The system portfolio selection is a fundamental frontier issue in the development planning and demonstration of weapon equipment.The scientific and reasonable development of the weapon system portfolio is of great sig...The system portfolio selection is a fundamental frontier issue in the development planning and demonstration of weapon equipment.The scientific and reasonable development of the weapon system portfolio is of great significance for optimizing the design of equipment architecture,realizing effective resource allocation,and increasing the campaign effectiveness of integrated joint operations.From the perspective of system-ofsystems,this paper proposes a unified framework called structure-oriented weapon system portfolio selection(SWSPS)to solve the weapon system portfolio selection problem based on structural invulnerability.First,the types of equipment and the relationship between the equipment are sorted out based on the operation loop theory,and a heterogeneous combat network model of the weapon equipment system is established by abstracting the equipment and their relationships into different types of nodes and edges respectively.Then,based on the combat network model,the operation loop comprehensive evaluation index(OLCEI)is introduced to quantitatively describe the structural robustness of the combat network.Next,a weapon system combination selection model is established with the goal of maximizing the operation loop comprehensive evaluation index within the constraints of capability requirements and budget limitations.Finally,our proposed SWSPS is demonstrated through a case study of an armored infantry battalion.The results show that our proposed SWSPS can achieve excellent performance in solving the weapon system portfolio selection problem,which yields many meaningful insights and guidance to the future equipment development planning.展开更多
Pesticides are agricultural inputs that can significantly reduce yield losses,regulate plant growth,effectively liberate agricultural productivity,and improve food security.The availability of pesticides in economies ...Pesticides are agricultural inputs that can significantly reduce yield losses,regulate plant growth,effectively liberate agricultural productivity,and improve food security.The availability of pesticides in economies worldwide is ensured by redistribution through international trade,with different economies playing different roles in this process.In this study,we measured and ranked the importance of economies using nine node metrics.We found that the clustering coefficient was negatively correlated with the other eight node metrics,whereas the other eight node metrics were positively correlated with each other and could be grouped into three communities(betweenness;in-degree,PageRank,authority,and in-closeness;out-degree,hub,and out-closeness).We further investigated the structural robustness of international pesticide trade networks proxied by large component size under three types of shocks to economies(node removal in descending,random,and ascending orders).The results showed that,except for the clustering coefficient,international pesticide trade networks are relatively robust under shocks to economies in ascending order but fragile under shocks to economies in descending order.By contrast,removing nodes with a clustering coefficient in ascending and descending order yielded similar robustness curves.Moreover,the structural robustness related to large component size evolved over time and exhibited an inverse U-shaped pattern.展开更多
Local damages to a structure will cause disproportional collapse if the system is lack of robustness.This structural safety cannot be guaranteed by traditional ways, such as reliability analysis tools and construction...Local damages to a structure will cause disproportional collapse if the system is lack of robustness.This structural safety cannot be guaranteed by traditional ways, such as reliability analysis tools and construction management approaches. Therefore, it is very important to develop related theories for structural robustness.This paper presents a methodology to quantitatively assess the structural robustness from the topological point of view. In the proposed method, the structural failure is viewed as a feedback process. The transformations between the damage input and failure output form a closed-loop. The decisive factor of the operation of such a closed-loop is thought as the structural topology. Furthermore, the damage input and the failure output of the structure are measured by the uncertain disturbance and the change of the topology, respectively. After the sensitivity of the structural topology to the uncertain disturbance is studied, the transfer matrix is discovered to indicate the rationality of the topological relationship. The importance of each loading path, the structural robustness and the most vulnerable part of the system can be found concisely in accordance with this matrix.展开更多
The traditional robust controller is designed to meet the requirement considering both the disturbance and the plant uncertainty while the controller uncertainty is always neglected.The structural optimal robustness o...The traditional robust controller is designed to meet the requirement considering both the disturbance and the plant uncertainty while the controller uncertainty is always neglected.The structural optimal robustness of the closed-loop system is proposed based on the analysis of the robust radii of both the plant and the controller.The subspace angle is introduced to measure the "distance" of two subspaces,and its metric is equivalent to the gap metric.The optimal robust controller based on gap metric is designed to control the rate of the line of sight for an electromechancial target tracking system.It is shown from simulations that the optimal robust controller with the biggest robust radius is superior on the ability of disturbance rejection,and high tracking performance when additive uncertainty exists compared with the robust controller with smaller robust radius.展开更多
In this study,we investigate the robustness of pair structures for nuclear yrast states,that is,whether the structures of relevant collective pairs as building blocks of different yrast states are the same.We focus on...In this study,we investigate the robustness of pair structures for nuclear yrast states,that is,whether the structures of relevant collective pairs as building blocks of different yrast states are the same.We focus on deformed and transitional nuclei and study the yrast states of^(28)Si,^(50)Cr,and^(132)Xe,whose experimental R_(4/2)values are 2.60,2.40,and 2.16,respectively,using the nucleon-pair approximation(NPA)and shell-model effective interactions.For each yrast state,we consider optimized pair structures to be those providing the energy minimum for this state.To find the minimum,many full NPA calculations are performed with varying pair structures,and the numerical optimization procedure of the conjugate gradient method is implemented.Our results suggest that optimized pair structures remain the same for all states within a rotational band of a deformed nucleus.Our results also suggest that after backbending,that is,changing of the intrinsic state,the structure of the S pair,which is essential to build the monopole pairing correlation,remains approximately unchanged,whereas the structures of the non-S pairs,which are essential to build the quadrupole correlation,change significantly.展开更多
Combining the characteristics of servo systems , tracking variable structure control law is studied. Two kinds of new variable control law , the generalized exponential approaching vari- able structure control law and...Combining the characteristics of servo systems , tracking variable structure control law is studied. Two kinds of new variable control law , the generalized exponential approaching vari- able structure control law and the integral variable structure control law are put forward for dis- crete time domain. Taking pump-controlled-motor rotational speed servo system for example , the experiment investigation and digital simulation of integral variable structure control law for dis- crete time domain are performed , the rightness of conclusions are verified.展开更多
The concept of structural robustness and relevant design guidelines have been in existence in the progressive collapse literature since the 1970s following the partial collapse of the Ronan Point apartment building;ho...The concept of structural robustness and relevant design guidelines have been in existence in the progressive collapse literature since the 1970s following the partial collapse of the Ronan Point apartment building;however,in the more general context,research on the evaluation and enhancement of structural robustness is still relatively limited.This paper is aimed to provide a general overview of the current state of research concerning structural robustness.The focus is placed on the quantification and the associated evaluation methodologies,rather than specific measures to ensure prescriptive robustness requirements.Some associated concepts,such as redundancy and vulnerability,will be discussed and interpreted in the general context of robustness such that the corresponding methodologies can be compared quantitatively using a comparable scale.A framework methodology proposed by the authors is also introduced in line with the discussion of the literature.展开更多
Recently,Mach–Zehnder modulators based on thin-film lithium niobate have attracted broad interest for their potential for high modulation bandwidth,low insertion loss,high extinction ratio,and high modulation efficie...Recently,Mach–Zehnder modulators based on thin-film lithium niobate have attracted broad interest for their potential for high modulation bandwidth,low insertion loss,high extinction ratio,and high modulation efficiency.The periodic capacitively loaded traveling-wave electrode is optimally adopted for ultimate high-performances in this type of modulator.However,such an electrode structure on a silicon substrate still suffers from the velocity mismatch and substrate leakage loss for microwave signals.Here,we introduce a thin-film lithium niobate modulator structure using this periodic capacitively loaded electrode on a silicon substrate.Backside holes in the silicon substrate are prepared to solve robustly the above difficulties.The fabricated device exhibits an insertion loss of 0.9 dB,a halfwave-voltage–length product of 2.18 V·cm,and an ultra-wide bandwidth well exceeding 67 GHz for a 10-mm-long device.Data transmissions with rates up to 112 Gb/s are demonstrated.The proposed structure and fabrication strategy are compatible for other types of monolithic and heterogeneous integrated thin-film lithium niobate modulators on a silicon substrate.展开更多
Structural robustness is the concept to evaluate whether local damages to the structure will cause disproportional consequences. It is one of the most important indexes to keep the structural safety, especially to con...Structural robustness is the concept to evaluate whether local damages to the structure will cause disproportional consequences. It is one of the most important indexes to keep the structural safety, especially to consider a special loading named as "human active damage". In the present paper, the loaded structure is analyzed by a weighted graph. The joints and members of the structure correspond to the vertexes and edges of the graph, and the ratio of the most dangerous stress state to the material strength of each member is treated as the weight of each edge. Based on the quantitative description of the structural topology, the structure graph is expressed as a hierarchical model which is built by a set of vertex-connected units. The local damage can be expressed as the deterioration of the unit(s), while the final possible failure mode of the structure can be obtained by a specific assignment of its weighted graph. In this way, the relationship between the structural behavior and the combined damages of the subordinate units in each hierarchy can be formed as an envelope diagram. This diagram exactly shows the contribution of each subordinate unit to the robustness of the whole structure. Furthermore, the most vulnerable part, as well as the topologic difference between the subordinates, can be found visually.展开更多
Structural collapse under blast loads is a very complex process. For several decades, the engineering profession has considered some approaches to analyze the essential physics of collapse phenomena. Recently, the int...Structural collapse under blast loads is a very complex process. For several decades, the engineering profession has considered some approaches to analyze the essential physics of collapse phenomena. Recently, the interest in this topic has risen to an apex since the collapse of the World Trade Center towers. A two-step analysis approach to capture the characteristics of structural collapse during explosions is proposed. A numerical example is presented to illustrate the performance of the presented approach.展开更多
Ti3C2Tx has been emerging as an attractive platform to prepare composite catalysts,and their assembly into integrated catalytic mate rials repre sents a key step forward toward practical applications.Howeve r,the swel...Ti3C2Tx has been emerging as an attractive platform to prepare composite catalysts,and their assembly into integrated catalytic mate rials repre sents a key step forward toward practical applications.Howeve r,the swelling behavior of Ti3C2Tx leads to significant structure change,which challenges the stability of Ti3C2Tx-based integrated functional materials for catalytic applications.Here we report a facile synthesis of Pd/Ti3C2Tx■graphene hydrogels in which Pd/Ti3C2Tx are spatially encapsulated in the 3 D porous graphene framework.The porous interconnected structure not only affords efficient mass transfer and desirable functional accessibility to catalytic active sites,but also effectively buffers the swelling behavior of Ti3C2Tx.When applied for catalytic hydrogenation of nitroaromatic compounds,the mechanically robust Pd/Ti3C2Tx■graphene hydrogels exhibit efficient activities,easy separability,and good cyclability.This work is expected to promote the application of Ti3C2Tx-based functional materials for practical applications involving interactions with salt solutions,such as supercapacitors,catalysis,and water purification.展开更多
One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that ...One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that Boolean networks,which are a promising model of biological networks,do not always represent the conservation law.This paper thus addresses a kind of conservation law as a generic property of Boolean networks.In particular,we consider the problem of finding network structures on which,for any Boolean operation on nodes,the number of active nodes,i.ev nodes whose state is one,is constant over time.As a solution to the problem,we focus on the strongly-connected network structures and present a necessary and sufficient condition.展开更多
Negative Poisson's ratio(NPR) structure has outstanding performances in lightweight and energy absorption, and it can be widely applied in automotive industries. By combining the front anti-collision beam, crash b...Negative Poisson's ratio(NPR) structure has outstanding performances in lightweight and energy absorption, and it can be widely applied in automotive industries. By combining the front anti-collision beam, crash box and NPR structure, a novel NPR bumper system for improving the crashworthiness is first proposed in the work. The performances of the NPR bumper system are detailed studied by comparing to traditional bumper system and aluminum foam filled bumper system. To achieve the rapid design while considering perturbation induced by parameter uncertainties, a multi-objective robust design optimization method of the NPR bumper system is also proposed. The parametric model of the bumper system is constructed by combining the full parametric model of the traditional bumper system and the parametric model of the NPR structure. Optimal Latin hypercube sampling technique and dual response surface method are combined to construct the surrogate models. The multi-objective robust optimization results of the NPR bumper system are then obtained by applying the multi-objective particle swarm optimization algorithm and six sigma criteria. The results yielded from the optimizations indicate that the energy absorption capacity is improved significantly by the NPR bumper system and its performances are further optimized efficiently by the multi-objective robust design optimization method.展开更多
基金This work was supported by the National Natural Science Foundation of China(71690233,71971213,71571185)Scientific Research Foundation of National University of Defense Technology(ZK19-16).
文摘The system portfolio selection is a fundamental frontier issue in the development planning and demonstration of weapon equipment.The scientific and reasonable development of the weapon system portfolio is of great significance for optimizing the design of equipment architecture,realizing effective resource allocation,and increasing the campaign effectiveness of integrated joint operations.From the perspective of system-ofsystems,this paper proposes a unified framework called structure-oriented weapon system portfolio selection(SWSPS)to solve the weapon system portfolio selection problem based on structural invulnerability.First,the types of equipment and the relationship between the equipment are sorted out based on the operation loop theory,and a heterogeneous combat network model of the weapon equipment system is established by abstracting the equipment and their relationships into different types of nodes and edges respectively.Then,based on the combat network model,the operation loop comprehensive evaluation index(OLCEI)is introduced to quantitatively describe the structural robustness of the combat network.Next,a weapon system combination selection model is established with the goal of maximizing the operation loop comprehensive evaluation index within the constraints of capability requirements and budget limitations.Finally,our proposed SWSPS is demonstrated through a case study of an armored infantry battalion.The results show that our proposed SWSPS can achieve excellent performance in solving the weapon system portfolio selection problem,which yields many meaningful insights and guidance to the future equipment development planning.
基金the National Natural Science Foundation of China(72171083)the Shanghai Outstanding Academic Leaders Plan,and the Fundamental Research Funds for the Central Universities.
文摘Pesticides are agricultural inputs that can significantly reduce yield losses,regulate plant growth,effectively liberate agricultural productivity,and improve food security.The availability of pesticides in economies worldwide is ensured by redistribution through international trade,with different economies playing different roles in this process.In this study,we measured and ranked the importance of economies using nine node metrics.We found that the clustering coefficient was negatively correlated with the other eight node metrics,whereas the other eight node metrics were positively correlated with each other and could be grouped into three communities(betweenness;in-degree,PageRank,authority,and in-closeness;out-degree,hub,and out-closeness).We further investigated the structural robustness of international pesticide trade networks proxied by large component size under three types of shocks to economies(node removal in descending,random,and ascending orders).The results showed that,except for the clustering coefficient,international pesticide trade networks are relatively robust under shocks to economies in ascending order but fragile under shocks to economies in descending order.By contrast,removing nodes with a clustering coefficient in ascending and descending order yielded similar robustness curves.Moreover,the structural robustness related to large component size evolved over time and exhibited an inverse U-shaped pattern.
文摘Local damages to a structure will cause disproportional collapse if the system is lack of robustness.This structural safety cannot be guaranteed by traditional ways, such as reliability analysis tools and construction management approaches. Therefore, it is very important to develop related theories for structural robustness.This paper presents a methodology to quantitatively assess the structural robustness from the topological point of view. In the proposed method, the structural failure is viewed as a feedback process. The transformations between the damage input and failure output form a closed-loop. The decisive factor of the operation of such a closed-loop is thought as the structural topology. Furthermore, the damage input and the failure output of the structure are measured by the uncertain disturbance and the change of the topology, respectively. After the sensitivity of the structural topology to the uncertain disturbance is studied, the transfer matrix is discovered to indicate the rationality of the topological relationship. The importance of each loading path, the structural robustness and the most vulnerable part of the system can be found concisely in accordance with this matrix.
基金Sponsored by the Science and Technology Project of the Department of Education of Heilongjiang Province(Grant No.12511015)the Defense Pre-Research Project of China (Grant No.51309040201)
文摘The traditional robust controller is designed to meet the requirement considering both the disturbance and the plant uncertainty while the controller uncertainty is always neglected.The structural optimal robustness of the closed-loop system is proposed based on the analysis of the robust radii of both the plant and the controller.The subspace angle is introduced to measure the "distance" of two subspaces,and its metric is equivalent to the gap metric.The optimal robust controller based on gap metric is designed to control the rate of the line of sight for an electromechancial target tracking system.It is shown from simulations that the optimal robust controller with the biggest robust radius is superior on the ability of disturbance rejection,and high tracking performance when additive uncertainty exists compared with the robust controller with smaller robust radius.
基金Supported by the National Natural Science Foundation of China(11875134,11875188,12175071,11975151,11961141003)the Shanghai Key Laboratory of Particle Physics and Cosmology(21DZ2271500-2)。
文摘In this study,we investigate the robustness of pair structures for nuclear yrast states,that is,whether the structures of relevant collective pairs as building blocks of different yrast states are the same.We focus on deformed and transitional nuclei and study the yrast states of^(28)Si,^(50)Cr,and^(132)Xe,whose experimental R_(4/2)values are 2.60,2.40,and 2.16,respectively,using the nucleon-pair approximation(NPA)and shell-model effective interactions.For each yrast state,we consider optimized pair structures to be those providing the energy minimum for this state.To find the minimum,many full NPA calculations are performed with varying pair structures,and the numerical optimization procedure of the conjugate gradient method is implemented.Our results suggest that optimized pair structures remain the same for all states within a rotational band of a deformed nucleus.Our results also suggest that after backbending,that is,changing of the intrinsic state,the structure of the S pair,which is essential to build the monopole pairing correlation,remains approximately unchanged,whereas the structures of the non-S pairs,which are essential to build the quadrupole correlation,change significantly.
文摘Combining the characteristics of servo systems , tracking variable structure control law is studied. Two kinds of new variable control law , the generalized exponential approaching vari- able structure control law and the integral variable structure control law are put forward for dis- crete time domain. Taking pump-controlled-motor rotational speed servo system for example , the experiment investigation and digital simulation of integral variable structure control law for dis- crete time domain are performed , the rightness of conclusions are verified.
文摘The concept of structural robustness and relevant design guidelines have been in existence in the progressive collapse literature since the 1970s following the partial collapse of the Ronan Point apartment building;however,in the more general context,research on the evaluation and enhancement of structural robustness is still relatively limited.This paper is aimed to provide a general overview of the current state of research concerning structural robustness.The focus is placed on the quantification and the associated evaluation methodologies,rather than specific measures to ensure prescriptive robustness requirements.Some associated concepts,such as redundancy and vulnerability,will be discussed and interpreted in the general context of robustness such that the corresponding methodologies can be compared quantitatively using a comparable scale.A framework methodology proposed by the authors is also introduced in line with the discussion of the literature.
基金This work was partially supported by the National Natural Science Foundation of China(NSFC)(Nos.62135012,62105107,and 61961146003)Leading Innovative and Entrepreneur Team Introduction Program of Zhejiang(No.2021R01001)。
文摘Recently,Mach–Zehnder modulators based on thin-film lithium niobate have attracted broad interest for their potential for high modulation bandwidth,low insertion loss,high extinction ratio,and high modulation efficiency.The periodic capacitively loaded traveling-wave electrode is optimally adopted for ultimate high-performances in this type of modulator.However,such an electrode structure on a silicon substrate still suffers from the velocity mismatch and substrate leakage loss for microwave signals.Here,we introduce a thin-film lithium niobate modulator structure using this periodic capacitively loaded electrode on a silicon substrate.Backside holes in the silicon substrate are prepared to solve robustly the above difficulties.The fabricated device exhibits an insertion loss of 0.9 dB,a halfwave-voltage–length product of 2.18 V·cm,and an ultra-wide bandwidth well exceeding 67 GHz for a 10-mm-long device.Data transmissions with rates up to 112 Gb/s are demonstrated.The proposed structure and fabrication strategy are compatible for other types of monolithic and heterogeneous integrated thin-film lithium niobate modulators on a silicon substrate.
文摘Structural robustness is the concept to evaluate whether local damages to the structure will cause disproportional consequences. It is one of the most important indexes to keep the structural safety, especially to consider a special loading named as "human active damage". In the present paper, the loaded structure is analyzed by a weighted graph. The joints and members of the structure correspond to the vertexes and edges of the graph, and the ratio of the most dangerous stress state to the material strength of each member is treated as the weight of each edge. Based on the quantitative description of the structural topology, the structure graph is expressed as a hierarchical model which is built by a set of vertex-connected units. The local damage can be expressed as the deterioration of the unit(s), while the final possible failure mode of the structure can be obtained by a specific assignment of its weighted graph. In this way, the relationship between the structural behavior and the combined damages of the subordinate units in each hierarchy can be formed as an envelope diagram. This diagram exactly shows the contribution of each subordinate unit to the robustness of the whole structure. Furthermore, the most vulnerable part, as well as the topologic difference between the subordinates, can be found visually.
基金the National Basic Research Program(973) of China (No. 2002CB412709)the National Natural Science Foundation of China (No. 50378054)
文摘Structural collapse under blast loads is a very complex process. For several decades, the engineering profession has considered some approaches to analyze the essential physics of collapse phenomena. Recently, the interest in this topic has risen to an apex since the collapse of the World Trade Center towers. A two-step analysis approach to capture the characteristics of structural collapse during explosions is proposed. A numerical example is presented to illustrate the performance of the presented approach.
基金support from the National Natural Science Foundation of China(Nos.51802040,51977071 and 21802020)Key Laboratory of Coal to Ethylene Glycol and Its Related Technology,Chinese Academy of Sciences(No.201901)+1 种基金Natural Science Foundation of Hunan Prvoince(No.2017JJ2040)the Fundamental Research Funds for the Central Universities。
文摘Ti3C2Tx has been emerging as an attractive platform to prepare composite catalysts,and their assembly into integrated catalytic mate rials repre sents a key step forward toward practical applications.Howeve r,the swelling behavior of Ti3C2Tx leads to significant structure change,which challenges the stability of Ti3C2Tx-based integrated functional materials for catalytic applications.Here we report a facile synthesis of Pd/Ti3C2Tx■graphene hydrogels in which Pd/Ti3C2Tx are spatially encapsulated in the 3 D porous graphene framework.The porous interconnected structure not only affords efficient mass transfer and desirable functional accessibility to catalytic active sites,but also effectively buffers the swelling behavior of Ti3C2Tx.When applied for catalytic hydrogenation of nitroaromatic compounds,the mechanically robust Pd/Ti3C2Tx■graphene hydrogels exhibit efficient activities,easy separability,and good cyclability.This work is expected to promote the application of Ti3C2Tx-based functional materials for practical applications involving interactions with salt solutions,such as supercapacitors,catalysis,and water purification.
基金supported by Grant-in-Aid for Scientific Research(B)#17H03280 from the Ministry of Education,Culture,Sports,Science and Technology of Japan.
文摘One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that Boolean networks,which are a promising model of biological networks,do not always represent the conservation law.This paper thus addresses a kind of conservation law as a generic property of Boolean networks.In particular,we consider the problem of finding network structures on which,for any Boolean operation on nodes,the number of active nodes,i.ev nodes whose state is one,is constant over time.As a solution to the problem,we focus on the strongly-connected network structures and present a necessary and sufficient condition.
基金supported by the National Natural Science Foundation of China(Grant Nos.51605219&51375007)the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20160791&SBK2015022352)+1 种基金the Visiting Scholar Foundation of the State Key Lab of Mechanical Transmission in Chongqing University(Grant Nos.SKLMT-KFKT-201608,SKLMTKFKT-2014010&SKLMT-KFKT-201507)the Fundamental Research Funds for the Central Universities(Grant No.NE2016002)
文摘Negative Poisson's ratio(NPR) structure has outstanding performances in lightweight and energy absorption, and it can be widely applied in automotive industries. By combining the front anti-collision beam, crash box and NPR structure, a novel NPR bumper system for improving the crashworthiness is first proposed in the work. The performances of the NPR bumper system are detailed studied by comparing to traditional bumper system and aluminum foam filled bumper system. To achieve the rapid design while considering perturbation induced by parameter uncertainties, a multi-objective robust design optimization method of the NPR bumper system is also proposed. The parametric model of the bumper system is constructed by combining the full parametric model of the traditional bumper system and the parametric model of the NPR structure. Optimal Latin hypercube sampling technique and dual response surface method are combined to construct the surrogate models. The multi-objective robust optimization results of the NPR bumper system are then obtained by applying the multi-objective particle swarm optimization algorithm and six sigma criteria. The results yielded from the optimizations indicate that the energy absorption capacity is improved significantly by the NPR bumper system and its performances are further optimized efficiently by the multi-objective robust design optimization method.