Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with...Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.展开更多
Axiomatic design(AD) is a popular design method,and satisfying the independence axiom is the basis of AD.However,AD doesn't provide methods to decompose functions then keep them independent and to handle coupled de...Axiomatic design(AD) is a popular design method,and satisfying the independence axiom is the basis of AD.However,AD doesn't provide methods to decompose functions then keep them independent and to handle coupled design.A few of ways of handling coupled design are mainly passive resolutions when coupled design exists,but not efficient to each product design.Hence,this paper presents an innovative approach to design and decompose functions of complex products based on functional connections,aiming at actively avoiding functional coupling.By contrasting with component networks,four kinds of relations among functions are identified,including spatial,energy,material,and information connection.Then the definitions of these relations and the dominant connection are given.Based on the definitions,the principles of functional decomposition and design are developed,in which each non-leaf function is broken into sub functions centered on its dominant connection with avoidance of functional cross and coupling,and sequentially satisfies the independence axiom.Then the operational flow of the proposed approach is constructed.Determining the dominant connection of a function,decomposing the function into sub functions in terms of the dominant connection and reverse examination and optimization are planed as the core steps in each zigzagging.Input process output(IPO) analysis is introduced to obtain the dominant connection of a function,some rules for examining and optimizing the decomposition results reversely according to oriented object theory are presented as well.An illustrative example about the pouring function of squeeze casting equipments presented demonstrates how to use the proposed approach,and indicates its effectiveness.The proposed approach expands the principles of AD,constructs a guidance policy for independent functional design of complex products based on AD,and can help decrease or actively avoid coupled design and improve design efficiency.展开更多
Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculi...Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculiar to the gear, there will be large amounts of design parameters in gear design, and the influences of gear parameters changing on gear trains, transmission system and the whole equipment have to be taken into account, which increases the complexity of optimization problem. This paper puts forward to apply functionally graded materials(FGMs) to gears and then conduct the optimization. According to the force situation of gears, the material distribution form of FGM gears is determined. Then based on the performance parameters analysis of FGMs and the practical working demands for gears, a multi-objective optimization model is formed. Finally by using the goal driven optimization(GDO) method, the optimal material distribution is achieved, which makes gear weight and the maximum deformation be minimum and the maximum bending stress do not exceed the allowable stress. As an example, the applying of FGM to automotive transmission gear is conducted to illustrate the optimization design process and the result shows that under the condition of keeping the normal working performance of gear, the method achieves in greatly reducing the gear weight. This research proposes a FGM gears design method that is able to largely reduce the weight of gears by optimizing the microscopic material parameters instead of changing the macroscopic dimension parameters of gears, which reduces the complexity of gear weight optimization problem.展开更多
To improve aerodynamic performance of wind turbine airfoils,the shape profile characteristic of the airfoil is investigated.Application of conformal transformation,one functional and integrated expression of wind turb...To improve aerodynamic performance of wind turbine airfoils,the shape profile characteristic of the airfoil is investigated.Application of conformal transformation,one functional and integrated expression of wind turbine airfoils is presented.Using the boundary layer theory,the aerodynamic model with roughness of wind turbine airfoils is introduced by studying flow separation around the airfoil.Based on the shape expression and aerodynamic performance of airfoils,the function design of wind turbine airfoils is carried out that the maximum lift-drag ratio and low roughness sensitivity are designed objects.Three wind turbines airfoils with different thickness are gained which are used at tip part of blades.As an example,the aerodynamic performance of one designed airfoil with relative thickness of 15%is simulated in different conditions of clean surface,rough surface,laminar flow and turbulent flow.The comparison of aerodynamic performance between the designed airfoil and one popular NACA airfoil is completed which can verify the better performance of the designed airfoil and reliability of the designed method.展开更多
According to the technical characteristics of short fixed wheelbase of a high-speed carriage, a subgrade-track integrated space mechanical response analysis model is proposed for trains under the action ofbiaxial load...According to the technical characteristics of short fixed wheelbase of a high-speed carriage, a subgrade-track integrated space mechanical response analysis model is proposed for trains under the action ofbiaxial load after the comparison of the stress distribution characteristics of the ballast track subgrade bed structures for high-speed railway under the action of uniaxial load and biaxial load. The loading threshold value (high-cycle long-term dynamic strength) under the circum- stance where the cumulative deformation of subgrade structure gradually develops and finally reaches the convergent state, and its relationship with the foundation coefficient K30 were deduced, based on the characteristics of cumulative defor- mation evolution obtained from the unit structure filling model test under the action of cyclic loading. In view of structure stability and frost resistance requirements of the railway subgrade in cold regions, technical conditions to maintain good service performance of subgrade structure of high-speed railway ballasted track are discussed and analyzed. Study results show that the additive effect manifests itself obviously for railway train bogies under the action of biaxial load than uni- axial load, which has a significant dynamic effect on the subgrade bed bottom and a slight effect on the surface layer. Thus, the adoption of a biaxial load model in the design of a high-speed railway subgrade accurately reflects the vehicle load. Pursuant to the structure design principle, the design method of the subgrade structure of high-speed railway ballasted track is proposed to meet the technical requirements such as structural strength, bearing stiffness and high-cyclic and long-term stability. Technical indicators are obtained for the variation of thickness of the surface layer of reinforced sub- grade bed in the double-layer subgrade mode along with the change of K30 at the subgrade bed bottom. The double-layer structure mode of "closure on the upper layer and drainage on the lower layer" was proposed in order to meet the water- proofing and drainage requirements of the upper layer of the subgrade bed in cold regions. A dense-framework graded gravel filler with weak water permeability at a coefficient of 10 4 cm/s is used on the upper layer and the void-framework graded gravel filler at the water permeability coefficient of 10 2 cm/s is adopted on the lower layer.展开更多
In the process of particle settling in a dilute,a density graded distribution of the liquid below the suspension needs to be designed according to the gravity of the suspension prior to sedimentation.In the present pa...In the process of particle settling in a dilute,a density graded distribution of the liquid below the suspension needs to be designed according to the gravity of the suspension prior to sedimentation.In the present paper a compositionally graded W-Mo composite was formed via the settling of the W and Mo particles,with a density gradient distributed in the initial clear liquid along the settling direction.展开更多
Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop pr...Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a "black-box" and their gradients are not available or not reliable. On the basis of the reliable design space (RDS) concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing (RSP) approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.展开更多
The purpose of this paper is to investigate the application of topology description function (TDF) in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving techni...The purpose of this paper is to investigate the application of topology description function (TDF) in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the 'Hamilton-Jacobi-type' equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson's ratio, the other with negative Poisson's ratio. The examples show the method based on TDF is effective for material design.展开更多
Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presente...Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presented, by which a Al 2O 3/(W,Ti)C ceramic tool material FG 2 was developed. Multi objective optimization method was employed in designing the compositional distribution of this ceramic tool material. The results of both continuous and intermittent cutting tests are indicative of the much better cutting behavior of the functionally gradient ceramic tool FG 2 than that of the common ceramic tool SG 4.展开更多
The expansion of agricultural function is one of the important means for modern agricultural projects to promote agricultural economic benefits. Successful modern agricultural projects require good creative ideas and ...The expansion of agricultural function is one of the important means for modern agricultural projects to promote agricultural economic benefits. Successful modern agricultural projects require good creative ideas and design programs. While developing high-efficient modern agricultural production activities,we should fully explore the intangible value of agricultural production activities,combine agriculture with agricultural products,natural conditions,cultural conception and other effective resources,to expand agricultural functions,and promote comprehensive benefits. In order to build a sustainable modern agricultural project operation system,Naya Mountain Villa project planning is taken as an example for analysis. Naya Mountain Villa began construction in 2011; the creative planning based on the agricultural expansion function was carried out in 2013; it had successful access to the capital market in 2015. The project realizes the effective integration of agricultural production system and agricultural function expansion,constructs a set of long-term stable profiting models,and lays an important foundation for entering the capital market. The project is a representative example of the function-expanding modern agricultural project. Through the analysis of the design ideas of the project,this paper discusses the function expansion elements of basic resources,public welfare and agricultural function expansion methods,the formation of general ideas,source and construction logic of creative thinking,and summarizes and abstracts some inspiring design methods of agricultural function expansion. Through the analysis of the key points in the design of the specific technical aspects of the project,this paper provides a reference for solving common difficult problems in the practical design. The summary and refinement of the thinking logic,thinking construction and specific design method of the project is inspiring and repeatable to some extent,which can provide reference for the relevant researchers.展开更多
The function of the UHVDC test base of the State Grid Corporation of China (SGCC) is oriented to serve UHVDC power transmission and substation projects, especially power transmission from West China to East China, and...The function of the UHVDC test base of the State Grid Corporation of China (SGCC) is oriented to serve UHVDC power transmission and substation projects, especially power transmission from West China to East China, and to promote localization of UHVDC transmission and substation equipment. In essentials, this test base consists of UHVDC test transmission line, corona cage, outdoor test site, UHV test hall, pollution and environment laboratory, electromagnetic environment simulation test site, insulator laboratory, arrester laboratory and live equipment test field. This paper introduces the function and design idea of the test base, presents the main performance parameters of the above-mentioned test facilities, and summarizes the matters of concern when siting and planning.展开更多
To deal with a bottom up process model for design reuses a specific extended house of quality(EHOQ)is proposed Two kinds of supported functions,basic supported functions and new supported functions,are defined.Two ...To deal with a bottom up process model for design reuses a specific extended house of quality(EHOQ)is proposed Two kinds of supported functions,basic supported functions and new supported functions,are defined.Two processes to determine two kinds of functions are presented A kind of EHOQ matrix for a company is given and its management steps are studied.展开更多
In the implementation of quality function deployment (QFD), the determination of the target values of engineering characteristics is a complex decision process with multiple variables and multiple objectives that sh...In the implementation of quality function deployment (QFD), the determination of the target values of engineering characteristics is a complex decision process with multiple variables and multiple objectives that should trade off, and optimize all kinds of conflicts and constraints. A fuzzy linear programming model (FLP) is proposed. On the basis of the inherent fuzziness of QFD system, triangular fuzzy numbers are used to represent all the relationships and correlations, and then, the functional relationships between the customer needs and engineering characteristics and the functional correlations among the engineering characteristics are determined with the information in the house of quality (HoQ) fully used. The fuzzy linear programming (FLP) model aims to find the optimal target values of the engineering characteristics to maximize the customer satisfaction. Finally, the proposed method is illustrated by a numerical example.展开更多
文摘Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.
基金supported by Guangdong Provincial & Ministry of Education IAR Project of China (Grant No. 2009A090100026)Guangxi Provincial Science and Technology Infrastructure Construction Project of China (Grant No. Guikeneng 0842006,09-007-05)
文摘Axiomatic design(AD) is a popular design method,and satisfying the independence axiom is the basis of AD.However,AD doesn't provide methods to decompose functions then keep them independent and to handle coupled design.A few of ways of handling coupled design are mainly passive resolutions when coupled design exists,but not efficient to each product design.Hence,this paper presents an innovative approach to design and decompose functions of complex products based on functional connections,aiming at actively avoiding functional coupling.By contrasting with component networks,four kinds of relations among functions are identified,including spatial,energy,material,and information connection.Then the definitions of these relations and the dominant connection are given.Based on the definitions,the principles of functional decomposition and design are developed,in which each non-leaf function is broken into sub functions centered on its dominant connection with avoidance of functional cross and coupling,and sequentially satisfies the independence axiom.Then the operational flow of the proposed approach is constructed.Determining the dominant connection of a function,decomposing the function into sub functions in terms of the dominant connection and reverse examination and optimization are planed as the core steps in each zigzagging.Input process output(IPO) analysis is introduced to obtain the dominant connection of a function,some rules for examining and optimizing the decomposition results reversely according to oriented object theory are presented as well.An illustrative example about the pouring function of squeeze casting equipments presented demonstrates how to use the proposed approach,and indicates its effectiveness.The proposed approach expands the principles of AD,constructs a guidance policy for independent functional design of complex products based on AD,and can help decrease or actively avoid coupled design and improve design efficiency.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2015AA042505)
文摘Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculiar to the gear, there will be large amounts of design parameters in gear design, and the influences of gear parameters changing on gear trains, transmission system and the whole equipment have to be taken into account, which increases the complexity of optimization problem. This paper puts forward to apply functionally graded materials(FGMs) to gears and then conduct the optimization. According to the force situation of gears, the material distribution form of FGM gears is determined. Then based on the performance parameters analysis of FGMs and the practical working demands for gears, a multi-objective optimization model is formed. Finally by using the goal driven optimization(GDO) method, the optimal material distribution is achieved, which makes gear weight and the maximum deformation be minimum and the maximum bending stress do not exceed the allowable stress. As an example, the applying of FGM to automotive transmission gear is conducted to illustrate the optimization design process and the result shows that under the condition of keeping the normal working performance of gear, the method achieves in greatly reducing the gear weight. This research proposes a FGM gears design method that is able to largely reduce the weight of gears by optimizing the microscopic material parameters instead of changing the macroscopic dimension parameters of gears, which reduces the complexity of gear weight optimization problem.
基金Supported by the National Natural Science Foundation of China(No.51205430)Natural Science Foundation of ChongQing(No.cstc2011ijA70002)China Postdoctoral Science Foundation(No.2013T60842)
文摘To improve aerodynamic performance of wind turbine airfoils,the shape profile characteristic of the airfoil is investigated.Application of conformal transformation,one functional and integrated expression of wind turbine airfoils is presented.Using the boundary layer theory,the aerodynamic model with roughness of wind turbine airfoils is introduced by studying flow separation around the airfoil.Based on the shape expression and aerodynamic performance of airfoils,the function design of wind turbine airfoils is carried out that the maximum lift-drag ratio and low roughness sensitivity are designed objects.Three wind turbines airfoils with different thickness are gained which are used at tip part of blades.As an example,the aerodynamic performance of one designed airfoil with relative thickness of 15%is simulated in different conditions of clean surface,rough surface,laminar flow and turbulent flow.The comparison of aerodynamic performance between the designed airfoil and one popular NACA airfoil is completed which can verify the better performance of the designed airfoil and reliability of the designed method.
基金financially supported by the State Key Development Program for Basic Research of China(973 Program,Grant No.2013CB036204)
文摘According to the technical characteristics of short fixed wheelbase of a high-speed carriage, a subgrade-track integrated space mechanical response analysis model is proposed for trains under the action ofbiaxial load after the comparison of the stress distribution characteristics of the ballast track subgrade bed structures for high-speed railway under the action of uniaxial load and biaxial load. The loading threshold value (high-cycle long-term dynamic strength) under the circum- stance where the cumulative deformation of subgrade structure gradually develops and finally reaches the convergent state, and its relationship with the foundation coefficient K30 were deduced, based on the characteristics of cumulative defor- mation evolution obtained from the unit structure filling model test under the action of cyclic loading. In view of structure stability and frost resistance requirements of the railway subgrade in cold regions, technical conditions to maintain good service performance of subgrade structure of high-speed railway ballasted track are discussed and analyzed. Study results show that the additive effect manifests itself obviously for railway train bogies under the action of biaxial load than uni- axial load, which has a significant dynamic effect on the subgrade bed bottom and a slight effect on the surface layer. Thus, the adoption of a biaxial load model in the design of a high-speed railway subgrade accurately reflects the vehicle load. Pursuant to the structure design principle, the design method of the subgrade structure of high-speed railway ballasted track is proposed to meet the technical requirements such as structural strength, bearing stiffness and high-cyclic and long-term stability. Technical indicators are obtained for the variation of thickness of the surface layer of reinforced sub- grade bed in the double-layer subgrade mode along with the change of K30 at the subgrade bed bottom. The double-layer structure mode of "closure on the upper layer and drainage on the lower layer" was proposed in order to meet the water- proofing and drainage requirements of the upper layer of the subgrade bed in cold regions. A dense-framework graded gravel filler with weak water permeability at a coefficient of 10 4 cm/s is used on the upper layer and the void-framework graded gravel filler at the water permeability coefficient of 10 2 cm/s is adopted on the lower layer.
文摘In the process of particle settling in a dilute,a density graded distribution of the liquid below the suspension needs to be designed according to the gravity of the suspension prior to sedimentation.In the present paper a compositionally graded W-Mo composite was formed via the settling of the W and Mo particles,with a density gradient distributed in the initial clear liquid along the settling direction.
基金supported by Natural Science and Engineering Research Council (NSERC) of Canada
文摘Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a "black-box" and their gradients are not available or not reliable. On the basis of the reliable design space (RDS) concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing (RSP) approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.
基金Project supported by the National Natural Science Foundation of China (No.10332010) the Innovative Research Team Program (No. 10421202) the National Basic Research Program of China (No. 2006CB601205) and the Program for New Century Excellent Talents in Universities of China (2004).
文摘The purpose of this paper is to investigate the application of topology description function (TDF) in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the 'Hamilton-Jacobi-type' equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson's ratio, the other with negative Poisson's ratio. The examples show the method based on TDF is effective for material design.
文摘Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presented, by which a Al 2O 3/(W,Ti)C ceramic tool material FG 2 was developed. Multi objective optimization method was employed in designing the compositional distribution of this ceramic tool material. The results of both continuous and intermittent cutting tests are indicative of the much better cutting behavior of the functionally gradient ceramic tool FG 2 than that of the common ceramic tool SG 4.
文摘The expansion of agricultural function is one of the important means for modern agricultural projects to promote agricultural economic benefits. Successful modern agricultural projects require good creative ideas and design programs. While developing high-efficient modern agricultural production activities,we should fully explore the intangible value of agricultural production activities,combine agriculture with agricultural products,natural conditions,cultural conception and other effective resources,to expand agricultural functions,and promote comprehensive benefits. In order to build a sustainable modern agricultural project operation system,Naya Mountain Villa project planning is taken as an example for analysis. Naya Mountain Villa began construction in 2011; the creative planning based on the agricultural expansion function was carried out in 2013; it had successful access to the capital market in 2015. The project realizes the effective integration of agricultural production system and agricultural function expansion,constructs a set of long-term stable profiting models,and lays an important foundation for entering the capital market. The project is a representative example of the function-expanding modern agricultural project. Through the analysis of the design ideas of the project,this paper discusses the function expansion elements of basic resources,public welfare and agricultural function expansion methods,the formation of general ideas,source and construction logic of creative thinking,and summarizes and abstracts some inspiring design methods of agricultural function expansion. Through the analysis of the key points in the design of the specific technical aspects of the project,this paper provides a reference for solving common difficult problems in the practical design. The summary and refinement of the thinking logic,thinking construction and specific design method of the project is inspiring and repeatable to some extent,which can provide reference for the relevant researchers.
文摘The function of the UHVDC test base of the State Grid Corporation of China (SGCC) is oriented to serve UHVDC power transmission and substation projects, especially power transmission from West China to East China, and to promote localization of UHVDC transmission and substation equipment. In essentials, this test base consists of UHVDC test transmission line, corona cage, outdoor test site, UHV test hall, pollution and environment laboratory, electromagnetic environment simulation test site, insulator laboratory, arrester laboratory and live equipment test field. This paper introduces the function and design idea of the test base, presents the main performance parameters of the above-mentioned test facilities, and summarizes the matters of concern when siting and planning.
基金This project is supported by Provincial Natural Science Foundation of both Hebei (No.699059) and Tianjin(No.003804611).
文摘To deal with a bottom up process model for design reuses a specific extended house of quality(EHOQ)is proposed Two kinds of supported functions,basic supported functions and new supported functions,are defined.Two processes to determine two kinds of functions are presented A kind of EHOQ matrix for a company is given and its management steps are studied.
基金supported by the National Natural Science Foundation of China (70571041).
文摘In the implementation of quality function deployment (QFD), the determination of the target values of engineering characteristics is a complex decision process with multiple variables and multiple objectives that should trade off, and optimize all kinds of conflicts and constraints. A fuzzy linear programming model (FLP) is proposed. On the basis of the inherent fuzziness of QFD system, triangular fuzzy numbers are used to represent all the relationships and correlations, and then, the functional relationships between the customer needs and engineering characteristics and the functional correlations among the engineering characteristics are determined with the information in the house of quality (HoQ) fully used. The fuzzy linear programming (FLP) model aims to find the optimal target values of the engineering characteristics to maximize the customer satisfaction. Finally, the proposed method is illustrated by a numerical example.