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Robustness of complex networks with the local protection strategy against cascading failures

Jianwei Wang ?

School of Business Administration,Northeastern University,Shenyang 110819,PR China

a r t i c l e i n f o Article history:

Received 22May 2012

Received in revised form 21September 2012Accepted 21September 2012

Available online 28November 2012Keywords:

Cascading failure Complex network BA network

Mitigation strategy Power grid

a b s t r a c t

Considering the role of the neighboring nodes of an overload node,we articulate a local protection strat-egy to address the problem of the optimal defense in the cascading propagation.From two aspects of the global robustness and the different attacks,we numerically demonstrate the effectiveness of this strategy on Barabási–Albert (BA)scale-free networks and the power grid,and show that the robustness of diverse networks against cascading failures can be improved dramatically.And we numerically ?nd the optimal value of the parameter,at which two types of networks can reach the strongest robust level against cas-cading failures.Next,in BA networks we verify this ?nding by theoretical analysis.Our results may be very useful for constructing the optimal protection strategy in realistic networks and for leading to insights into the mitigation of cascading failures.

1.Introduction

Over the past decade,there has been a lot of research related with the robustness and stability of networks (Albert et al.,2000;Wu et al.,2011;Schneider et al.,2011;Zhang et al.,2012).In par-ticular,great efforts have been dedicated to the research on cascad-ing failures,which has been one of the most central topics in the network safety.In real life,cascading failures induced by targeted attacks and random failures can occur in many natural and man-made systems,and frequently trigger many catastrophic events,e.g.,the largest blackout in US history took place on 14August 2003(Glanz and Perez-Pena,2003),the Western North American blackouts in July and August 1996(Sachtjen et al.,2000),Internet collapse (Pastor-Satorras et al.,2001)caused by congestion,and the large-scale bankruptcy (Wang et al.,2010)witnessed during the recent global economical recession.

In fact,in many infrastructure networks,there exists the load on nodes,and the load can be redistributed from one node to other nodes,which may lead to the imbalance of the load on the entire network,and further trigger the cascading propagation.Cascading failures are generally induced by random failures or intentional at-tacks on a few nodes and take frequently place on the single and non-interacting networks.Therefore,earlier studies on cascading failures pay close attention to analyzing the evolving characteristics of cascading failures and mainly focus on the cascading modeling

(Wang and Chen,2008;Wu et al.,2008;Chang and Wu,2011;Wang and Rong,2009;Wang et al.,2008),the cascade control and defense strategies (Motter,2004;Sch?fer et al.,2006;Simonsen et al.,2008),the attack strategies (Motter and Lai,2002;Zhao et al.,2005;Wang and Rong,2009,2011),the cascading phenomena in the diverse networks (Bao et al.,2008;Gleeson,2008;Zheng et al.,2007),and so https://www.doczj.com/doc/a911707112.html,ter,many researchers ?nd that catastrophic events induced by cascading failures can also occur in coupled networks,for instance,electrical blackouts in Italy on 28September 2003result from a cascade of failures between the power grid and computer network.Motivated by that fact,Buldyrev et al.(2010)developed a framework for understanding the robustness of interacting networks against cascading failures and present exact analytical solutions for the critical fraction of nodes.After that,cascading fail-ures on coupled networks have started to be studied actively and a number of important aspects of cascading failures in coupled net-works (Vespignani,2010;Parshani et al.,2010;Gao et al.,2012;Brummitt et al.,2012)have been discussed.In all cited studies above,most works on cascading failures from the single network to coupled networks have focused only on the modeling of cascad-ing failure,the cascade control and defense strategies,or a funda-mental property of coupled networks without considering the load.However,there are few works about investigating how by the extra protection strategies of the neighboring nodes of an over-load node to enhance the robustness of complex networks against cascading failures.In fact,in many infrastructure networks,when a node overloads,its neighboring nodes can provide some protec-tion resources to avoid its failure.Therefore we deserve a careful investigation.

Tel.:+8602483672631.

E-mail address:jwwang@https://www.doczj.com/doc/a911707112.html,

To this end,taking into account the protection strategy pro-vided by the neighboring nodes of an overload node,we propose a new mitigation method.Without changing the total protection capacities of the whole network,we numerically investigate its effectiveness on improving the robustness of BA scale-free net-works(Barabási and Albert,1999)against cascading failures and ?nd that the simple local protection method can dramatically opti-mize the resilience of BA networks.In addition,adopting the mit-igation strategy,we numerically discuss how BA networks can reach the strongest robust level against cascading failures and?nd, compared with previous results,the optimal value of the parame-ter decreases.We verify this result by the theoretical analysis.In addition,we examine the effectiveness of the mitigation strategy on improving the robustness of the power grid against cascading failures and give the optimal protection strategy to avoid potential cascading failures.

The rest of this paper is organized as follows:in Section2we introduce the protection method.In Section3we numerically demonstrate the effectiveness of the mitigation strategy on improving the network robustness against cascading failures.In Section4the numerical simulations in BA networks are veri?ed by theoretical analysis.Finally,some summaries and conclusions are shown in Section5.

2.The mitigation strategy

In general,a simple network can be represented by an undi-rected and unweighted graph G=(V,E),where V is the set of nodes (for instance the stations in a railway transportation system,the substations in the power grid,or the routers in the Internet),and E is the set of undirected and unweighted edges(the lines connect-ing couples of stations,transmission lines connecting two substa-tions,or the cables connecting two routers).

Next,we introduce our protection method in detail.In previous studies,the rule that the overload nodes are immediately removed from the network is widely adopted.However,few works discuss this problem:when the load on a node exceeds its capacity, whether there exist some strategies to maintain its normal and ef?cient functioning to avoid the cascading propagation or not? In fact,in realistic networks,for example in traf?c networks,when a traf?c intersection saturates,traf?c police can ease the traf?c ?ows.Motivated by this case,Wang and Rong(2009)constructed a cascading model of an overload node with the breakdown prob-ability.However,this mechanism with the breakdown probability increases the total price of the whole network.Therefore,without changing the total price of the whole network,how to protect the overload nodes has become one of the key issues in the control and the defense of cascading failures.To this end,considering that the neighboring nodes of an overload node may provide some protec-tion resources to this overload node to maintain its normal and ef?cient functioning,we propose a local protection method(see Fig.1).In Fig.1,when the load on node i exceeds its capacity,we de?ne the extra capacity D C i;C

received by node i from its neigh-boring nodes to

D C i;C

i ?

m2C i

peC màL mTe1T

where C i,C m,and L m represent the set of the neighboring nodes of node i,the capacity of node m to handle the load,and the initial load of node m,respectively.The parameter p represents a random num-ber in0and1,which decides to the strength of the protection re-sources provided by the neighboring nodes.When p=0,the neighboring nodes of the overload node cannot provide the extra capacity,i.e.,without adopting the mitigation strategy.While when p=1,the strongest protection is provided by the neighboring nodes.The expression C màL m ensures that node m can handle the initial load on it after providing some protection resources to node i.In this mitigation strategy,we can see that the total price of the whole net-work is not changed.For simplicity,we apply this strategy to a sim-ple cascading model(Wang et al.,2008).In fact,our method can also be applied to other cascading models.Our purpose of this paper is to analyze to what extent this mitigation strategy can enhance the net-work robustness against cascading failures and what is the optimal strategy of the parameter selection after adopting this protection method.Next,we simply introduce the cascading model(Wang et al.,2008).The initial load L i on node i in a network is de?ned as L i?k a

with k i being the degree of node i(i.e.,the link number that node i connects other nodes),where a is a tunable parameter.The capacity C i of node i is de?ned as C i=(1+b)L i,where the constant b is an adjustable parameter characterizing the tolerance of the net-work against cascading failures.After node i fails,the additional load D L j received by node j,one of its neighboring nodes,is proportional to its initial load L j,i.e.,D L j?L i L j=e

m2C i

L mT,where C i represents the set of the neighboring nodes of node i.According to the protection strategy,at t time,when the load on node i exceeds its capacity, the capacity C i,t of node i can dynamically be adjusted to

C i;t?C i;tà1t

m2C i

peC m;tà1àL mTe2T

and the capacities of the neighboring nodes of node i can simulta-neously be adjusted to

C m2C

?C m2C

;tà1

àpeC m2C

;tà1

àL m2C

Te3TOur aim is to investigate the effect of the capacity adjustment on the network robustness.Here we only focus on the cascading prop-agation induced by removing a single node.A failed node can lead to the load redistribution,and then cascading failures may occur. This process will be repeated until the load of all nodes is less than their capacities,and at this moment,cascading failures can be con-sidered to be completed.We quantify the effectiveness of the mit-igation strategy on improving the network robustness against cascading failures by two measures:the avalanche size S and the proportion P(S).The avalanche size S is de?ned as:S?

i2N

s i=n, where N and n represent the set and the number of all nodes in the network,respectively,and s i represents the number of the breakdown nodes induced by removing node i.The measure P(S) represents the proportion between the number of the protected nodes after adopting the mitigation method and the number of the broken nodes induced before adopting the mitigation

strategy.

220J.Wang/Safety Science53(2013)219–225

3.Simulation analysis of the mitigation strategy

Taking into account the role of the network structure in the cas-cading propagation and the ubiquity of scale-free networks in nat-ural and human-made systems,we ?rstly investigate the effectiveness of the mitigation strategy on improving the robust-ness of the scale-free networks against cascading failures.The de-gree distribution of the scale-free networks satis?es a power law form:P (k )$k àc ,where k is the number of links of a randomly cho-sen node in the network and c is the scaling exponent.For simplic-ity,the scale-free network is generated by using the standard Barabási–Albert model (Barabási and Albert,1999).Starting from m 0fully connected nodes,a new node with m (m 6m 0)edges is added to the existing network at each time step according to the preferential attachment.In computer simulations,for all networks,the network size N is equal to 5000,and the parameters m 0and m are equal to 2.Therefore,the average degree h k i is approximately equal to 4.

In Fig.2,we compare the average avalanche size S after and be-fore adopting the protection strategy in four cases of a =0.4,a =0.7,a =1.0,and a =1.3.Numerical results are obtained by averaging over 50experiments on 10independent networks.The mitigation areas marked show that the robustness of BA networks against cas-cading failures can be improved dramatically.By computer simula-tions,we observe that the parameter p plays an important role in the effective control of cascading failures,i.e.,the bigger the value p ,the stronger the robustness of BA networks.Therefore,by reason-ably increasing the value p ,we can more effectively protect BA net-works against cascading failures.In addition,we also ?nd that the average avalanche size S after and before adopting the protection strategy shows the threshold-like behaviors marked by the critical threshold b c .The critical threshold b c is widely applied to many cas-cading models (Wang and Chen,2008;Wu et al.,2008;Wang and Rong,2009;Wang et al.,2008;Parshani et al.,2010;Gao et al.,2012)and can quantify the network robustness against cascading failures,that is,the smaller the value of b c ,the stronger the network robustness,and the lower the price of the whole network.There-fore,to maximize the robustness and minimize the cost,according to the role of the value b c ,the aim of many studies is to ?nd the opti-mal value of the parameters in the cascading model,at which the value b c is smallest.In the left sub-?gure in Fig.3,according the estimated b c obtained by the minimal value when S <0.002,in two cases of p =0.5and p =0.9,we can observe that BA networks can obtain the strongest robust level against cascading failures when a %0.8,which is different from the optimal value (a =1)without adopting the protection method (Wang et al.,2008)(While in the case of p =0.1,the optimal value a %1).We will verify the re-sults by the latter theoretical analysis.In addition,in the right-?g-ure in Fig.3,we can observe that,as the value a increases,according

to the proportion P (S ),the improvement of the robustness of BA networks is bigger and bigger.And when b P 0.1(a =0.4),b P 0.088(a =0.7),b P 0.08(a =1.0),and b P 0.076(a =1.3),P (S )>0.99.

Next,we focus on the role of the mitigation strategy on improv-ing the network robustness when the diverse types of nodes are at-tacked.We simply apply two attacks,i.e.,attacking the nodes with the highest load (HL)and attacking the ones with the lowest load (LL).In the HL,we attack the nodes in the descending order of their load (if some nodes happen to have the same highest load,we ran-domly choose one of them).While in the LL,we attack the nodes in the descending order of their load (if some nodes happen to have the same highest load,we randomly choose one of them).By the normalized average avalanche size S attack ,we quantify the network robustness after and before adopting the mitigation strategy,of

which S attack ?P

i 2A s i =n A en à1T,where A ,n A ,and n represent the set and the number of nodes attacked and the number of all nodes in a network,respectively.In computer simulations,for both the HL and the LL,we choose 50nodes as the attacked objects and numerical results are obtained by averaging over 50experiments on 10independent networks.In Fig.4,for the HL and the LL,we ob-serve that the mitigation strategy can dramatically enhance the network robustness against cascading failures and also ?nd that,the bigger the value p ,the stronger the network robustness.In Fig.5,by the proportion P (S ),surprisingly,we ?nd that the effec-tiveness orders of the mitigation method in two attacks are differ-ent,i.e.,as the value a increases,in the LL the protection method is more and more effective,while in the HL,the case is the opposite.In fact,this phenomenon is mainly originated from the effect of the value a on the node capacity.Because the bigger the value a ,the stronger the increased capacity of the nodes with the higher degree than the ones with the lower degree,for the LL,the neighboring nodes (the degrees of these nodes are generally bigger than the node attacked)of the node with the smallest degree attacked can provide the more protection resources,which lead to the results observed in the right sub-?gure in Fig.5.While for the HL,the case is on the contrary.

Next,taking into account the important role of the infrastruc-ture networks,we apply the protection method to the power grid of the western United States (Watts and Strogatz,1998)with 4941nodes and 6594edges.From two aspects of the global removal and two attacks,we investigate the effectiveness of the mitigation strategy on enhancing the robustness of the power grid against cascading failures.In Fig.6,we also observe that the robustness level of the power grid against cascading failures can obtain the signi?cant improvement and that and the effect of the value p on the cascading propagation.In the left sub-?gure in Fig.7,after adopting the mitigation strategy,we examine the cor-relation between the proportion P (S )and the parameter b

when

J.Wang /Safety Science 53(2013)219–225221

222J.Wang/Safety Science53(2013)219–225

a=0.4,a=0.7,a=1.0,and a=1.3and?nd that as the value a in-creases,the protection method is more and more effective.And

when b P0.196(a=0.4),b P0.196(a=0.7),b P0.188(a=1.0), and b P0.18(a=1.3),P(S)>0.99.In the right sub-?gure in Fig.7, according the estimated b c obtained by the minimal value when

S<0.002,after adopting the mitigation strategy,we compare the

value b c in the different value a and?nd that when a=0.4and a=0.7the power grid can obtain the stronger robust level against cascading failures.In Figs.8and9,for the HL and the LL,we inves-

tigate the effect of the mitigation strategy on improving the

robustness of the power grid against cascading failures and?nd

the similar results with ones in BA networks.

4.Theoretical analysis of cascading model

After adopting the mitigation strategy,we analyze the correla-

tion between the parameter a and the critical threshold b c in BA networks.Our aim is to seek for the the minimal value b c.There-fore,after node i,we assume the load on its neighboring node j fails to exceed its capacity,thus the extra capacity D C j;C

received by

node j can further protect node j.According to the capacity C j

and the extra D C j;C

of node j,to avoid the cascading propagation

induced by the load redistribution on node i,the neighboring node

j of node i should satisfy

L jtD L j

e4THere,

D C j;C

j ?

n2C j

peC nàL nT?

n2C j

pee1tbTk a

àk a

T?p b

n2C j

k a

e5T

So,the above inequality(4)is represented as

k a

tk a

k a

m2C i

k a

tp b

n2C j

k a

e6T

Next,by the probability theory and the network structure,we

focus on the mathematical expectations of the expressions

m2C i

k a

and

n2C j

k a

.Taking into account the characteristic of

the no degree–degree correlation in BA networks,we have

m2C i

k a

X k max

k0?k min

k i Pek0j k iTk0a?

X k max

k0?k min

k i

k0Pek0Tk0a

k i h k at1i

e7T

where P(k0j k i)(In BA network,P(k0j k i)=k0P(k0)/h k i)is the conditional

probability that node i with the degree k i has a neighbor node with

the degree k0.Similarly,we have

n2C j

k a

X k max

k0?k min

k j Pek0j k iTk0a?

X k max

k0?k min

k j

k0Pek0Tk0a

k j h k at1i

e8T

So,the above inequality(6)is simpli?ed to

k aà1

h k i

h k a i

k aà1

h k i

k a

h k itp h k a i

Analyzing the above inequality(9),we can obtain the critical

threshold b c in three ranges of a<1,a=1,and a>

J.Wang/Safety Science53(2013)219–225223

b c ?

k a à1

max h k i h k a t1i k a à1max h k i

k a à1

max

h k itp h k a t1i a >1h k i h k 2i h k i

h k itp h k 2i a ?1k a à1min

h k i h k

a t1

i k a à1

min h k i

k a à1

min h k itp h k a t1i

a <1

8>>>><>

>>>:e10T

Here,k max and k min represent the minimum and maximum de-gree of nodes in a network,respectively.When the value p is equal

to 0,the equation has been veri?ed by Wang et al.(2008).Next,for p –0,we ?rst compare the value b c in two cases of a >1and a =1.When a >1,we have

k a à1

max h k i

k a à1

max h k i tp h k a t1

h k i h k i tp h k a t1

k a à1max

e11T

p h k

a t1

k a max

X N i ?1

k 2

i e

k i k max

Ta à1

e12T

Therefore,according the Eq.(10)and the inequality (12)and the

correctness of the Eq.(12)when p =0,we can get b c (a >1)>b c (-a =1).Similarly,in the case of a <1,we can also obtain b c (a <1)>b c (a =1).

However,in Fig.3,we observe that the optimal value a is about 0.8.The smaller deviation between computer simulations and the-oretical analysis mainly derives from the above approximation in the analytical predictions,i.e.,two nodes i and j connected by other other simultaneously have the minimum degree.In fact,in BA net-works generated by the BA model,according to the evolving mech-anism of the BA model,two nodes with the lowest degree can be not connected by each other.For example,for a BA network with 5000nodes and 9997edges,there is not a connection between two nodes with the minimum degree,which may lead to the differ-ence in comparison.

By the Eq.(10),we further analyze the effect of the mitigation strategy on the critical threshold b c .We compare the value b c

224J.Wang /Safety Science 53(2013)219–225

two cases of p=0and p–0,correspond to not adopting and adopt-ing the mitigation,respectively.We calculate the value b c,p–0/b c,p=0, i.e.,

b c;p–0=b c;p?0?

k aà1

max

h k i

k aà1

max

h k itp h k at1i

a>1

h k i

h k itp h k2i

a?1

k aà1

min

h k i

k a

min

h k itp h k a i

a<1

>>>

e13T

For simplicity,we only calculate the value b c,p–0/b c,p=0in the case of a=1.We?rst calculate the value h k2i.For a BA network with the?nite size,its degree distribution is P(k)=2m2kà3,where

m is equal to k min(here k min?1

2h k i).Thus,h k2i in a BA network can

be calculated by

h k2i?

Z k max

k min PekTk2dk?

Z k max

k min

2k2

min

kà1dk

?2k2

min

elnk maxàlnk minTe14T

In BA networks,k max can be calculated by R1

k max

PekTdk?1=N,i.e.,

Z1 k max 2m2kà3dk?1=N)k max?

????

k mine15T

So,we have

h k2i?k2

min lnN?

h k i2lnN

e16T

Therefore,when a=1,we can get

b c;p–0=b c;p?0?

4tp h k i lnN

e17T

In computer simulations,the parameter p,the average degree h k i,and the network size N is0.5,4,and5000,respectively.So,only in the case of p=0.5,we can obtain b c,p=0.5/b c,p=0%0.05545,which shows that the network robustness can dramatically be improved. In addition,we also?nd that the bigger the value p,the smaller the value b c,the stronger the network robustness.

5.Conclusion

In summary,by the local dynamical adjustment of the capacity of an overload node,without changing the total price of the whole net-work,we propose a method to effectively protect the overload node to avoid its breakdown.Applying a simple cascading model,we numerically investigate the effectiveness of the mitigation strategy on improving the robustness against cascading failures in BA scale-free networks and the power grid.According to the average ava-lanche size and the proportion between the protected nodes by the mitigation strategy and the failed nodes before adopting the mitigation strategy,we?nd that the mitigation strategy can effec-tively enhance the network robustness and obtain the correlation between the network robustness and some parameters.In addition, after applying the mitigation strategy,we obtain the optimal value a,at which both BA networks and the power grid can reach the strongest robust level against cascading failures.We also verify the result in BA networks by the latter theoretical analysis.Consid-ering that the mitigation strategy can be easily applied to many real-life networks,these results may be very useful for guiding the improvement robustness of infrastructure networks and avoiding various cascading-failure-induced disasters in the real world.Acknowledgements

This work was supported by the National Natural Science Foun-dation of China under Grant Nos.71101022and70801011and the Fundamental Research Funds for the Central Universities under Grant No.N110406003.

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J.Wang/Safety Science53(2013)219–225225

With的用法全解

With的用法全解 with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。一、 with结构的构成它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词 +动词不定式； 5. with或without-名词/代词 +分词。下面分别举例： 1、 She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语）

2、 With the meal over ， we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。） The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语）He could not finish it without me to help him.（without+代词 +不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语） Without anything left in the with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。二、with结构的用法 with是介词，其意义颇多，一时难掌握。为帮助大家理清头绪，以教材中的句子为例，进行分类，并配以简单的解释。在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件（详见上述例句）。 1.带着，牵着…… (表动作特征)。如： Run with the kite like this.

with的复合结构和独立主格结构

1. with+宾语+形容词。比如：. The boy wore a shirt with the neck open, showing his bare chest. 那男孩儿穿着一件衬衫，颈部敞开，露出光光的胸膛。Don’t talk with your mouth full. 嘴里有食物时不要讲话。 2. with+宾语+副词。比如：She followed the guide with her head down. 她低着头，跟在导游之后。 What a lonely world it will be with you away. 你不在，多没劲儿呀！ 3. with+宾语+过去分词。比如：He was listening to the music with his eyes half closed. 他眼睛半闭着听音乐。She sat with her head bent. 她低着头坐着。 4. with+宾语+现在分词。比如：With winter coming, it’s time to buy warm clothes. 冬天到了，该买些保暖的衣服了。 He soon fell asleep with the light still burning. 他很快就睡着了，（可）灯还亮着。 5. with+宾语+介词短语。比如：He was asleep with his head on his arms. 他的头枕在臂膀上睡着了。 The young lady came in, with her two- year-old son in her arms. 那位年轻的女士进来了，怀里抱着两岁的孩子。 6. with+宾语+动词不定式。比如： With nothing to do in the afternoon, I went to see a film. 下午无事可做，我就去看了场电影。Sorry, I can’t go out with all these dishes to wash. 很抱歉，有这么多盘子要洗，我不能出去。 7. with+宾语+名词。比如： He died with his daughter yet a school-girl.他去逝时，女儿还是个小学生。 He lived a luxurious life, with his old father a beggar . 他过着奢侈的生活，而他的老父亲却沿街乞讨。(8)With so much work to do ,I can't go swimming with you. (9)She stood at the door,with her back towards us. (10)He entered the room,with his nose red with cold. with复合结构与分词做状语有啥区别 [ 标签：with, 复合结构, 分词状语] Ciro Ferrara 2009-10-18 16:17 主要是分词形式与主语的关系满意答案好评率：100%

with复合结构专项练习96126

with复合结构专项练习（二）一请选择最佳答案 1）With nothing_______to burn，the fire became weak and finally died out. A.leaving B.left C.leave D.to leave 2）The girl sat there quite silent and still with her eyes_______on the wall. A.fixing B.fixed C.to be fixing D.to be fixed 3）I live in the house with its door_________to the south.（这里with结构作定语） A.facing B.faces C.faced D.being faced 4）They pretended to be working hard all night with their lights____. A.burn B.burnt C.burning D.to burn 二：用with复合结构完成下列句子 1）_____________（有很多工作要做），I couldn't go to see the doctor. 2）She sat__________（低着头）。 3）The day was bright_____.（微风吹拂） 4）_________________________，（心存梦想）he went to Hollywood. 三把下列句子中的划线部分改写成with复合结构。 1）Because our lessons were over，we went to play football. _____________________________. 2）The children came running towards us and held some flowers in their hands. _____________________________. 3）My mother is ill，so I won't be able to go on holiday. _____________________________. 4）An exam will be held tomorrow，so I couldn't go to the cinema tonight. _____________________________.

with的用法大全

with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。一、 with结构的构成它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。下面分别举例：

1、 She came into the room，with her nose red because of cold.(with+名词+形容词，作伴随状语) 2、 With the meal over ， we all went home.(with+名词+副词，作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语，作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.(with+名词+不定式，作伴随状语) He could not finish it without me to help him.(without+代词 +不定式，作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词，作伴随状语) 6、Without anything left in the cupboard， she went out to get something to eat.(without+代词+过去分词，作为原因状语) 二、with结构的用法在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件(详见上述例句)。

with的复合结构

基本用法它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语或非谓语动词充当一、with或without+名词/代词+形容词例句:1.I like to sleep with the windows open. 我喜欢把窗户开着睡觉。(伴随情况) 2.With the weather so close and stuffy, ten to one it'll rain presently. 大气这样闷，十之八九要下雨(原因状语) 二、with或without+名词/代词+副词例句:1.She left the room with all the lights on. 她离开了房间，灯还亮着。(伴随情况) 2.The boy stood there with his head down. 这个男孩低头站在那儿。(伴随情况) 三、with或without+名词/代词+介词短语例句:1.He walked into the dark street with a stick in his hand. 他走进黑暗的街道时手里拿着根棍子。(伴随情况) 2. With the children at school, we can't take our vacation when we want to. 由于孩子们在上学，所以当我们想度假时而不能去度假。(原因状语) 四、with或without+名词/代词+非谓语动词 1、with或without+名词/代词+动词不定式，此时，不定式表示将发生的动作。例句: 1.With no one to talk to, John felt miserable. 由于没人可以说话的人，约翰感到很悲哀。(原因状语)

with用法归纳

with用法归纳（1）“用……”表示使用工具，手段等。例如： ①We can walk with our legs and feet. 我们用腿脚行走。 ②He writes with a pencil. 他用铅笔写。（2）“和……在一起”，表示伴随。例如： ①Can you go to a movie with me? 你能和我一起去看电影'>电影吗？ ②He often goes to the library with Jenny. 他常和詹妮一起去图书馆。（3）“与……”。例如： I’d like to have a talk with you. 我很想和你说句话。（4）“关于，对于”，表示一种关系或适应范围。例如： What’s wrong with your watch? 你的手表怎么了？（5）“带有，具有”。例如： ①He’s a tall kid with short hair. 他是个长着一头短发的高个子小孩。 ②They have no money with them. 他们没带钱。（6）“在……方面”。例如： Kate helps me with my English. 凯特帮我学英语。（7）“随着，与……同时”。例如： With these words, he left the room. 说完这些话，他离开了房间。 [解题过程] with结构也称为with复合结构。是由with+复合宾语组成。常在句中做状语，表示谓语动作发生的伴随情况、时间、原因、方式等。其构成有下列几种情形： 1.with+名词(或代词)+现在分词此时，现在分词和前面的名词或代词是逻辑上的主谓关系。例如:1)With prices going up so fast, we can't afford luxuries. 由于物价上涨很快，我们买不起高档商品。（原因状语） 2)With the crowds cheering, they drove to the palace. 在人群的欢呼声中，他们驱车来到皇宫。（伴随情况） 2.with+名词(或代词)+过去分词此时，过去分词和前面的名词或代词是逻辑上的动宾关系。

With的复合结构

With的复合结构介词with without +宾语+宾语的补足语可以构成独立主格结构，上面讨论过的独立主格结构的几种情况在此结构中都能体现。 1. with+名词代词+形容词 He doesn’t like to sleep with the windows open. = He doesn’t like to sleep when the windows are open. He stood in the rain, with his clothes wet. = He stood in the rain, and his clothes were wet. With his father well-known, the boy didn’t want to study. 2. with+名词代词+副词 Our school looks even more beautiful with all the lights on. = Our school looks even more beautiful if when all the lights are on. The boy was walking, with his father ahead. = The boy was walking and his father was ahead. 3. with+名词代词+介词短语 He stood at the door, with a computer in his hand. He stood at the door, computer in hand. = He stood at the door, and a computer was in his hand. Vincent sat at the desk, with a pen in his mouth. Vincent sat at the desk, pen in mouth. = Vincent sat at the desk, and he had a pen in his mouth. 4. with+名词代词+动词的-ed形式 With his homework done, Peter went out to play. = When his homework was done, Peter went out to play. With the signal given, the train started. = After the signal was given, the train started. I wouldn’t dare go home without the job finished. = I wouldn’t dare go home because the job was not finish ed. 5. with+名词代词+动词的-ing形式 The girl hid her box without anyone knowing where it was. = The girl hid her box and no one knew where it was. Without anyone noticing, he slipped through the window. = When no one was noticing, he slipped through the window. 6. with+名词代词+动词不定式 The little boy looks sad, with so much homework to do. = The little boy looks sad because he has so much homework to do. with the window closed with the light on with a book in her hand with a cat lying in her arms with the problem solved with the new term to begin

with用法小结

with用法小结一、with表拥有某物 Mary married a man with a lot of money . 马莉嫁给了一个有着很多钱的男人。 I often dream of a big house with a nice garden . 我经常梦想有一个带花园的大房子。 The old man lived with a little dog on the lonely island . 这个老人和一条小狗住在荒岛上。二、with表用某种工具或手段 I cut the apple with a sharp knife . 我用一把锋利的刀削平果。 Tom drew the picture with a pencil . 汤母用铅笔画画。三、with表人与人之间的协同关系 make friends with sb talk with sb quarrel with sb struggle with sb fight with sb play with sb work with sb cooperate with sb I have been friends with Tom for ten years since we worked with each other, and I have never quarreled with him . 自从我们一起工作以来，我和汤姆已经是十年的朋友了，我们从没有吵过架。四、with 表原因或理由 John was in bed with high fever . 约翰因发烧卧床。 He jumped up with joy . 他因高兴跳起来。 Father is often excited with wine . 父亲常因白酒变的兴奋。五、with 表“带来”，或“带有,具有”，在…身上，在…身边之意

with复合宾语的用法(20201118215048)

with+复合宾语的用法一、with的复合结构的构成二、所谓"with的复合结构”即是"with+复合宾语”也即"with +宾语+宾语补足语” 的结构。其中的宾语一般由名词充当（有时也可由代词充当）；而宾语补足语则是根据具体的需要由形容词，副词、介词短语，分词短语（包括现在分词和过去分词）及不定式短语充当。下面结合例句就这一结构加以具体的说明。三、1、with +宾语+形容词作宾补四、①He slept well with all the windows open.（82 年高考题）上面句子中形容词open作with的宾词all the windows的补足语， ②It' s impolite to talk with your mouth full of food. 形容词短语full of food 作宾补。Don't sleep with the window ope n in win ter 2、with+宾语+副词作宾补 with Joh n away, we have got more room. He was lying in bed with all his clothes on. ③Her baby is used to sleeping with the light on.句中的on 是副词，作宾语the light 的补足语。 ④The boy can t play with his father in.句中的副词in 作宾补。 3、with+宾语+介词短语。 we sat on the grass with our backs to the wall. his wife came dow n the stairs,with her baby in her arms. They stood with their arms round each other. With tears of joy in her eyes ,she saw her daughter married. ⑤She saw a brook with red flowers and green grass on both sides. 句中介词短语on both sides 作宾语red flowersandgreen grass 的宾补， ⑥There were rows of white houses with trees in front of them.，介词短语in front of them 作宾补。 4、with+宾词+分词（短语这一结构中作宾补用的分词有两种，一是现在分词，二是过去分词，一般来说，当分词所表示的动作跟其前面的宾语之间存在主动关系则用现在分词，若是被动关系，则用过去分词。 ⑦In parts of Asia you must not sit with your feet pointing at another person.（高一第十课），句中用现在分词pointing at…作宾语your feet的补足语，是因它们之间存在主动关系，或者说point 这一动作是your feet发出的。 All the after noon he worked with the door locked. She sat with her head bent. She did not an swer, with her eyes still fixed on the wall. The day was bright,with a fresh breeze（微风）blowing. I won't be able to go on holiday with my mother being ill. With win ter coming on ,it is time to buy warm clothes. He soon fell asleep with the light still bur ning. ⑧From space the earth looks like ahuge water covered globe,with a few patches of land stuk ing out above the water而在下面句子中因with的宾语跟其宾补之间存在被动关系，故用过去分词作宾补：

(完整版)with的复合结构用法及练习

with复合结构一. with复合结构的常见形式 1.“with+名词/代词+介词短语”。 The man was walking on the street, with a book under his arm. 那人在街上走着，腋下夹着一本书。 2. “with+名词/代词+形容词”。 With the weather so close and stuffy, ten to one it’ll rain presently. 天气这么闷热，十之八九要下雨。 3. “with+名词/代词+副词”。 The square looks more beautiful than even with all the light on. 所有的灯亮起来，广场看起来更美。 4. “with+名词/代词+名词”。 He left home, with his wife a hopeless soul. 他走了，妻子十分伤心。 5. “with+名词/代词+done”。此结构过去分词和宾语是被动关系，表示动作已经完成。 With this problem solved, neomycin 1 is now in regular production. 随着这个问题的解决，新霉素一号现在已经正式产生。 6. “with+名词/代词+-ing分词”。此结构强调名词是-ing分词的动作的发出者或某动作、状态正在进行。 He felt more uneasy with the whole class staring at him. 全班同学看着他，他感到更不自然了。 7. “with+宾语+to do”。此结构中，不定式和宾语是被动关系，表示尚未发生的动作。 So in the afternoon, with nothing to do, I went on a round of the bookshops. 由于下午无事可做，我就去书店转了转。二. with复合结构的句法功能 1. with 复合结构，在句中表状态或说明背景情况，常做伴随、方式、原因、条件等状语。With machinery to do all the work, they will soon have got in the crops. 由于所有的工作都是由机器进行，他们将很快收完庄稼。（原因状语） The boy always sleeps with his head on the arm. 这个孩子总是头枕着胳膊睡觉。（伴随状语）The soldier had him stand with his back to his father. 士兵要他背对着他父亲站着。（方式状语）With spring coming on, trees turn green. 春天到了，树变绿了。（时间状语） 2. with 复合结构可以作定语 Anyone with its eyes in his head can see it’s exactly like a rope. 任何一个头上长着眼睛的人都能看出它完全像一条绳子。【高考链接】 1. ___two exams to worry about, I have to work really hard this weekend.（04北京） A. With B. Besides C. As for D. Because of 【解析】A。“with+宾语+不定式”作状语，表示原因。 2. It was a pity that the great writer died, ______his works unfinished. (04福建) A. for B. with C. from D.of 【解析】B。“with+宾语+过去分词”在句中作状语，表示状态。 3._____production up by 60%, the company has had another excellent year. (NMET) A. As B.For C. With D.Through 【解析】C。“with+宾语+副词”在句中作状语，表示程度。

With复合结构的用法小结

With复合结构的用法小结 with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。一、with结构的构成它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词+动词不定式； 5. with或without-名词/代词+分词。下面分别举例： 1、She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语） 2、With the meal over ，we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。）The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语）He could not finish it without me to help him.（without+代词+不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语）Without anything left in the cupboard，shewent out to get something to eat.（without+代词+过去分词，作为原因状语）二、with结构的用法在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件（详见上述例句）。 With结构在句中也可以作定语。例如： 1.I like eating the mooncakes with eggs. 2.From space the earth looks like a huge water-covered globe with a few patches of land sticking out above the water. 3.A little boy with two of his front teeth missing ran into the house. 三、with结构的特点 1. with结构由介词with或without+复合结构构成。复合结构中第一部分与第二部分语法上是宾语和宾语补足语关系，而在逻辑上，却具有主谓关系，也就是说，可以用第一部分作主语，第二部分作谓语，构成一个句子。例如：With him taken care of，we felt quite relieved.（欣慰）→（He was taken good care of.）She fell asleep with the light burning. →（The light was burning.）With her hair gone，there could be no use for them. →（Her hair was gone.） 2. 在with结构中，第一部分为人称代词时，则该用宾格代词。例如：He could not finish it without me to help him. 四、几点说明： 1. with结构在句子中的位置：with 结构在句中作状语，表示时间、条件、原因时一般放在

山大复合材料结构与性能复习题参考答案.doc

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3、说明增强体在结构复合材料中的作用能够强化基体的材料称为增强体。增强体在复合材料中是分散相。复合材料中的增强体，按几何形状可分为颗粒状、纤维状、薄片状和由纤维编制的三维立体结构。喑属性可分为有机增强体和无机增强体。复合材料中最主要的增强体是纤维状的。对于结构复合材料，纤维的主要作用是承载，纤维承受载荷的比例远大于基体；对于多功能复合材料，纤维的主要作用是吸波、隐身、防热、耐磨、耐腐蚀和抗震等其中一种或多种，同时为材料提供基本的结构性能；对于结构陶瓷复合材料，纤维的主要作用是增加韧性。 4、说明纤维增强复合材料为何有最小纤维含量和最大纤维含量在复合材料中，纤维体积含量是一个很重要的参数。纤维强度高，基体韧性好，若加入少量纤维，不仅起不到强化作用反而弱化，因为纤维在基体内相当于裂纹。所以存在最小纤维含量，即临界纤维含量。若纤维含量小于临界纤维量，则在受外载荷作用时，纤维首先断裂，同时基体会承受载荷，产生较大变形，是否断裂取决于基体强度。纤维量增加，强度下降。当纤维量大于临界纤维量时，纤维主要承受载荷。纤维量增加强度增加。总之，含量过低，不能充分发挥复合材料中增强材料的作用；含量过高，由于纤维和基体间不能形成一定厚度的界面过渡层, 无法承担基体对纤维的力传递，也不利于复合材料抗拉强度的提高。 5、如何设才计复合材料材料设计是指根据对?材料性能的要求而进行的材料获得方法与工程途径的规划。复合材料设计是通过改变原材料体系、比例、配置和复合工艺类型及参数，来改变复合材料的性能，特别是是器有各向异性，从而适应在不同位置、不同方位和不同环境条件下的使用要求。复合材料的可设计性赋予了结构设计者更大的自由度，从而有可能设计出能够充分发掘与应用材料潜力的优化结构。复合材料制品的设计与研制步骤可以归纳如下： 1）通过论证明确对于材料的使用性能要求，确定设计目标 2）选择材料体系（增强体、基体） 3）确定组分比例、几何形态及增强体的配置 4）确定制备工艺方法及工艺参数

介词with的用法大全

介词with的用法大全 With是个介词，基本的意思是“用”，但它也可以协助构成一个极为多采多姿的句型，在句子中起两种作用；副词与形容词。 with在下列结构中起副词作用： 1.“with+宾语+现在分词或短语”，如： (1) This article deals with common social ills, with particular attention being paid to vandalism. 2.“with+宾语+过去分词或短语”，如： (2) With different techniques used, different results can be obtained. (3) The TV mechanic entered the factory with tools carried in both hands. 3.“with+宾语+形容词或短语”，如： (4) With so much water vapour present in the room, some iron-made utensils have become rusty easily. (5) Every night, Helen sleeps with all the windows open. 4.“with+宾语＋介词短语”，如： (6) With the school badge on his shirt, he looks all the more serious. (7) With the security guard near the gate no bad character could do any thing illegal. 5.“with+宾语＋副词虚词”，如： (8) You cannot leave the machine there with electric power on. (9) How can you lock the door with your guests in? 上面五种“with”结构的副词功能，相当普遍，尤其是在科技英语中。接着谈“with”结构的形容词功能，有下列五种：一、“with+宾语+现在分词或短语”，如： (10) The body with a constant force acting on it. moves at constant pace. (11) Can you see the huge box with a long handle attaching to it ? 二、“with+宾语+过去分词或短语” (12) Throw away the container with its cover sealed. (13) Atoms with the outer layer filled with electrons do not form compounds. 三、“with+宾语+形容词或短语”，如： (14) Put the documents in the filing container with all the drawers open.

with的复合结构用法小结

With 复合结构用法小结 “With + 复合结构”又称为“with结构”，在句中表状态或说明背景情况，常做伴随，方式，原因，条件等状语。具体结构如下： 1. With + 名词 + 介词短语? (1) He was asleep with his head on his arm. ? (2) The man came in with a whip in his hand. ? 在书面语中。上句也可以说成：The man came in, whip in hand. 2．with + 名词 + 形容词（强调名词的特性或状态）? (1)With the weather so close and stuffy, ten to one it'll rain presently.天气这么闷热，十之八九要下雨。? (2)He used to sleep with the windows open. 3. With + 名词 + 副词? (1)With John away, we've got more room. 约翰走了，我们的地方大了一些。? (2)The square looks more beautiful than ever with all the light on. 4. With + 名词 + -ed 分词（强调名词是 -ed分词动作的承受者或动作已经发生） ?(1)With this problem solved, neopenicillin 1 is now in regular production. 随着这个问题的解决，新霉素一号现在已正式生产。 ?(2)All the afternoon he worked with the door locked. 5. with + 名词 + -ing分词（强调名词是 -ing分词的动作的发出者或某动作，状态正在进行）? (1)I won’t be able to go on holiday with my mother being ill. ? (2)He felt more uneasy with the whole class staring at him. ? (3)With the field leveled and irrigation channels controlling the volume of water(水量), no such problem arose again. 6. with + 名词 + to do （不定式动作尚未发生）? (1)So in the afternoon, with nothing to do, I went on a round of the bookshops. 由于下午无事可做，我就去书店转了转。 ?(2)I can't go out with all these dishes to wash. 一、 with结构的构成它是由介词with或without+复合结构构成，复合结构作介词with或without 的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词 +动词不定式； 5. with或without-名词/代词 +分词。下面分别举例： 1、 She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语） 2、 With the meal over ， we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。） The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语） He could not finish it without me to help him.（without+代词 +不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语） Without anything left in the with结构是许多英语复合结构中最