Application of the genetic algorithm to the multi-objective optimization of air bearings
Application of the genetic algorithm to the multi-objective
optimization of air bearings
Nenzi Wang*and Yau-Zen Chang
Department of Mechanical Engineering,Chang Gung University,259Wen-Hwa1st Road,Tao-Yuan333,Taiwan,ROC
Received8August2003;accepted3November2003
A feasible solution must be obtained in a reasonable time with high probability of global optimum for a complex tribologi-cal design problem.To meet this decisive requirement in a multi-objective optimization problem,the popular and powerful genetic algorithms(GAs)are adopted in an illustrated air bearing design.In this study,the goal of multi-objective optimization is achieved by incorporating the criterion of Pareto optimality in the selection of mating groups in the GAs.In the illustrated example the diversity of group members in the evolution process is much better maintained by using Pareto ranking method than that with the roulette wheel selection scheme.The?nal selection of the optimal point of the points satis?ed the Pareto optimality is based on the minimum–maximum objective deviation criterion.It is shown that the application of the GA with the Pareto ranking is especially useful in dealing with multi-objective optimizations.A hybrid selection scheme combining the Pareto ranking and roulette wheel selections is also presented to deal with a problem with a combined single objective.With the early generations running the Pareto ranking criterion,the resultant divergence preserved in the population bene?ts the overall GA’s performance.The presented procedure is readily adoptable for parallel computing,which deserves further study in tribological designs to improve the computational e?ciency.
KEY WORDS:genetic algorithm,optimization,air bearings
1.Introduction
Most real-world optimization problems involve more than one objective.The objectives frequently con?ict with each other.For instance,the quality of a product is usually con?icting with its fabrication cost. The usual treatment of multi-objective problems in tribology?eld is considering a single objective or a weighted sum of several objectives of interest in the search process.In2001,Hashimoto and Matsumoto [1]presented a hybrid optimization technique combin-ing the direct search method and the successive quad-ratic programming to?nd the optimum solution of high-speed hydrodynamic journal bearings.The objec-tive function in their study was a weighted sum of nor-malized temperature rise,lubricant?ow,and journal rotating speed.Yoshimoto and Kohno[2]investigated the static and dynamic characteristics of aerostatic cir-cular porous thrust bearings.The objectives of interest were load capacity,static and dynamic sti?ness,and damping.The results were plotted for each of the objectives with its relevant dimensionless variable. Another example for porous air bearing optimization procedure was proposed by Cui and Ono[3]to maxi-mize the damping ratio at the natural frequency while maintaining the required sti?ness in the lower fre-quency.The optimization was conducted by using design charts.These studies were intended for the opti-mization of several objectives.
The values of weighting factors in a weighted sum approach for a multi-objective problem were usually selected without strong justi?cation from the designers regardless of the objectives are normalized or not.For example,Wang et al.[4]minimized a weighted sum of normalized air?ow and the reciprocal of load capacity of an aerostatic pad.The weightings used for the two objectives were0.78and0.22,respectively.Kang et al.
[5]studied the air-lubricated sliders of hard disk drives to improve dynamic characteristic and operating perfor-mance.They used the method of modi?ed feasible direc-tions to solve the multi-criteria optimization problem. The weightings for the objectives:?ying height,and ver-tical,pitch,and roll sti?ness were100,0.25,0.05,and 0.005,respectively.Choi and Kang[6]also used the method of feasible directions to optimize the weighted sum of normalized?ying height and roll angle of the subambient pressure shaped rail sliders.In the analysis the pitch angle of the sliders was treated as a constraint and the weightings used were100and1for the two objectives.Since the?nal solution of a weighted sum optimization problem is in?uenced by the predeter-mined weightings,the e?ectiveness of the optimum
*To whom correspondence should be addressed.E-mail:nenzi@
https://www.sodocs.net/doc/37945914.html,.tw
1023-8883/04/0800–0119/0ó2004Plenum Publishing Corporation Tribology Letters,Vol.17,No.2,August2004(ó2004)119
solution is usually limited.Therefore,no single solution can be treated as an optimum solution to a problem with multiple con?icting objectives.A solution scheme for a multi-objective optimization problem should give in to a number of trade-o?optimal solutions.
The main reason for the weighted sum approach being commonly used in the tribological designs is due to the use of classical optimization methods,such as the method of feasible directions,simplex method and pattern search type method.In these methods the searches are basically guided by previous optimal point and can at best ?nd one solution in one simulation run.These characteristics make the methods inconve-nient to obtain a set of optimal solutions for a multi-objective optimization problem.
Recently,genetic algorithms (GAs)are popular in many tribological optimization problems for their high probability to obtain global optimum [7–11].The GAs can also be used to handle constrained discrete optimi-zation problem easily [12].The other global,non-linear optimization method,simulated annealing (SA),is also used in the applications of tribological designs [13].However,the GAs and SA were adopted to deal with a single objective or a preset weighted sum objective in the aforementioned studies.An important feature of the evolutionary algorithms for optimizations is these algorithms can ?nd multiple optimal solutions in one single run due to their population-based approach.And the GAs are the most well-known methods among the evolutionary algorithms.This makes GAs ideal candidates for solving multi-objective optimiza-tion problems.In this study,the GA is adopted as the optimization method for the solution of air bearing design problem with multiple objectives.The approach is not limited to the illustrated example,but is also useful for other complex optimization problems,such as advanced air bearing design for hard disk drives.
2.The porous air bearing
The illustrated tribological component in this opti-mization study is an externally pressurized porous air
bearing.The bearing pad has four square porous materials,which provide air cushions to separate the moving surfaces.The porous materials are symmetri-cally located about the geometric center of the pad.The ?ow characteristic of the porous material is a function of its permeability and geometry.The size and ?ow characteristic of the porous pads and their location determine the performance of the aerostatic bearing.Figure 1shows a schematic diagram of the externally pressurized porous air bearing.The four design variables are supply air pressure p S àá
,porous material width L B àá,porous material edge to bearing edge distance L L àá,and permeability of the porous material k p àáof given thickness.
The pressure generated in the parallel-surface bear-ing is obtained by solving iteratively the steady-state isoviscous compressible ?uid Reynolds equation,equa-tion (1),for the air ?lm and the Darcy’s law,equation (2),for porous material.The detail of the numerical solution minimized for the computational time can be found in Ref.[10].The governing equations are o 2p 2
o x to 2p
2
o y ?12
h
3k p o ^p 2o ^z
in porous material region
otherwise
(
e1T
o 2^p
2o x to 2^p 2o y to 2^p 2o ^z
?0e2T
where p and ^p
are the air pressure in the ?lm and por-ous material,respectively;x ;y and ^x
;^y ;^z are the coordinates for the ?lm and porous material,respec-tively;h is the ?lm thickness;and k p is the permeability coe?cient of the porous material.For the right-hand side of equation (1)the calculation of pressure in the location outside the porous pad is zero,otherwise the non-zero term is used to take into account the e?ect of air?ow in/out of the porous boundary to meet the mass conservation principle.Since the porous pads of the square bearing are symmetrical about the bearing’s geometric center,the computation of pressure distribu-tion can be performed in a quarter of the bearing.The boundary conditions for the left-lower quarter of the air bearing in the computational model are p e0;y T?
p ex ;0T?p 0,and o p o x x ?B =2
?o p
o y
y ?B =2
?0.In the por-ous pad and air ?lm interface p ex ;y Tequals ^p
e^x ;^y ;0T.Each side of the square bearing pad has a length of 100mm.The ranges selected for the variables are 200–600kPa for supply air pressure,5–15mm for porous material width,5–25mm for porous material to pad edge distance,and 2–10?10à15m 2for the permeability of porous material.In the analysis,the ?lm thickness of the porous air bearing is 10l m and the thickness of the porous material is 5
mm.
Figure 1.The schematic diagram of the four-porous-pad air thrust bearing.The air bearing is square shape and each porous-pad is
located symmetrically about the geometric center.
120N.Wang,Y.-Z.Chang /Genetic algorithm to the multi-objective optimization
3.Objectives and design space
Since the pressure distribution of the air ?lm is a function of aforementioned four design variables,the goal of this study is to ?nd an optimum setting of these variables with high con?dence to satisfy multiple objectives simultaneously.The common objectives for optimizing an air bearing of this type can be the fol-lowings:(1)maximizing load capacity,(2)maximizing bearing sti?ness,(3)maximizing the damping capabil-ity,and (4)minimizing the air?ow through the aero-static pad.Some of the design parameters may have certain constraints.In the cases when several objectives have to be satis?ed in the process of ?nding an opti-mal setting of the variables,the usual treatment is to linearly combine weighted objectives into a single objective.For example,a design that is to maximize load capacity and bearing sti?ness while limiting the air ?ow of the bearing,a single objective function can be de?ned as:
f p S ;L B ;L L ;k p àá?
W ?k _m
e3a T
or
f p S ;L B ;L L ;k p àá
?c 1?W tc 2? k
tc 3?1_m e3b Twhere W is the bearing load capacity;k is the coe?-cient of bearing sti?ness (spring constant);_m
is the air mass ?ow rate.In equation (3b)the objectives shown with bars are the normalized objectives.The constants (c 1–c 3)are used to weight the relative importance of individual objective.The sum of these weighting factors is usually one and the weighting factors have to be pre-determined before performing the calculations.The determination of ideal weighting may require extended experience and usually be di?cult to obtain in a multi-objective optimization problem.A minimization pro-blem with multiple objectives may be stated as
minimize f m x eTsubject to
x 2X
e4T
where f is the objective function,x is the design vector,m is the number of objectives,and X de?nes the domain of x .For an objective is to be maximized,the minimization is performed by seeking the maximum negative value of that objective.
4.Criterion space and Pareto optimality
For a single objective optimization problem the searching process is straightforward.The usual proce-dure is listed in the following.(1)Select an optimiza-
tion method suitable for the problem in hand,(2)Proceed the optimization,(3)Verify the results.How-ever,for multi-objective problems,the process may not be trivial.First of all,an ideal set of weighting factors for the objectives is not easy to determine.In addition,a preset combined objective may restrict the under-standing of the whole objective function space (criter-ion space)of a problem.In the context of Pareto optimality (to be introduced in the later of this sec-tion),the dominated designs are the points in the cri-terion space that are inferior to at least one other point for the prescribed objectives.For those designs are not dominated by any other designs in the criter-ion space are the optimal designs in a multi-objective optimization.The visualization of a two-dimensional criterion space (objective function space)can be useful for the understanding of the Pareto optimality.The same concept and approach can be applied with little modi?cation to the optimization problems with more than two objectives.
In this study two non-linear objectives were used to illustrate the procedure.The goal was to maximize the bearing sti?ness k eTwhile minimizing the air mass ?ow _m
eTto the bearing.In the ranking process to determine the selection priority in the GAs,the dominated designs are to be determined.A design that is domi-nated by other design,such as a design with higher sti?ness and a smaller ?ow,is excluded from the initial rank.The Pareto optimality [14,15]can be de?ned as follows:a design variable vector x ?2X is Pareto opti-mal for equation (4)if and only if there is no vector x 2X with the characteristics
f i x eT f i x ?eTfor all i ,i ?1;2;...;m e5a T
f i x eT for at least one i ;i ?1;2;...;m e5b T Since the solution x ?is no worse than x in all objec-tives and x ?is strictly better than x in at least one objective,it can be said that x ?is non dominated by x or x ?is non inferior to x .Among the non-dominated solutions,the most popular criterion to select one best compromise Pareto solution is the min–max method [15].The goal is to ?nd a point that the maximum deviation of objective is minimized.With m objectives,the problem is to determine x ?from min ?max àz 1;z 2;...;z m á1;max à z 1;z 2;...;z m á2;...;: max z 1;z 2;...;z m eTN ? ; where the deviations z i ?f i x eTàf min i or in a normal-ized form z i ?f i x eTàf min i j j f max i àf min i ,and N is the number of non-dominated points. The three major GA operations are (1)creation of mating pool (selection);(2)crossover (mating);and (3) N.Wang,Y.-Z.Chang /Genetic algorithm to the multi-objective optimization 121 mutation.In the case of a single objective optimization,the most common selection scheme of the GA in the reproduction process is the so-called roulette wheel selection.The chance of a member to be selected as a parent to produce o?spring is linearly proportional to its ?tness (objective function value).Before the selec-tion the function values are converted to positive values within 1:1f high àf low and 0:1f high àf low by adding 0:1f high à1:1f low to each of the function values [15]. In this study,the single-point crossover is used with crossover probability being one.Each of the variables is decoded in 12binary bits and the bit mutation prob-ability is 1.0%.For all the simulated cases,the popula-tion size is 60and evolves to 60th generation.The uniform random number generator in the computing code has a non-repeat period about 3:1?1018[16].In the computational model,the grid size of the aerostatic pad is 150in each coordinate direction.The CPU time for a single design calculation is about 7.0s.in a 2.0GHz-CPU personal computer.For all the results presented in this study,the sti?ness and air mass ?ow are normalized by dividing 400N/l m and 5?10à5g/min,respectively.The ?tness deviations are also in normalized values by dividing their maximum amount. 5.Simulation results Figure 2is generated by plotting the objective func-tion values of 3600randomly selected designs in the porous air bearing problem.Since the two objectives are to maximize the bearing sti?ness and to minimize the air ?ow,the non-dominated points (the Pareto points)are on the lower-right portion in the criterion space.All the other points are dominated by these Par-eto points.Figure 3shows the Pareto curve of non-dominated points in the GA’s ?rst generation of the 60members.These Pareto points are assigned as rank 1.The results of deviation distribution are plotted in ?gure 4.It can be seen that,point 10is the one with minimum deviation,which can be treated as an ‘‘ideal’’solution if no special preference is favored.In the multi-objective problem of this study,the rank of a member is based on the Pareto optimality.In the ranking process,the ?rst rank is determined from the ?rst set of Pareto points.The points of sec-ond rank are then determined using the same criterion after the points of the ?rst rank are removed.The pro-cess is continued until all the points are ranked in a generation.The chance of a point being selected in the mating group to produce o?spring is inversely propor-tional to its rank number.Figure 5shows the seven ranks of the ?rst generation of the simulated problem with 60members. The successful operation of the GAs relies heavily on maintaining the diversity of the members in the population during the evolutionary process.If a single objective (f ?k =_m )is set,the roulette wheel selection may converge prematurely.Figure 6shows the prema-ture convergence as early as in the 10th generation by roulette wheel selection.Note that in the ?gure the cri-terion spaces in the 10th,30th,and 60th generations are blown up to show the details due to fast conver-gence.The slopes of curves formed by the lower-right points in the 10th,30th,and 60th generations are Figure 2.The criterion space (two objectives:maximum bearing sti?ness and minimum air mass ?ow)of the studied porous air bearing.The values of the four design variables for the 3600cases are randomly selected in the design space.The sti?ness and air mass ?ow are normalized by dividing 400N/l m and 5?10à5g/min,respectively. 122N.Wang,Y.-Z.Chang /Genetic algorithm to the multi-objective optimization nearly the same.With the Pareto optimality ranking scheme,the diversity of the members are maintained during the evolution (?gure 7),which results in improved ?tness and the quality of ?nal results.The distribution of the maximum deviation of the Pareto points (52points of the total 60points)of rank 1is shown in ?gure 8.It can be seen that the ideal design is at point 31.Figure 9shows the ?tness history for a given objec-tive (f ?k =_m )during the evolution and the variations of corresponding design variables.A comparison of the roulette wheel selection and Pareto optimality ranking with 60members of the evolutionary history of ?tness is shown in ?gure 10.In the same plot,the other two cases with 30members adopting the hybrid selection scheme are also displayed.It can be seen that N.Wang,Y.-Z.Chang /Genetic algorithm to the multi-objective optimization 123 124N.Wang,Y.-Z.Chang/Genetic algorithm to the multi-objective optimization N.Wang,Y.-Z.Chang/Genetic algorithm to the multi-objective optimization125 in the early generations the optimal?tness is lower with the roulette wheel selection due to only30mem-bers were used in the population.Because of the diver-sity retained in the?rst20or30generations with Pareto ranking selection,a better result is achieved in the60th generation with only a half of the computa-tional load.Figure11shows the convergence plot in the criterion space for several https://www.sodocs.net/doc/37945914.html,pare with?gure6,the diversity is retained in the30th gen-eration by using Pareto ranking.For the optimized air bearing the supply air pressure is200kPa,the porous material size is5mm,the porous material location is 24.5mm,and the permeability of the porous material is2.26?10à15m2. A preliminary study of parallel computation of the proposed multi-objective optimization approach was also conducted.The approach is straightforward and is highly recommended for its easy-implementation.The cluster con?guration is similar to the one used in a previous study[17].In an eight-computing-node clus-ter,an average speed up of6.7can be obtained.The main reason of the high speed up in the parallel version 126N.Wang,Y.-Z.Chang/Genetic algorithm to the multi-objective optimization is due to the sequence of?tness computation for each member in a generation of GA is of little importance. Thus,the computing load can be shared in each of the nodes in the cluster simultaneously.The evaluation of objective functions is the main loading of this type of analysis and the overhead of the communication in the computation is small. 6.Conclusion and recommendations For a complex tribological design problem,a feasi-ble solution is a solution obtained in a reasonable time with high probability of achieving the global optimum solution.To meet this decisive condition in a multi-objective optimization problem,the popular and powerful genetic algorithm is adopted in the illu-strated air bearing design.The goal of multi-objective optimization is achieved by incorporating the criterion of Pareto optimality in the selections of the mating groups in the GA.On behalf of easy-illustration,only two objectives of the air bearing design were opti-mized simultaneously.For three-objective problems, the criterion space will be three-dimensional and the corresponding Pareto curves will be surfaces not easy to visualize.A problem with more than three objec-tives is di?cult to envision.Nevertheless,to accu-rately predict the performance of similar bearings several important objectives can be considered simul-taneously using the same procedure exempli?ed in this study. In the illustrated example with1%bit mutation probability,the population diversity in the evolution process is much better maintained with the Pareto ranking method than that with the roulette wheel selection scheme.The?nal selection of the optimal design of the points satisfying the Pareto optimality is based on the minimum–maximum objective devia-tion criterion.It can be seen that the GA with Par-eto ranking can preserve the non-dominated designs with wide range of objectives in the end of the evo-lution.If some of the objective is to be emphasized in the?nal design stage(in addition to the min–max criterion for a?nal‘‘ideal’’design),it can be selected from the Pareto points easily.The same result cannot be achieved in a weighted sum approach,which requires a recalculation for a new set of weightings. For some optimization problem,a combined single objective of several objectives may be desired.For this N.Wang,Y.-Z.Chang/Genetic algorithm to the multi-objective optimization127 type of problem a hybrid selection scheme combining the Pareto ranking and roulette wheel selection is pre-sented.With the early generations running the Pareto ranking criterion,the divergence preserved in the population bene?ts the overall GA’s performance.In the later search procedure the roulette wheel selection scheme can further promote the optimum?tness to some higher value as demonstrated in this study.The suggested approach is much simpler than the schemes using some forms of parallel island model(mainly to preserve the diversity of the population among the islands),which may have many parameters to be?ne-tuned to avoid premature convergence. In1989,Goldberg[18]stated:in a world where serial algorithms are usually made parallel through countless tricks and contortions,it is no small irony that genetic algorithms(highly parallel algorithms)are made serial through equally unnatural tricks and turns.His remark is still very true in the tribology community since very little work has been done in mapping GAs to parallel computing environment.The bottleneck has been and still is determined by the ease of accessing a parallel sys-tem.The presented GAs are readily adoptable for paral-lel computing,which deserves further study to the applications of tribological design to improve computa-tional e?ciency.References [1]H.Hashimoto and K.Matsumoto,ASME J.Tribol.123(2001) 305. [2]S.Yoshimoto and K.Kohno,ASME J.Tribol.123(2001)501. [3]C.Cui and K.Ono,ASME J.Tribol.119(1997)486. [4]N.Wang,C.-L.Ho and K.-C.Cha,Tribol.Trans.43(2000)377. [5]T.-S.Kang,D.-H.Choi and T.-G.Jeong,ASME J.Tribol.123 (2001)541. [6]D.-H.Choi and T.-S.Kang,ASME J.Tribol.121(1999)575. [7]S.Boedo and L.Eshkabilov,Tribol.Trans.46(2003)134. [8]H.Kotera and S.Shima,Tribol.Trans.43(2000)837. [9]H.Kotera,T.Hirasawa,S.Senga and S.Shimam,Tribol.Trans. 43(2000)842. [10]N.Wang and Y.-Z.Chang,Tribol.Trans.45(2002)471. [11]T.Kato and H.Soutome,Tribol.Trans.44(2001)137. [12]D.-H.Choi and K.-C.Yoon,ASME J.Tribol.123(2001)181. [13]M.O’Hara,Y.Hu and D.Bogy,ASME J.Tribol.122(2000) 257. [14]K.Deb,Multi-Objective Optimization using Evolutionary Algo- rithms(John Wiley&Sons,West Sussex,England2001). [15]A.D.Belegundu and T.R.Chandrupatla,Optimization Concepts and Applications in Engineering(Prentice Hall,New Jersey, 1999). [16]H.W.Press,S.A.Teukolsky,W.T.Vetterling and B.P.Flannery, Numerical Recipes in Fortran90(Cambridge University Press, Cambridge1996). [17]N.Wang,Y.-Z.Chang and C.-M.Tsai,Tribol.Trans.47(2004) 34. [18]D.E.Goldberg,Genetic Algorithms in Search,Optimization,and Machine Learning.(Addison-Wesley,Reading,MA1989). 128N.Wang,Y.-Z.Chang/Genetic algorithm to the multi-objective optimization The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中 定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way... “tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法 不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke. 表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法 The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started. way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3； t h e-w a y-的用法 The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。 way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句 t h e_w a y的用法大全 The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. 从那天起,其他同学是夹着书本来上课,而他们却带着"失败"的思想负担来上课. The way的用法及其含义（三） 三、the way的语义 1. the way=as（像） Please do it the way I’ve told you.请按照我告诉你的那样做。 I'm talking to you just the way I'd talk to a boy of my own.我和你说话就像和自己孩子说话一样。 Plant need water the way they need sun light. 植物需要水就像它们需要阳光一样。 2. the way=how（怎样，多么） No one can imagine the way he misses her.没人能够想象出他是多么想念她！ I want to find out the way a volcano has formed.我想弄清楚火山是怎样形成的。 He was filled with anger at the way he had been treated.他因遭受如此待遇而怒火满腔。That’s the way she speaks.她就是那样讲话的。 3. the way=according as （根据） The way you answer the questions, you must be an excellent student.从你回答问题来看，你一定是名优秀的学生。 The way most people look at you, you'd think a trash man was a monster.从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物。 The way I look at it, it’s not what you do that matters so much.依我看，重要的并不是你做什么。 I might have been his son the way he talked.根据他说话的样子，好像我是他的儿子一样。One would think these men owned the earth the way they behave.他们这样行动，人家竟会以为他们是地球的主人。 一．Way：“方式”、“方法” 1.表示用某种方法或按某种方式 Do it (in) your own way. Please do not talk (in) that way. 2.表示做某事的方式或方法 It’s the best way of studying [to study] English.。 There are different ways to do [of doing] it. 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句 正：I don’t like the way he spoke. I don’t like the way that he spoke. I don’t like the way in which he spoke.误：I don’t like the way how he spoke. 4. the way 的从句 That’s the way (=how) he spoke. I know where you are from by the way you pronounce my name. That was the way minority nationalities were treated in old China. Nobody else loves you the way(=as) I do. He did not do it the way his friend did. 二．固定搭配 1. In a/one way：In a way he was right. 2. In the way /get in one’s way I'm afraid your car is in the way， If you are not going to help，at least don't get in the way. You'll have to move－you're in my way. 3. in no way Theory can in no way be separated from practice. 4. On the way (to……) Let’s wait a few moments. He is on the way Spring is on the way. Radio forecasts said a sixth-grade wind was on the way. She has two children with another one on the way. 5. By the way By the way，do you know where Mary lives? 6. By way of Learn English by way of watching US TV series. 8. under way 1. Elbow one’s way He elbowed his way to the front of the queue. 2. shoulder one’s way 3. feel one‘s way 摸索着向前走；We couldn’t see anything in the cave, so we had to feel our way out 4. fight/force one’s way 突破。。。而前进The surrounded soldiers fought their way out. 5.. push/thrust one‘s way（在人群中）挤出一条路He pushed his way through the crowd. 6. wind one’s way 蜿蜒前进 7. lead the way 带路，领路；示范 8. lose one‘s way 迷失方向 9. clear the way 排除障碍，开路迷路 10. make one’s way 前进，行进The team slowly made their way through the jungle. 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. “the way+从句”结构的意义及用法 首先让我们来看下面这个句子： Read the following passage and talk about it with your classmates. Try to tell what you think of Tom and of the way the children treated him. 在这个句子中，the way是先行词，后面是省略了关系副词that 或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1．the way之后，引导定语从句的关系词是that而不是how,因此，<<现代英语惯用法词典>>中所给出的下面两个句子是错误的：This is the way how it happened. This is the way how he always treats me. 2. 在正式语体中，that可被in which所代替；在非正式语体中，that则往往省略。由此我们得到the way后接定语从句时的三种模式：1) the way +that-从句2) the way +in which-从句3) the way +从句 例如：The way(in which ,that) these comrades look at problems is wrong.这些同志看问题的方法不对。 The way(that ,in which)you’re doing it is completely crazy.你这么个干法，简直发疯。 We admired him for the way in which he faces difficulties. Wallace and Darwin greed on the way in which different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way (that) he did it. I liked the way (that) she organized the meeting. 3.the way(that)有时可以与how(作“如何”解)通用。例如： That’s the way (that) she spoke. = That’s how she spoke. I should like to know the way/how you learned to master the fundamental technique within so short a time. 4．the way的其它用法：以上我们讲的都是用作先行词的the way，下面我们将叙述它的一些用法。 定冠词the的12种用法 定冠词the 的12 种用法，全知道?快来一起学习吧。下面就和大家分享，来欣赏一下吧。 定冠词the 的12 种用法，全知道? 定冠词the用在各种名词前面，目的是对这个名词做个记号，表示它的特指属性。所以在词汇表中，定冠词the 的词义是“这个，那个，这些，那些”，可见，the 即可以放在可数名词前，也可以修饰不可数名词，the 后面的名词可以是单数，也可以是复数。 定冠词的基本用法： (1) 表示对某人、某物进行特指，所谓的特指就是“不是别的，就是那个!”如： The girl with a red cap is Susan. 戴了个红帽子的女孩是苏珊。 (2) 一旦用到the，表示谈话的俩人都知道说的谁、说的啥。如： The dog is sick. 狗狗病了。(双方都知道是哪一只狗) (3) 前面提到过的，后文又提到。如： There is a cat in the tree.Thecat is black. 树上有一只猫，猫是黑色的。 (4) 表示世界上唯一的事物。如： The Great Wall is a wonder.万里长城是个奇迹。(5) 方位名词前。如： thenorth of the Yangtze River 长江以北地区 (6) 在序数词和形容词最高级的前面。如： Who is the first?谁第一个? Sam is the tallest.山姆最高。 但是不能认为，最高级前必须加the，如： My best friend. 我最好的朋友。 (7) 在乐器前。如： play the flute 吹笛子 Way用法 A:I think you should phone Jenny and say sorry to her. B:_______. It was her fault. A. No way B. Not possible C. No chance D. Not at all 说明：正确答案是A. No way，意思是“别想！没门！决不！” 我认为你应该打电话给珍妮并向她道歉。 没门！这是她的错。 再看两个关于no way的例句： （1）Give up our tea break? NO way! 让我们放弃喝茶的休息时间？没门儿！ （2）No way will I go on working for that boss. 我决不再给那个老板干了。 way一词含义丰富，由它构成的短语用法也很灵活。为了便于同学们掌握和用好它，现结合实例将其用法归纳如下： 一、way的含义 1. 路线 He asked me the way to London. 他问我去伦敦的路。 We had to pick our way along the muddy track. 我们不得不在泥泞的小道上择路而行。 2. （沿某）方向 Look this way, please. 请往这边看。 Kindly step this way, ladies and gentlemen. 女士们、先生们，请这边走。 Look both ways before crossing the road. 过马路前向两边看一看。 Make sure that the sign is right way up. 一定要把符号的上下弄对。 3. 道、路、街，常用以构成复合词 a highway（公路），a waterway（水路），a railway（铁路），wayside（路边） way/time的特殊用法 1、当先行词是way意思为”方式.方法”的时候,引导定语从句的关系词有下列3种形式： Way在从句中做宾语 The way that / which he explained to us is quite simple. Way在从句中做状语 The way t hat /in which he explained the sentence to us is quite simple. 2、当先行词是time时,若time表示次数时,应用关系代词that引导定语从句,that可以省略; 若time表示”一段时间”讲时,应用关系副词when或介词at/during + which引导定语从句 1.Is this factory _______ we visited last year? 2.Is this the factory-------we visited last year? A. where B in which C the one D which 3. This is the last time _________ I shall give you a lesson. A. when B that C which D in which 4.I don’t like the way ________ you laugh at her. A . that B on which C which D as 5.He didn’t understand the wa y ________ I worked out the problem. A which B in which C where D what 6.I could hardly remember how many times----I’ve failed. A that B which C in which D when 7.This is the second time--------the president has visited the country. A which B where C that D in which 8.This was at a time------there were no televisions, no computers or radios. A what B when C which D thatThe way常见用法
The way的用法及其含义(二)
(完整版)the的用法
“the way+从句”结构的意义及用法
way 用法
The way的用法及其含义(一)
way 的用法
the-way-的用法讲解学习
way的用法总结大全
the_way的用法大全教案资料
the way 的用法
The way的用法及其含义(三)
way的用法
the way的用法大全
“the-way+从句”结构的意义及用法知识讲解
定冠词the的12种用法
Way的用法
way与time的特殊用法