout and overall optimization design of non ribbed thin-walled stainless steel water tank structures.

Design and optimization of a hybrid cooling configuration combining PCM and liquid cooling for Li-ion battery using data-based response surface approximation model

Effective thermal management is crucial for safe operation of electric vehicles. This study proposes a novel hybrid cooling system that using phase change material (PCM) and liquid cooling to address issues such as leakage, non-uniform temperatures under high discharge rates. A comprehensive 3D model was developed to analyze the influence of geometric parameters on the cooling system. Response surface approximation modeling was used to optimize the layout parameters of the PCM. The results show that the hybrid cooling outperforms other methods, maintaining the cell temperature with 35 ℃ and the temperature difference within 4 ℃. The thickness of the PCM is a significant factor, as it increases heat storage capacity and reduces temperature; however, exceeding a certain threshold leads to increased thermal resistance. A non-uniform PCM layout can reduce the temperature difference by 26 %. An optimal PCM thickness of 2.5 mm to 3 mm ensures that the maximum temperature remains below 32.5 ℃, with a temperature difference within 2 ℃. The lowest temperature difference is achieved with a vertical layout height of 70 mm and a horizontal layout thickness of 3 mm. These findings are valuable for enhancing the thermal management of lithium-ion battery.

Optimization of Guide Vane Centrifugal Pumps Based on Response Surface Methodology and Study of Internal Flow Characteristics

The methodologies of computational fluid dynamics (CFD) and response surface method (RSM) were integrated to uncover the optimal correlational framework for intricate hydraulic geometric parameters of guide vane centrifugal pumps. Parameters such as blade number, blade wrap angle, blade outlet angle, and relative axial distance between the guide vane and impeller, as well as radial distance, are embraced as optimization design variables. Meanwhile, pump head and efficiency were chosen as responsive variables. An analysis of 46 sets of hydraulic performance data was carried out by using the Box–Behnken experimental design method. Subsequently, response surface approximation models were established between hydraulic parameters and the efficiency, as well as the head. The optimal design point was predicted and a simulation of the hydraulic characteristics for the optimal scheme was conducted; the errors were 0.846% for head and 0.256% for efficiency between the simulation results with predicted results from RSM. The optimized model demonstrates noteworthy enhancements in hydraulic performance in comparison to the original model. By analyzing the internal flow of the optimized model under transient conditions, it was found that, as the internal flow of the flow passage components is relatively disordered at small flow rates, the amplitude of pressure pulsation is affected a lot. At other flow rates, the inside pressure pulsation waveform exhibits pronounced periodicity, and the primary causes of pressure pulsation in various flow components are not the same. Wall dissipation and turbulent dissipation emerge as significant contributors to the entropy generation in this centrifugal pump. The magnitude of entropy generation is correlated with the flow rate and the structural configuration of the pump’s components. High-entropy regions concentrate around the leading and trailing edges of the blades.

Shape optimization of a corner‐recessed square tall building to reduce mean wind pressure using a multi‐objective genetic algorithm

SummaryThe current study aims to determine how the corner recession affects tall buildings with square plans. A series of numerical simulations have been conducted to find the parametric models' wind pressure. Visualization tools, such as contour plots and streamlines, present the wind flow near the buildings. Numerical simulations are conducted using RANS k‐ℇ turbulence models considering a length scale of 1:300. Subsequently, a shape optimization study has been carried out to propose a suitable percentage of corner recession, which should minimize the wind pressure on different faces of the building. As design factors, the amount of corner recession (S) and the wind incidence angle (Ø) are taken, along with the mean pressure coefficients (Cp) on the various building faces. Due to the eight axes symmetry of the building configuration, the random sampling technique is used for the Design of Experiment while accounting for the 0°–45° wind angle of attack. The Response Surface Approximation (RSA) is used to construct surrogate models of the objective functions. The RSA models are validated with wind tunnel test results presented in previously published articles. The optimization study is carried out using the multi‐objective genetic algorithm technique.

Searching for optimal Latin hypercube designs by a local greedy strategy

The Latin hypercube design (LHD), because of its one-dimensional projection uniformity, is commonly used in computer experiment. The randomly generated LHD may have too many concentrated design points, and factors may be highly correlated. In this article, we suggested a local greedy strategy for searching optimal LHDs. Our strategy consists of two parts. One is a swap process for doing a local greedy search in a polynomial time. The other is a simulated annealing process for jumping out of the possible local optima. Our strategy is flexible and adapts to various space-filling criteria of LHDs. The simulated experiments illustrated that our proposed algorithm can produce LHDs with well space-filling property and orthogonality. Compared to other classical design algorithms, our algorithm performed better on the criteria related to the point distance and the column correlation. Moreover, for the response surface approximation, the Kriging model using our produced optimal LHD performed more robust on the surface prediction.

Optimization of geometric indicators of a ventricular pump using computational fluid dynamics, surrogate model, response surface approximation, kriging and particle swarm optimization algorithm

Optimization of geometric indicators of a ventricular pump using computational fluid dynamics, surrogate model, response surface approximation, kriging and particle swarm optimization algorithm

Effect of Multifactor Interaction on the Accuracy of RV Reducers

The rotary vector (RV) reducer is one of the widely used mechanical components in industrial systems, specifically in robots. The stability of the transmission performance of the RV reducer is crucial for the efficient operation of industrial equipment. The manufacturing and assembly errors of various components of the RV reducer during the production process are important factors that affect the transmission performance. However, in previous research work, the coupling effect of multiple errors on the transmission accuracy of RV reducer has not been fully considered. Furthermore, a vague relationship between system transmission errors and various errors also has not been thoroughly discussed, which presents a challenge to analyze and optimize the errors of components using the simulation technology of virtual prototype. Therefore, we propose a novel approach to use the response surface method (RSM) to investigate the transmission accuracy of RV reducer. Firstly, based on the constructed virtual prototype of RV reducer, the individual effects of different original errors on the overall transmission error are analyzed. Secondly, a response surface approximation model using RSM is constructed to analyze the effect of multiple error interactions on the transmission accuracy of the RV reducer, and the potential functional relationship between multiple error factors and the overall transmission error is also explored. Finally, the authenticity of the proposed approach is verified by setting up some comparative experiments. This study provides a reference for the efficient analysis and optimization of the transmission accuracy of RV reducers.

Optimized Lightweight Frame for Intelligent New-energy Vehicles

In this paper, a joint optimization method based on multi-objective response surface approximation model and finite element simulation program is proposed to realize the lightweight optimization of new-energy vehicle frames. Under the premise of satisfying the constraints of strength, frequency and vibration, the thickness of different important parts is optimized to achieve the goal of minimizing the quality of intelligent vehicles. In order to obtain the stress distribution of each part and the vibration frequency of the frame, various finite element analyses of the intelligent vehicle frame are analyzed. In order to achieve optimization, this paper adopts the response surface method for multi-objective optimization. Sample data was generated by the central composite design, and the response surface optimization method was used to filter out 5 design variables that had a large impact on the frame. As a result, the weight of the frame was reduced from 25.05 kg to 19.86 kg, a weight reduction of 20.7%, achieving a significant weight reduction effect. This method provides important reference value and guiding significance for the optimization of frame and its lightweight. In this way, the design of the frame can be better optimized to make it lighter, thereby improving the performance of the smart car. At the same time, this method can also be applied to optimization problems in other fields to achieve more efficient and accurate optimization goals.

Lightweight design of temporary support device of rectangular shield for the robot system of coal mine roadway excavation

Owing to the existing problems of the temporary shield support device in a coal mine, such as considerable component weight, difficult disassembly, and large chamber installation, the design of the temporary rectangular shield support device was optimized. A module division method combining the functional analysis method and a similar feature clustering method was proposed, which completes the division of the functional module and establishes the structural module. A structural optimization method of “variable density topology optimization, parameter sensitivity analysis and Optimal Space-Filling Design (OSF)” was proposed. A variable-density topology optimization model of the device was established using the variable-density topology optimization method. The key variables of the device were determined using a parameter sensitivity analysis. The sample points of the critical variables were generated using the optimal space-filling design method, the approximate response surface models of mass, displacement, and stress were constructed, and the optimal solution of the device’s weight was obtained under the constraint conditions of pressure and displacement. A lightweight matching method of modularization based on transportability, disassembly, maintainability, and reliability was proposed, and the optimal matching scheme for the volume and mass of the device was determined. As a result, the weight of the temporary shield support device was reduced by 11.2%, and the maximum stress was reduced by 13.4%, under the premise of ensuring reliability. It realizes the convenience of transportation and high efficiency of assembly and disassembly in different design requirements, which is of great significance to accelerate the intelligent construction of coal mine.

Multi-objective performance optimization of target surface of bionic blue whale-skin impinged by array jet

Jet impingement cooling technology is usually applied to combustor liner with large heat load. With the continuous improvement of high capacity and low emission of heavy-duty gas turbines,the research on low resistance and high cooling efficiency cooling technology is particularly important. To meet these urgent needs, based on the blue whale skin structure, a new array impingement target surface cooling structure was proposed from the perspective of bionics. The flow and heat transfer characteristics of the array impingement bionic target surface cooling structure were numerically simulated under high Reynolds number (Re) and high Heat flux density (q) conditions. The influence of groove depth (H, 1 to 3 mm), radius ratio (R/H, 1 to 3) and spacing ratio (P/H, 10 to 20) on the cooling performance of impingement target surface was analyzed. Multi-objective performance optimization of the bionic structure was carried out by using the second-order response surface approximation model (RSM) and the second-generation non-inferior sequencing genetic algorithm (NSGA-II), and the performance of the optimized structure was tested. The results show that the above optimization method is accurate and effective, and the optimal bionic structure is H = 1.212 mm, R/H = 1.132, P/H = 12.078. Compared with the plane target surface, the average Nusselt number (Nuave), flow friction factor (f), and comprehensive thermal coefficient (F) of the optimal bionic groove structure increased by 14.5%, 1.1% and 14.1%，respectively. The structure and multi-objective optimization method proposed in this paper can provide a certain reference for the design of new efficient cooling structure of heavy-duty gas turbines combustor liner.

Research of composite resistance and design of the test matrix of low-speed impacts

In this paper, low-velocity impact resistance for composite laminates is introduced. The resistance function for the parameters of low-velocity impact performs 2-order Taylor’s series expansion. The orthogonal design and Latin hypercube design are presented and their strongpoint and shortcoming are also indicated. The low-velocity impact simulation model of the composite plate is established. The computed results are compared with the existing standard test from ASTM D7136M-05 and the simulation parameters of the model are modified. By calculating and analyzing typical honeycomb sandwich models with different configurations, the damage-area resistance is extracted from the results. The discrete and abstract variables are treated as continuous integer variables to fit the resistance formula of the composite material. Response surface approximation is used to form a hyper surface formula for parameters. The sensitivity analysis of it reveals that the two most influential factors, related to the resistance definition, which is convenient for the subsequent structural design of the composites. In contrast to the previously defined Taylor’s series expansion, the initial coefficients of the resistance formula are obtained. The resistance hyper surface function obtained from the simulation data is used to design the 7-point low-speed impact tests using Latin hypercube design, which employed to verify and validate the simulations, for purposes of saving on the cost of testing and improving the accuracy of analysis.

Multi‐Objective Topology Optimization of Synchronous Reluctance Motor Using Response Surface Approximation Derived by Deep Learning

In this paper, we propose a novel multi‐objective topology optimization with response surface approximation interpolating various topologies, which is derived by deep learning with training data in the actual design space. The response surface is constructed by means of autoencoder with the training data of geometrically diverse shapes of targeted devices, which can express the interpolations that combine the multiple characteristic structures. The global topology search is performed based on the gradient information of the response surface, by which we can obtain the initial shapes for level set optimization to efficiently obtain easily manufactured and excellent Pareto optimal solutions. The effectiveness of the proposed method is demonstrated by optimizing multi‐flux barriers in a synchronous reluctance motor for the objective functions of average torque and torque ripple. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Topology optimization of an airfoil fin microchannel heat exchanger using artificial intelligence

High-performance microchannel heat exchangers are needed to supply heat for power conversion for nuclear microreactors. An airfoil fin microchannel design, constructed of Alloy 617 with helium as the working fluid, is analyzed and optimized using a design of experiments with artificial intelligence techniques. The use of airfoil fins offers the potential to reduce pressure drop across the heat exchanger, as compared to other types of channel configurations. A framework for topology optimization of airfoil fin printed circuit heat exchangers (PCHEs) has been developed that can be readily extended to different fin sizes and shapes, as well as different inlet and operating conditions, materials of construction, and working fluids. An optimization procedure is developed that employs computational fluid dynamics for a set of design points identified using Latin hypercube sampling. Computational fluid dynamics is used to analyze a simplified two-channel configuration where five design parameters are varied – inlet angle, fin scale, extent of staggering, transverse and longitudinal pitches. Two methods (a 5D polynomial and a regression neural network) are compared for generating surrogate models and the resulting response surface approximation is input to a genetic algorithm that is used to identify a set of optimal parameters. The optimal geometries are found across six channel Reynolds numbers ranging from 1000 to 5000, since inlet conditions affect flow through the heat exchanger. A set of optimal designs that maximizes heat transfer and minimizes pressure drop is identified, and a thermal stress analysis is performed on the optimal design. Correlations for the Nusselt number and Darcy friction factor are developed that can be useful for thermal hydraulic analyses using system codes. Thermal stresses are analyzed and a brief discussion of the status of code cases of PCHEs for nuclear applications is given. Testing and thermomechanical modeling is needed to facilitate future code compliance of PCHEs for high pressure and high temperature applications.

Multi-Variate Optimization of Polymer Electrolyte Membrane Fuel Cells in Consideration of Effects of GDL Compression and Intrusion

This study applies, tests, and compares comprehensive surrogate-based optimization techniques to optimize the performance of polymer electrolyte membrane fuel cells (PEMFCs). Moreover, parametric cases considering four important design variables, i.e., gas diffusion layer thickness (), channel depth (), channel width (), and land width (), are defined using the latin hypercube sampling technique under reasonable constraint conditions. Multidimensional, two-phase PEMFC model simulations are performed to generate the training and test data under these design conditions. Three famous surrogate models, i.e., response surface approximation (RSA), radial basis neural network (RBNN), and kriging (KRG), are employed to construct objective functions for the PEMFC cell voltages operating in the galvanostatic mode, and their accuracies are tested and compared using root mean square error and adjusted R-square. The surrogates are then linked to stochastic optimization algorithms, i.e., genetic algorithm and particle swarm optimization, to determine the optimal design points. A comparative study of these surrogates reveals that the KRG model outperforms the RBNN and RSA models in terms of prediction capability. Furthermore, the PEMFC model simulations at the optimal design points clearly demonstrate that performance improvements of around 56–69 mV at 2.0 A cm−2 are achieved with the optimum design values compared to typical PEMFC design conditions.

Efficient Surrogate Modeling and Design Optimization of Compact Integrated On-Chip Inductors Based on Multi-Fidelity EM Simulation Models

High-performance and small-size on-chip inductors play a critical role in contemporary radio-frequency integrated circuits. This work presents a reliable surrogate modeling technique combining low-fidelity EM simulation models, response surface approximations based on kriging interpolation, and space mapping technology. The reported method is useful for the development of broadband and highly accurate data-driven models of integrated inductors within a practical timeframe, especially in terms of the computational expense of training data acquisition. Application of the constructed surrogate model for rapid design optimization of a compact on-chip inductor is demonstrated. The optimized EM-validated design solution can be reached at a low computational cost, which is a considerable improvement over existing approaches. In addition, this work provides a description and illustrates the usefulness of a multi-fidelity design optimization method incorporating EM computational models of graduated complexity and local polynomial approximations managed by an output space mapping optimization framework. As shown by the application example, the final design solution is obtained at the cost of a few high-fidelity EM simulations of a small-size integrated coil. A supplementary description of variable-fidelity EM computational models and a trade-off between model accuracy and its processing time complements the work.

Optimization of a Wavy Microchannel Heat Sink with Grooves

In this study, a wavy microchannel heat sink with grooves using water as the working fluid is proposed for application to cooling microprocessors. The geometry of the heat sink was optimized to improve heat transfer and pressure loss simultaneously. To achieve optimization goals, the average friction factor and thermal resistance were used as the objective functions. Three dimensionless parameters were selected as design variables: the distance between staggered grooves, groove width, and groove depth. A modified Latin hypercube sampling (LHS) method that combines the advantages of conventional LHS and a three-level full factorial method is also proposed. Response surface approximation was used to construct surrogate models, and Pareto-optimal solutions were obtained with a multi-objective genetic algorithm. The modified LHS was proven to have better performance than the conventional LHS and full factorial methods in the present optimization problem. A representative optimal design showed that both the thermal resistance and friction factor improved by 1.55% and 3.00%, compared to a reference design, respectively.