Robust optimization approach for aerodynamic design has been developed and applied to supercritical wing aerodynamic design. The aerodynamic robust optimization design system consists of genetic optimization algorithm...Robust optimization approach for aerodynamic design has been developed and applied to supercritical wing aerodynamic design. The aerodynamic robust optimization design system consists of genetic optimization algorithm, improved back propagation （BP） neural network and deformation grid technology. In this article, the BP neural network has been improved in two major aspects to enhance the training speed and precision. Uniformity sampling is adopted to generate samples which will be used to establish surrogate model. The testing results show that the prediction precision of the improved BP neural network is reliable. On the assumption that the law of Mach number obeys normal distribution, supercritical wing configuration considering fuselage interfering of a certain aerobus has been taken as a typical example, and five design sections and twist angles have been optimized. The results show that the optimized wing, which considers robust design, has better aerodynamic characteristics. What＇s more, the intensity of shock wave has been reduced.展开更多
The influence of processing parameters on the precision of parts fabricated by fused deposition modeling （FDM） technology is studied based on a series of performed experiments. Processing parameters of FDM in terms ...The influence of processing parameters on the precision of parts fabricated by fused deposition modeling （FDM） technology is studied based on a series of performed experiments. Processing parameters of FDM in terms of wire-width compensation, extrusion velocity, filing velocity, and layer thickness are chosen as the control fac- tors. Robust design analysis and multi-index fuzzy comprehensive assessment method are used to obtain the opti- mal parameters. Results show that the influencing degrees of these four factors on the precision of as-processed parts are different. The optimizations of individual parameters and their combined effects are of the same impor- tance for a high precision manufacturing.展开更多
The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According t...The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.展开更多
A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines （NURBS） free form deformation method based on NURBS basis function is introduce...A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines （NURBS） free form deformation method based on NURBS basis function is introduced to the airfoil parameterization. Second, aerodynamic characteristics are evaluated by solving Navier-Stokes equations, and theγ-Reθt transition model coupling with shear-stress transport （SST） turbulent model is introduced to simulate boundary layer transition. A numerical simulation of transition flow around NLF0416 airfoil is conducted to test the code. The comparison between numerical simulation results and wind tunnel test data approves the validity and applicability of the present transition model. Third, the optimization system is set up, which uses the separated particle swarm optimization （SPSO） as search algorithm and combines the Kriging models as surrogate model during optimization. The system is applied to carry out robust design about the uncertainty of lift coefficient and Mach number for NASA NLF-0115 airfoil. The data of optimized airfoil aerodynamic characteristics indicates that the optimized airfoil can maintain laminar flow stably in an uncertain range and has a wider range of low drag.展开更多
Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the trans...Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.展开更多
Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simpli...Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression（SVR） metamodel is combined with the Monte Carlo simulation（MCS） method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.展开更多
A method based on the robust design optimization is presented to handle the structural uncertainty problems. The variations caused in dynamic performance can be expressed by the mean response and the standard deviatio...A method based on the robust design optimization is presented to handle the structural uncertainty problems. The variations caused in dynamic performance can be expressed by the mean response and the standard deviation of the performance. The robust optimization approach, based on a multi-objective and non-deterministic method, attempts to both optimize the mean performance and minimize the variance of the performance simultaneously. The best possible design optimization is chosen by a trade-off decision. An example of robust design of a two degree freedom system is used to effectively illustrate the application in dynamics. The mass and stiffness uncertainty in the main system as well as the uncertainty of the mass, stiffness and damping in the absorber are considered all together in order to minimize the displacement response of the main system within a wide band of excitation frequencies. The robust optimization results show a significant improvement in performance compared with the conventional solution recommended from vibration textbooks. It is indicated that robust design methods have great potential for application in structural dynamics to deal with uncertainty problems.展开更多
This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert spac...This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA（q）, especially the MA（1） errors and the MA（2） errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.展开更多
A surrogate based particle swarm optimization （SBPSO） algorithm which combines the surrogate modeling technique and particle swarm optimization is applied to the reliability- based robust design （RBRD） of composit...A surrogate based particle swarm optimization （SBPSO） algorithm which combines the surrogate modeling technique and particle swarm optimization is applied to the reliability- based robust design （RBRD） of composite pressure vessels. The algorithm and efficiency of SBPSO are displayed through numerical examples. A model for filament-wound composite pressure vessels with metallic liner is then studied by netting analysis and its responses are analyzed by using Finite element method （performed by software ANSYS）. An optimization problem for maximizing the performance factor is formulated by choosing the winding orientation of the helical plies in the cylindrical portion, the thickness of metal liner and the drop off region size as the design variables. Strength constraints for composite layers and the metal liner are constructed by using Tsai-Wu failure criterion and Mises failure criterion respectively. Numerical examples show that the method proposed can effectively solve the RBRD problem, and the optimal results of the proposed model can satisfy certain reliability requirement and have the robustness to the fluctuation of design variables.展开更多
Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative ...Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.展开更多
It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability...It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability of opti mized structures. A new approach is proposed, in which cer tain perturbation loads are introduced and the corresponding compliance is added to the objective function as a penaliza tion. The stability of the optimized structures can thus be improved substantially by considering structural responses to the original and the introduced loads. Numerical exam ples show the simplicity and effectiveness of the proposed method.展开更多
The uncertainty of time, quantity and quality of recycling products leads tothe bad stability and flexibility of remanufacturing logistics networks, and general design onlycovered the minimizing logistics cost, thus, ...The uncertainty of time, quantity and quality of recycling products leads tothe bad stability and flexibility of remanufacturing logistics networks, and general design onlycovered the minimizing logistics cost, thus, robust design is presented here to solve theuncertainty. The mathematical model of remanufacturing logistics networks is built based onstochastic distribution of uncontrollable factors, and robust objectives are presented. Theintegration of mathematical simulation and design of experiment method is performed to do sensitiveanalysis. The influence of each factor and level on the system is investigated, and the main factorsand optimum combination are studied. The numbers of factors, level of each factor and designprocess of experiment are investigated as well. Finally, the process of robust design based ondesign of experiment is demonstrated by a detailed example.展开更多
This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated...This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.展开更多
The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less se...The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less sensitive to the variation of design variables.There are some important issues in RDO,such as how to judge robustness,deal with multi-objective problem and black-box situation.In this paper,two criteria are proposed to judge the deterministic optimal solution whether satisfies robustness requirment.The robustness measure based on maximum entropy is proposed.Weighted sum method is improved to deal with the objective function,and the basic framework of metamodel assisted robust optimization is also provided for improving the efficiency.Finally,several engineering examples are used to verify the advantages.展开更多
Traditionally,parameter design is carried out prior to tolerance design. However, this two-step design strategy cannot guarantee optimal robustness for products' quality. The proposed integrated robust design meth...Traditionally,parameter design is carried out prior to tolerance design. However, this two-step design strategy cannot guarantee optimal robustness for products' quality. The proposed integrated robust design method determined the optimal parameter and tolerance simultaneously by calculating the maximum tolerance region,thereby improving the quality of products. In addition,the proposed method did not need uncertainty analysis to obtain the maximum tolerance region,so that the calculation cost could be decreased. And the method avoided the difficulty of gaining costtolerance function as maximum tolerance region represented both demand of cost and robust. Finally,an amplifier circuit case was conducted for verification purpose. Based on the results, the proposed approach could provide robust solution with optimal maximum tolerance region.展开更多
This paper discusses many fundamental relationships between robust design methods and reliability improvement. There are 3 approaches in robust design, system design, parameter design and tolerance design. All three ...This paper discusses many fundamental relationships between robust design methods and reliability improvement. There are 3 approaches in robust design, system design, parameter design and tolerance design. All three approaches can be used to improve product reliability in different aspects. Robust design method and reliability engineering should be combined to enhance the overall product quality and reliability.展开更多
Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible reg...Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.展开更多
The uncertainty of time, quantity and quality of recycling products leads to the bad stability and flexibility of remanufacturing logistics networks, while general design only covers the minimizing logistics cost, so ...The uncertainty of time, quantity and quality of recycling products leads to the bad stability and flexibility of remanufacturing logistics networks, while general design only covers the minimizing logistics cost, so robust design is presented to solve it. The mathematical model of remanufacturing logistics networks is built on the stochastic distribution of uncontrollable factors, and robust objectives are presented. The basic elements of robust design of remanufacturing logistics are redefined, and each part of mathematical model is explained in detail as well. Robust design of remanufacturing logistics networks is a problem of multi-objective optimization in essence.展开更多
Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. Howeve...Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. However, fluctuations in the objective characteristic often exceed the allowable range in a design problem. Consequently, it is difficult to obtain sufficient robustness using conventional methods. This research defines adjustable control factors whose values can be adjusted within a given range to increase robustness and proposes a method to calculate robustness, including factors to adjust the objective characteristic and derive optimum ranges of the factors. The robustness index, which indicates the feasibility that the objective characteristic values are within the tolerance by the adjustment, is calculated by the Monte Carlo method, while the range of adjustable control factors is optimized using the Vector evaluated particle swarm optimization. Finally, an engineering example is presented to demonstrate the applicability of the proposed method.展开更多
This paper investigates systematically the problem of multivariate robustparameter design. First, a measurement criterion for the total variation of multivariate qualitycharacteristics is introduced by the result of i...This paper investigates systematically the problem of multivariate robustparameter design. First, a measurement criterion for the total variation of multivariate qualitycharacteristics is introduced by the result of information theory. Then the implementation procedurein the robust design is presented. After that, a simulation example from a practical industrialprocess is provided. Finally, some comments and further work are discussed.展开更多
文摘Robust optimization approach for aerodynamic design has been developed and applied to supercritical wing aerodynamic design. The aerodynamic robust optimization design system consists of genetic optimization algorithm, improved back propagation （BP） neural network and deformation grid technology. In this article, the BP neural network has been improved in two major aspects to enhance the training speed and precision. Uniformity sampling is adopted to generate samples which will be used to establish surrogate model. The testing results show that the prediction precision of the improved BP neural network is reliable. On the assumption that the law of Mach number obeys normal distribution, supercritical wing configuration considering fuselage interfering of a certain aerobus has been taken as a typical example, and five design sections and twist angles have been optimized. The results show that the optimized wing, which considers robust design, has better aerodynamic characteristics. What＇s more, the intensity of shock wave has been reduced.
基金Supported by the Science and Technology Support Key Project of 12th Five-Year of China(2011BAD20B00-4)~~
文摘The influence of processing parameters on the precision of parts fabricated by fused deposition modeling （FDM） technology is studied based on a series of performed experiments. Processing parameters of FDM in terms of wire-width compensation, extrusion velocity, filing velocity, and layer thickness are chosen as the control fac- tors. Robust design analysis and multi-index fuzzy comprehensive assessment method are used to obtain the opti- mal parameters. Results show that the influencing degrees of these four factors on the precision of as-processed parts are different. The optimizations of individual parameters and their combined effects are of the same impor- tance for a high precision manufacturing.
文摘The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.
文摘A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines （NURBS） free form deformation method based on NURBS basis function is introduced to the airfoil parameterization. Second, aerodynamic characteristics are evaluated by solving Navier-Stokes equations, and theγ-Reθt transition model coupling with shear-stress transport （SST） turbulent model is introduced to simulate boundary layer transition. A numerical simulation of transition flow around NLF0416 airfoil is conducted to test the code. The comparison between numerical simulation results and wind tunnel test data approves the validity and applicability of the present transition model. Third, the optimization system is set up, which uses the separated particle swarm optimization （SPSO） as search algorithm and combines the Kriging models as surrogate model during optimization. The system is applied to carry out robust design about the uncertainty of lift coefficient and Mach number for NASA NLF-0115 airfoil. The data of optimized airfoil aerodynamic characteristics indicates that the optimized airfoil can maintain laminar flow stably in an uncertain range and has a wider range of low drag.
文摘Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.
基金Supported by National Natural Science Foundation of China(Grant No.51406148)National Science Technology Support Program of China(Grant No.2012BAA08B06)Postdoctoral Scientific Foundation of China(Grant No.2014M552444)
文摘Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression（SVR） metamodel is combined with the Monte Carlo simulation（MCS） method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.
文摘A method based on the robust design optimization is presented to handle the structural uncertainty problems. The variations caused in dynamic performance can be expressed by the mean response and the standard deviation of the performance. The robust optimization approach, based on a multi-objective and non-deterministic method, attempts to both optimize the mean performance and minimize the variance of the performance simultaneously. The best possible design optimization is chosen by a trade-off decision. An example of robust design of a two degree freedom system is used to effectively illustrate the application in dynamics. The mass and stiffness uncertainty in the main system as well as the uncertainty of the mass, stiffness and damping in the absorber are considered all together in order to minimize the displacement response of the main system within a wide band of excitation frequencies. The robust optimization results show a significant improvement in performance compared with the conventional solution recommended from vibration textbooks. It is indicated that robust design methods have great potential for application in structural dynamics to deal with uncertainty problems.
基金Supported by NSFC grant(10671129)the Special Funds for Doctoral Authorities of Education Ministry(20060270002)+1 种基金E-Institutes of Shanghai Municipal Education Commission(E03004)Shanghai Leading Academic Discipline Project(S30405)
文摘This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA（q）, especially the MA（1） errors and the MA（2） errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.
基金supported by the Natural Science Foundation of China(No.10772070)National Basic Research Program of China(No.2011CB013800)
文摘A surrogate based particle swarm optimization （SBPSO） algorithm which combines the surrogate modeling technique and particle swarm optimization is applied to the reliability- based robust design （RBRD） of composite pressure vessels. The algorithm and efficiency of SBPSO are displayed through numerical examples. A model for filament-wound composite pressure vessels with metallic liner is then studied by netting analysis and its responses are analyzed by using Finite element method （performed by software ANSYS）. An optimization problem for maximizing the performance factor is formulated by choosing the winding orientation of the helical plies in the cylindrical portion, the thickness of metal liner and the drop off region size as the design variables. Strength constraints for composite layers and the metal liner are constructed by using Tsai-Wu failure criterion and Mises failure criterion respectively. Numerical examples show that the method proposed can effectively solve the RBRD problem, and the optimal results of the proposed model can satisfy certain reliability requirement and have the robustness to the fluctuation of design variables.
文摘Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory,image recognition and digital logical mapping. In this paper,robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also,the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that,in robust design each weight only takes the value of i or -i,while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.
基金supported by State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,China(GZ1305)the National Natural Science Foundation of China(11002058 and 11372004)
文摘It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability of opti mized structures. A new approach is proposed, in which cer tain perturbation loads are introduced and the corresponding compliance is added to the objective function as a penaliza tion. The stability of the optimized structures can thus be improved substantially by considering structural responses to the original and the introduced loads. Numerical exam ples show the simplicity and effectiveness of the proposed method.
基金This project is supported by Provincial Natural Science Foundation of Shanghai, China (No. 02ZH14060).
文摘The uncertainty of time, quantity and quality of recycling products leads tothe bad stability and flexibility of remanufacturing logistics networks, and general design onlycovered the minimizing logistics cost, thus, robust design is presented here to solve theuncertainty. The mathematical model of remanufacturing logistics networks is built based onstochastic distribution of uncontrollable factors, and robust objectives are presented. Theintegration of mathematical simulation and design of experiment method is performed to do sensitiveanalysis. The influence of each factor and level on the system is investigated, and the main factorsand optimum combination are studied. The numbers of factors, level of each factor and designprocess of experiment are investigated as well. Finally, the process of robust design based ondesign of experiment is demonstrated by a detailed example.
文摘This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.
基金The study is supported by the National Numerical Wind tunnel project(No.2019ZT2-A05)the Nature Science Foundation of China(No.11902254).
文摘The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less sensitive to the variation of design variables.There are some important issues in RDO,such as how to judge robustness,deal with multi-objective problem and black-box situation.In this paper,two criteria are proposed to judge the deterministic optimal solution whether satisfies robustness requirment.The robustness measure based on maximum entropy is proposed.Weighted sum method is improved to deal with the objective function,and the basic framework of metamodel assisted robust optimization is also provided for improving the efficiency.Finally,several engineering examples are used to verify the advantages.
基金National Natural Science Foundation of China(No.61304218)
文摘Traditionally,parameter design is carried out prior to tolerance design. However, this two-step design strategy cannot guarantee optimal robustness for products' quality. The proposed integrated robust design method determined the optimal parameter and tolerance simultaneously by calculating the maximum tolerance region,thereby improving the quality of products. In addition,the proposed method did not need uncertainty analysis to obtain the maximum tolerance region,so that the calculation cost could be decreased. And the method avoided the difficulty of gaining costtolerance function as maximum tolerance region represented both demand of cost and robust. Finally,an amplifier circuit case was conducted for verification purpose. Based on the results, the proposed approach could provide robust solution with optimal maximum tolerance region.
文摘This paper discusses many fundamental relationships between robust design methods and reliability improvement. There are 3 approaches in robust design, system design, parameter design and tolerance design. All three approaches can be used to improve product reliability in different aspects. Robust design method and reliability engineering should be combined to enhance the overall product quality and reliability.
基金Foundation item. the National Natural Science Foundation of China （No. 50875164）
文摘Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.
基金the Shanghai National Scientific Foundation (02ZH14060)
文摘The uncertainty of time, quantity and quality of recycling products leads to the bad stability and flexibility of remanufacturing logistics networks, while general design only covers the minimizing logistics cost, so robust design is presented to solve it. The mathematical model of remanufacturing logistics networks is built on the stochastic distribution of uncontrollable factors, and robust objectives are presented. The basic elements of robust design of remanufacturing logistics are redefined, and each part of mathematical model is explained in detail as well. Robust design of remanufacturing logistics networks is a problem of multi-objective optimization in essence.
文摘Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. However, fluctuations in the objective characteristic often exceed the allowable range in a design problem. Consequently, it is difficult to obtain sufficient robustness using conventional methods. This research defines adjustable control factors whose values can be adjusted within a given range to increase robustness and proposes a method to calculate robustness, including factors to adjust the objective characteristic and derive optimum ranges of the factors. The robustness index, which indicates the feasibility that the objective characteristic values are within the tolerance by the adjustment, is calculated by the Monte Carlo method, while the range of adjustable control factors is optimized using the Vector evaluated particle swarm optimization. Finally, an engineering example is presented to demonstrate the applicability of the proposed method.
基金theNationalNaturalScienceFoundationofP.R.ChinaunderGrantNo. 79900018andNo.70372010, andbyAeronauticalScienceFoundationofP. R. ChinaunderGrantNo. 02J55001
文摘This paper investigates systematically the problem of multivariate robustparameter design. First, a measurement criterion for the total variation of multivariate qualitycharacteristics is introduced by the result of information theory. Then the implementation procedurein the robust design is presented. After that, a simulation example from a practical industrialprocess is provided. Finally, some comments and further work are discussed.
