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第2行： − − − [[Image:Networkfailure.gif|thumb|right|An animation demonstrating how a single failure may result in other failures throughout a network.]] − An animation demonstrating how a single failure may result in other failures throughout a network. − A cascading failure is a process in a system of [[interconnection|interconnected]] parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.+ − A cascading failure is a process in a system of interconnected parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems. − − 在一个部件相互连接的系统中，一个或几个部件的故障会引发其他部件的故障的过程就是'''<font color="#ff8000"> 级联失效 Cascading Failure</font>'''（也可译为级联故障）。这种故障可能发生在许多类型的系统中，包括电力输送、计算机网络、金融、交通系统、生物体、人体和生态系统。 − − − Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another. − − Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another. − + − + − 在电力输送中 − − − Cascading failure is common in [[power grid]]s when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in [[high voltage]] systems, where a [[single point of failure]] (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time. − − Cascading failure is common in power grids when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in high voltage systems, where a single point of failure (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time. − − 级联失效在电网中很常见，当其中一个元件(完全或部分)发生故障并将其负荷转移到系统中附近的元件时，就会推动那些附近的元件超出其容量，从而过载，并将其负荷转移到其他元件上。级联失效在高压系统中也很常见，在一个满载或轻度过载的系统中，一个'''<font color="#ff8000"> 单点故障 Single Point of Failure (SPF)</font>'''会导致系统所有节点突然出现尖峰。这种'''<font color="#ff8000"> 浪涌电流 Surge Current</font>'''可能会导致已经过载的节点发生故障，引发更多过载，从而在很短的时间内使整个系统瘫痪。 − − − − This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer. − − This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer. − − − Monitoring the operation of a system, in [[real-time computing|real-time]], and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures.<ref name="chao">{{cite arXiv |last1=Zhai |first1=Chao |title=Modeling and Identification of Worst-Case Cascading Failures in Power Systems |eprint=1703.05232 |class=cs.SY |year=2017}}</ref> − − Monitoring the operation of a system, in real-time, and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures. − − − One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element. − − One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element. − − − The question if power grid failures are correlated have been studied in Daqing Li et al.<ref>{{Cite journal|last=Daqing|first=Li|last2=Yinan|first2=Jiang|last3=Rui|first3=Kang|last4=Havlin|first4=Shlomo|date=2014-06-20|title=Spatial correlation analysis of cascading failures: Congestions and Blackouts|journal=Scientific Reports|language=En|volume=4|issue=1|pages=5381|doi=10.1038/srep05381|pmid=24946927|pmc=4064325|issn=2045-2322|bibcode=2014NatSR...4E5381D}}</ref> as well as by Paul DH Hines et al.<ref>{{Cite journal|last=Hines|first=Paul D. H.|last2=Dobson|first2=Ian|last3=Rezaei|first3=Pooya|date=2016|title=Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology|arxiv=1508.01775|journal=IEEE Transactions on Power Systems|pages=1|doi=10.1109/TPWRS.2016.2578259|issn=0885-8950}}</ref> − − The question if power grid failures are correlated have been studied in Daqing Li et al. as well as by Paul DH Hines et al. − + − − 案例 − − Cascading failure caused the following [[power outage]]s: − − Cascading failure caused the following power outages: − − + − * [[1965年东北大停电|1965年美国东北大停电]]+ − + − + − + − + − + − + − + − − − − − − * [[2006 European blackout|European Blackout in 2006]] − * [[2006年欧洲停电|2006年欧洲停电]] − * [[2012 northern India power grid failure|Blackout in Northern India in 2012]]+ − * [[2012年印度北部电网故障|2012年印度北部停电]] − * [[2016 South Australian blackout|Blackout in South Australia in 2016]]+ − * [[2016年南澳停电|2016年南澳停电]] − * [[2019 Argentina, Paraguay and Uruguay blackout|Blackout in southeast South America in 2019]] − * [[2019年阿根廷、巴拉圭和乌拉圭停电|2019年南美洲东南部停电]] − − − − == In computer networks == − 在计算机网络中 − − − − − Cascading failures can also occur in [[computer network]]s (such as the [[Internet]]) in which [[Network traffic control|network traffic]] is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term '''cascade failure'''. A cascade failure can affect large groups of people and systems. − − Cascading failures can also occur in computer networks (such as the Internet) in which network traffic is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term cascade failure. A cascade failure can affect large groups of people and systems. − − 级联失效也可能发生在计算机网络(如因特网)中，由于硬件或软件的故障或断开，导致网络中较大部分的网络通信严重受损或停止。在这种情况下，级联失效被称为术语<font color="#ff8000"> “cascade failure”</font>。级联失效会影响到大批人员和系统。 − − − − The cause of a cascade failure is usually the overloading of a single, crucial [[Router (computing)|router]] or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is [[routing|routed]] to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation. − − The cause of a cascade failure is usually the overloading of a single, crucial router or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is routed to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation. 第133行：
第54行： − + − 症状 − − − The symptoms of a cascade failure include: [[packet loss]] and high network [[lag|latency]], not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to [[congestion collapse]], which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication. − − The symptoms of a cascade failure include: packet loss and high network latency, not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to congestion collapse, which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication. − − 级联失效的症状包括: 数据包丢失和高网络延迟，不仅仅是对单个系统，而是对整个网络或互联网。高延迟和数包丢失是由于网络<font color="#ff8000"> 拥塞崩溃 congestion collapse</font>导致节点无法正常运行，这使得数据仍然存在于网络中，但是没有太多或任何有用的通道来传输它们。因此，路由仍然可被认为是有效的，而实际上它们并没有提供通信。 − − --[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“级联失效的症状”中的症状是不是可以思考换一下词语 印象中症状一般形容人 换成“表现”或其他是否更好 − --[[用户:WildBoar|WildBoar]]（[[用户讨论:WildBoar|讨论]]）我觉得两种表达都可以 − If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes.+ − If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes. − − − A common occurrence during a cascade failure is a '''walking failure''', where sections go down, causing the next section to fail, after which the first section comes back up. This '''ripple''' can make several passes through the same sections or connecting nodes before stability is restored. − − A common occurrence during a cascade failure is a walking failure, where sections go down, causing the next section to fail, after which the first section comes back up. This ripple can make several passes through the same sections or connecting nodes before stability is restored. − + − 历史 − − − Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure.{{Citation needed|date=January 2009}} − − Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure. − − + − − − 案例 − − − − Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more [[Hop (telecommunications)|hops]] and subsequently going through more systems that normally do not process the amount of traffic suddenly offered. − − Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more hops and subsequently going through more systems that normally do not process the amount of traffic suddenly offered. − − − − This can cause one or more systems along the alternative route to go down, creating similar problems of their own. − − This can cause one or more systems along the alternative route to go down, creating similar problems of their own. − − Also, related systems are affected in this case. As an example, [[Domain name system|DNS]] resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own. − − Also, related systems are affected in this case. As an example, DNS resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own. − − − In December 2012, a partial loss (40%) of [[Gmail]] service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an [https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ inappropriate ''all'' instead of the more appropriate ''some''.] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time. − − In December 2012, a partial loss (40%) of Gmail service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an [https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ inappropriate all instead of the more appropriate some.] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time. − + − − − Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the [[Hyatt Regency walkway collapse]], a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a [[zipper]]). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate [[factor of safety]] and/or alternate load paths to prevent this type of mechanical cascade failure.<ref name="petroski">{{cite book| title=To Engineer Is Human: The Role of Failure in Structural Design| first=Henry| last=Petroski| year=1992| isbn=978-0-679-73416-1| publisher=Vintage| place=| url-access=registration| url=https://archive.org/details/toengineerishuma00petr}}</ref> − − Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the Hyatt Regency walkway collapse, a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a zipper). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate factor of safety and/or alternate load paths to prevent this type of mechanical cascade failure. − − + − 其他例子+ − − − − 生物 − − − [[Biochemical cascade]]s exist in biology, where a small reaction can have system-wide implications. One negative example is [[ischemic cascade]], in which a small [[ischemia|ischemic]] attack releases [[toxin]]s which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in [[stroke]] patients to minimize the damage. − − Biochemical cascades exist in biology, where a small reaction can have system-wide implications. One negative example is ischemic cascade, in which a small ischemic attack releases toxins which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in stroke patients to minimize the damage. − − − − In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a [[keystone species]]. − − In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a keystone species. − + − − 电子学 − − − Another example is the [[Cockcroft–Walton generator]], which can also experience cascade failures wherein one failed [[diode]] can result in all the diodes failing in a fraction of a second. − − Another example is the Cockcroft–Walton generator, which can also experience cascade failures wherein one failed diode can result in all the diodes failing in a fraction of a second. − − − − Yet another example of this effect in a scientific experiment was the [[Implosion (mechanical process)|implosion]] in 2001 of several thousand fragile glass photomultiplier tubes used in the [[Super-Kamiokande]] experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction. − − Yet another example of this effect in a scientific experiment was the implosion in 2001 of several thousand fragile glass photomultiplier tubes used in the Super-Kamiokande experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction. − + − − − − {{main|Systemic risk}} {{main|Cascades in financial networks}} − {{主要}系统性风险}} {{主要}金融网络中的级联}}} − − − In [[finance]], the risk of cascading failures of financial institutions is referred to as ''[[systemic risk]]:'' the failure of one financial institution may cause other financial institutions (its [[Counterparty|counterparties]]) to fail, cascading throughout the system.<ref name="HuangVodenska2013">{{cite journal|last1=Huang|first1=Xuqing|last2=Vodenska|first2=Irena|last3=Havlin|first3=Shlomo|last4=Stanley|first4=H. Eugene|title=Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation|journal=Scientific Reports|volume=3|pages=1219|year=2013|issn=2045-2322|doi=10.1038/srep01219|pmid=23386974|pmc=3564037|arxiv=1210.4973|bibcode=2013NatSR...3E1219H}}</ref> − − In finance, the risk of cascading failures of financial institutions is referred to as systemic risk: the failure of one financial institution may cause other financial institutions (its counterparties) to fail, cascading throughout the system. − − − Institutions that are believed to pose systemic risk are deemed either "[[too big to fail]]" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat. − − Institutions that are believed to pose systemic risk are deemed either "too big to fail" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat. − − − Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. For detailed models in economics and finance, see Elliott et al. (2014) and Acemoglu et al. (2015).<ref name="Acemoglu Ozdaglar Tahbaz-Salehi 2015 pp. 564–608">{{cite journal | last=Acemoglu | first=Daron | last2=Ozdaglar | first2=Asuman | last3=Tahbaz-Salehi | first3=Alireza | title=Systemic Risk and Stability in Financial Networks | journal=American Economic Review | publisher=American Economic Association | volume=105 | issue=2 | year=2015 | issn=0002-8282 | doi=10.1257/aer.20130456 | pages=564–608| hdl=1721.1/100979 | hdl-access=free }}</ref><ref name="Elliott Golub Jackson 2014 pp. 3115–3153">{{cite journal | last=Elliott | first=Matthew | last2=Golub | first2=Benjamin | last3=Jackson | first3=Matthew O. | title=Financial Networks and Contagion | journal=American Economic Review | publisher=American Economic Association | volume=104 | issue=10 | year=2014 | issn=0002-8282 | doi=10.1257/aer.104.10.3115 | pages=3115–3153}}</ref> − − Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. For detailed models in economics and finance, see Elliott et al. (2014) and Acemoglu et al. (2015). − − − A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the [[2010 Flash Crash]]. − − A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the 2010 Flash Crash. − − − For another framework to study and predict the effect of cascading failures in finance see<ref>{{cite journal|last1=Li|first1=W|last2=Kenett|first2=DY|last3=Yamasaki|first3=K|last4=Stanley|first4=HE|last5=Havlin|first5=S|title=Ranking the economic importance of countries and industries|journal=Journal of Network Theory in Finance|volume=3|pages=1–17|year=2017|issn=2055-7795|doi=10.21314/JNTF.2017.031|arxiv=1408.0443}}</ref><ref name="HuangVodenska2013"/> − − For another framework to study and predict the effect of cascading failures in finance see − + − + − 相互依赖的级联失效+ − − − − − Fig. 1: Illustration of the interdependent relationship among different infrastructures − − 图1: 不同基础设施之间的相互依存关系的说明 − − − − Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = p_c. In the first-order case, the giant component approaches zero discontinuously − − − − − − Diverse [[infrastructure]]s such as [[water supply]], [[transportation]], fuel and [[power station]]s are coupled together and depend on each other for functioning, see Fig. 1. Owing to this coupling, interdependent networks are extremely sensitive to random failures, and in particular to [[Targeted threat|targeted attacks]], such that a failure of a small fraction of nodes in one network can triger an iterative cascade of failures in several interdependent networks.<ref>{{cite web|title=Report of the Commission to Assess the Threat to the United States from Electromagnetic Pulse (EMP) Attack|url=http://empcommission.org/docs/A2473-EMP_Commission-7MB.pdf}}</ref><ref>{{Cite journal|last=Rinaldi|first=S.M.|last2=Peerenboom|first2=J.P.|last3=Kelly|first3=T.K.|date=2001|title=Identifying, understanding, and analyzing critical infrastructure interdependencies|url=|journal= IEEE Control Systems Magazine|volume=21|pages=11–25|via=}}</ref> [[Power outage|Electrical blackouts]] frequently result from a cascade of failures between interdependent networks, and the problem has been dramatically exemplified by the several large-scale blackouts that have occurred in recent years. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. For example, the [[2003 Italy blackout]] resulted in a widespread failure of the [[Rail transport|railway network]], [[Health system|health care systems]], and [[financial services]] and, in addition, severely influenced the [[telecommunication network]]s. The partial failure of the communication system in turn further impaired the [[electrical grid]] management system, thus producing a positive feedback on the power grid.<ref>{{cite journal|last=V. Rosato |first=Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S.D., & Setola, R. |title=Modelling interdependent infrastructures using interacting dynamical models |journal=International Journal of Critical Infrastructures |year=2008 |volume=4 |pages=63–79 |doi=10.1504/IJCIS.2008.016092 }}</ref> This example emphasizes how inter-dependence can significantly magnify the damage in an interacting network system. A framework to study the cascading failures between coupled networks based on percolation theory was developed recently.<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> The cascading failures can lead to abrupt collapse compare to percolation in a single network where the breakdown of the network is continuous, see Fig. 2. Cascading failures in spatially embedded systems have been shown to lead to extreme vulnerability.<ref name="BashanBerezin2013">{{cite journal|last1=Bashan|first1=Amir|last2=Berezin|first2=Yehiel|last3=Buldyrev|first3=Sergey V.|last4=Havlin|first4=Shlomo|title=The extreme vulnerability of interdependent spatially embedded networks|journal=Nature Physics|year=2013|issn=1745-2473|doi=10.1038/nphys2727|volume=9|issue=10|pages=667–672|arxiv=1206.2062|bibcode=2013NatPh...9..667B}}</ref> For the dynamic process of cascading failures see ref.<ref>{{Cite journal|last=Zhou|first=D.|last2=Bashan|first2=A.|last3=Cohen|first3=R.|last4=Berezin|first4=Y.|last5=Shnerb|first5=N.|last6=Havlin|first6=S.|date=2014|title=Simultaneous first- and second-order percolation transitions in interdependent networks|url=|journal=Phys. Rev. E|volume=90|issue=1|pages=012803|bibcode=2014PhRvE..90a2803Z|doi=10.1103/PhysRevE.90.012803|pmid=25122338|arxiv=1211.2330}}</ref> A model for repairing failures in order to avoid cascading failures was developed by Di Muro et al.<ref>{{Cite journal|last=Di Muro|first=M. A.|last2=La Rocca|first2=C. E.|last3=Stanley|first3=H. E.|last4=Havlin|first4=S.|last5=Braunstein|first5=L. A.|date=2016-03-09|title=Recovery of Interdependent Networks|journal=Scientific Reports|language=En|volume=6|issue=1|pages=22834|doi=10.1038/srep22834|pmid=26956773|pmc=4783785|issn=2045-2322|arxiv=1512.02555|bibcode=2016NatSR...622834D}}</ref> − − Diverse infrastructures such as water supply, transportation, fuel and power stations are coupled together and depend on each other for functioning, see Fig. 1. Owing to this coupling, interdependent networks are extremely sensitive to random failures, and in particular to targeted attacks, such that a failure of a small fraction of nodes in one network can triger an iterative cascade of failures in several interdependent networks. Electrical blackouts frequently result from a cascade of failures between interdependent networks, and the problem has been dramatically exemplified by the several large-scale blackouts that have occurred in recent years. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. For example, the 2003 Italy blackout resulted in a widespread failure of the railway network, health care systems, and financial services and, in addition, severely influenced the telecommunication networks. The partial failure of the communication system in turn further impaired the electrical grid management system, thus producing a positive feedback on the power grid. This example emphasizes how inter-dependence can significantly magnify the damage in an interacting network system. A framework to study the cascading failures between coupled networks based on percolation theory was developed recently. The cascading failures can lead to abrupt collapse compare to percolation in a single network where the breakdown of the network is continuous, see Fig. 2. Cascading failures in spatially embedded systems have been shown to lead to extreme vulnerability. For the dynamic process of cascading failures see ref. A model for repairing failures in order to avoid cascading failures was developed by Di Muro et al. − − − Furthermore, it was shown that such systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system.<ref>{{Cite journal|last=Berezin|first=Yehiel|last2=Bashan|first2=Amir|last3=Danziger|first3=Michael M.|last4=Li|first4=Daqing|last5=Havlin|first5=Shlomo|date=2015-03-11|title=Localized attacks on spatially embedded networks with dependencies|journal=Scientific Reports|language=en|volume=5|issue=1|pages=8934|doi=10.1038/srep08934|pmid=25757572|pmc=4355725|issn=2045-2322|bibcode=2015NatSR...5E8934B}}</ref> − − Furthermore, it was shown that such systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system. + − == Model for overload cascading failures ==+ − 过载级联失效模型 − − A model for cascading failures due to overload propagation is the Motter–Lai model.<ref>{{Cite journal|last=Motter|first=A. E.|last2=Lai|first2=Y. C.|date=2002|title=Cascade-based attacks on complex networks|url=|journal=Phys. Rev. E|volume=66|issue=6 Pt 2|pages=065102|doi=10.1103/PhysRevE.66.065102|pmid=12513335|bibcode=2002PhRvE..66f5102M|arxiv=cond-mat/0301086}}</ref> The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al.<ref>{{Cite journal|last=Zhao|first=J.|last2=Li|first2=D.|last3=Sanhedrai|first3=H.|last4=Cohen|first4=R.|last5=Havlin|first5=S.|date=2016|title=Spatio-temporal propagation of cascading overload failures in spatially embedded networks|url=|journal=Nature Communications|volume=7|pages=10094|bibcode=2016NatCo...710094Z|doi=10.1038/ncomms10094|pmid=26754065|pmc=4729926}}</ref> − − A model for cascading failures due to overload propagation is the Motter–Lai model. The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al. − − 过载传播导致的级联失效的模型是Motter-Lai模型。赵继昌 Jichang Zhao等人对这种故障的时空传播进行了研究。 第443行：
第222行： − − −
无编辑摘要
{{short description|System of interconnected parts in which the failure of one or few parts can trigger the failure of others}}
{{short description|System of interconnected parts in which the failure of one or few parts can trigger the failure of others}}
[[Image:Networkfailure.gif|thumb|right|演示单个故障如何导致整个网络中其他故障的动画]]
[[Image:Networkfailure.gif|thumb|right|演示单个故障如何导致整个网络中其他故障的动画]]
演示单个故障如何导致整个网络中其他故障的动画。
演示单个故障如何导致整个网络中其他故障的动画。
在一个部件相互连接的系统中，一个或几个部件的故障会引发其他部件的故障的过程就是'''级联失效 Cascading Failure'''（也可译为级联故障）。这种故障可能发生在许多类型的系统中，包括电力输送、计算机网络、金融、交通系统、生物体、人体和生态系统。
当系统的一部分发生故障时，可能会发生级联失效。当这种情况发生时，其他部分必须对发生故障的部分进行补偿，这反过来又会使这些节点超载，使它们也发生故障，导致更多的节点相继发生故障。
当系统的一部分发生故障时，可能会发生级联失效。当这种情况发生时，其他部分必须对发生故障的部分进行补偿，这反过来又会使这些节点超载，使它们也发生故障，导致更多的节点相继发生故障。
== 在电力输送中 ==
== In power transmission ==
级联失效在电网中很常见，当其中一个元件(完全或部分)发生故障并将其负荷转移到系统中附近的元件时，就会推动那些附近的元件超出其容量，从而过载，并将其负荷转移到其他元件上。级联失效在高压系统中也很常见，在一个满载或轻度过载的系统中，一个'''单点故障 Single Point of Failure (SPF)'''会导致系统所有节点突然出现尖峰。这种'''浪涌电流 Surge Current'''可能会导致已经过载的节点发生故障，引发更多过载，从而在很短的时间内使整个系统瘫痪。
这个故障过程就像池塘上的涟漪一样，在系统的各个元件之间蔓延，直到系统中的所有元件都受到损害和/或系统在功能上与负载源断开。例如，在某些情况下，一个大型电网可能因为单个变压器的故障而崩溃。
这个故障过程就像池塘上的涟漪一样，在系统的各个元件之间蔓延，直到系统中的所有元件都受到损害和/或系统在功能上与负载源断开。例如，在某些情况下，一个大型电网可能因为单个变压器的故障而崩溃。
实时监测系统的运行情况，并明智地断开部件的连接，有助于阻止级联。另一种常见的技术是通过计算机模拟可能发生的故障来计算系统的安全边际，确定安全运行水平，在此水平之下，计算出的任何一种情况都不会引起级联失效，并确定网络中最有可能引起级联失效的部分。<ref name="chao">{{cite arXiv |last1=Zhai |first1=Chao |title=Modeling and Identification of Worst-Case Cascading Failures in Power Systems |eprint=1703.05232 |class=cs.SY |year=2017}}</ref>
实时监测系统的运行情况，并明智地断开部件的连接，有助于阻止级联。另一种常见的技术是通过计算机模拟可能发生的故障来计算系统的安全边际，确定安全运行水平，在此水平之下，计算出的任何一种情况都不会引起级联失效，并确定网络中最有可能引起级联失效的部分。<ref name="chao">{{cite arXiv |last1=Zhai |first1=Chao |title=Modeling and Identification of Worst-Case Cascading Failures in Power Systems |eprint=1703.05232 |class=cs.SY |year=2017}}</ref>
防止电网故障的主要困难之一是控制信号的速度比传播电力过载的速度慢，即由于控制信号和电力都以同样的速度运动，所以无法通过提前发出警告来隔离元件从而隔离故障。
防止电网故障的主要困难之一是控制信号的速度比传播电力过载的速度慢，即由于控制信号和电力都以同样的速度运动，所以无法通过提前发出警告来隔离元件从而隔离故障。
电网故障是否具有相关性的问题，李大庆 Daqing Li等人<ref>{{Cite journal|last=Daqing|first=Li|last2=Yinan|first2=Jiang|last3=Rui|first3=Kang|last4=Havlin|first4=Shlomo|date=2014-06-20|title=Spatial correlation analysis of cascading failures: Congestions and Blackouts|journal=Scientific Reports|language=En|volume=4|issue=1|pages=5381|doi=10.1038/srep05381|pmid=24946927|pmc=4064325|issn=2045-2322|bibcode=2014NatSR...4E5381D}}</ref> 以及保罗·DH·海恩斯 Paul DH Hines等人都有研究。<ref>{{Cite journal|last=Hines|first=Paul D. H.|last2=Dobson|first2=Ian|last3=Rezaei|first3=Pooya|date=2016|title=Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology|arxiv=1508.01775|journal=IEEE Transactions on Power Systems|pages=1|doi=10.1109/TPWRS.2016.2578259|issn=0885-8950}}</ref>
电网故障是否具有相关性的问题，李大庆 Daqing Li等人<ref>{{Cite journal|last=Daqing|first=Li|last2=Yinan|first2=Jiang|last3=Rui|first3=Kang|last4=Havlin|first4=Shlomo|date=2014-06-20|title=Spatial correlation analysis of cascading failures: Congestions and Blackouts|journal=Scientific Reports|language=En|volume=4|issue=1|pages=5381|doi=10.1038/srep05381|pmid=24946927|pmc=4064325|issn=2045-2322|bibcode=2014NatSR...4E5381D}}</ref> 以及保罗·DH·海恩斯 Paul DH Hines等人都有研究。<ref>{{Cite journal|last=Hines|first=Paul D. H.|last2=Dobson|first2=Ian|last3=Rezaei|first3=Pooya|date=2016|title=Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology|arxiv=1508.01775|journal=IEEE Transactions on Power Systems|pages=1|doi=10.1109/TPWRS.2016.2578259|issn=0885-8950}}</ref>
=== 案例 ===
=== Examples ===
级联失效曾导致以下停电:
级联失效曾导致以下停电:
* [[Northeast blackout of 1965|Blackout in Northeast America in 1965]]
* 1965年美国东北大停电
* 1999年巴西南部停电
* 2003年美国东北大停电
* [[1999 Southern Brazil blackout|Blackout in Southern Brazil in 1999]]
* 2003年意大利停电
* [[1999年巴西南部停电|1999年巴西南部停电]]
* 2003年伦敦大停电
* 2006年欧洲停电
* [[Northeast blackout of 2003|Blackout in Northeast America in 2003]]
* 2012年印度北部停电
* [[2003年东北大停电|2003年美国东北大停电]]
* 2016年南澳停电
* 2019年南美洲东南部停电
* [[2003 Italy blackout|Blackout in Italy in 2003]]
* [[2003年意大利停电|2003年意大利停电]]
* [[2003 London blackout|Blackout in London in 2003]]
* [[2003年伦敦大停电|2003年伦敦大停电]]
== 在计算机网络中 ==
级联失效也可能发生在计算机网络(如因特网)中，由于硬件或软件的故障或断开，导致网络中较大部分的网络通信严重受损或停止。在这种情况下，级联失效被称为术语“cascade failure”。级联失效会影响到大批人员和系统。
级联失效的原因通常是一个单个关键的路由器或节点的超载，导致节点宕机即使是短暂地宕机。它也可能是由于为了维护或升级而关闭一个节点引起的。在这两种情况下，流量都被路由到达或通过另一条(替代)路径。结果，这条替代路径变得过载，导致宕机，等等。它还会影响依赖该节点正常运行的系统。
级联失效的原因通常是一个单个关键的路由器或节点的超载，导致节点宕机即使是短暂地宕机。它也可能是由于为了维护或升级而关闭一个节点引起的。在这两种情况下，流量都被路由到达或通过另一条(替代)路径。结果，这条替代路径变得过载，导致宕机，等等。它还会影响依赖该节点正常运行的系统。
=== Symptoms ===
=== 症状 ===
级联失效的症状包括: 数据包丢失和高网络延迟，不仅仅是对单个系统，而是对整个网络或互联网。高延迟和数包丢失是由于网络拥塞崩溃 congestion collapse导致节点无法正常运行，这使得数据仍然存在于网络中，但是没有太多或任何有用的通道来传输它们。因此，路由仍然可被认为是有效的，而实际上它们并没有提供通信。
如果有够多的路由因为级联失效而中断，网络或互联网的一个完整部分就会无法访问。尽管我们不希望出现这种情况，但这有助于加快从故障中恢复，因为连接会超时，其他节点会放弃尝试与被切断的部分建立连接，从而减少相关节点的负载。
如果有够多的路由因为级联失效而中断，网络或互联网的一个完整部分就会无法访问。尽管我们不希望出现这种情况，但这有助于加快从故障中恢复，因为连接会超时，其他节点会放弃尝试与被切断的部分建立连接，从而减少相关节点的负载。
在级联失效中，一个常见的现象是行走故障，即各段下行，导致下一段故障，之后第一段回升。在恢复稳定之前，这种波纹可能会在相同的区段或连接节点上进行多次传递。
在级联失效中，一个常见的现象是行走故障，即各段下行，导致下一段故障，之后第一段回升。在恢复稳定之前，这种波纹可能会在相同的区段或连接节点上进行多次传递。
=== History ===
=== 历史 ===
级联故障是最近随着流量的大量增加以及系统和网络之间的高互联性而出现的。这个术语最早是在90年代末由一位荷兰的IT专业人员在这样的背景下使用的，后来慢慢成为一个形容这种大规模故障的比较常见的术语。
级联故障是最近随着流量的大量增加以及系统和网络之间的高互联性而出现的。这个术语最早是在90年代末由一位荷兰的IT专业人员在这样的背景下使用的，后来慢慢成为一个形容这种大规模故障的比较常见的术语。
=== 案例 ===
=== Example ===
网络故障通常始于单个网络节点故障。首先，正常经过该节点的流量停止，系统和用户会得到流量无法到达主机的错误提示。通常，ISP的冗余系统会很快做出反应，选择另一条通过不同骨干网的路径。这条替代路径通过的路由路径更长，跳数更多，随后还要经过更多的系统，而这些系统通常不会处理突发的流量。
网络故障通常始于单个网络节点故障。首先，正常经过该节点的流量停止，系统和用户会得到流量无法到达主机的错误提示。通常，ISP的冗余系统会很快做出反应，选择另一条通过不同骨干网的路径。这条替代路径通过的路由路径更长，跳数更多，随后还要经过更多的系统，而这些系统通常不会处理突发的流量。
这可能会导致替代路线上的一个或多个系统瘫痪，造成类似故障系统的问题。
这可能会导致替代路线上的一个或多个系统瘫痪，造成类似故障系统的问题。
此外，在这种情况下，相关系统也会受到影响。例如，DNS解析可能会失败，那些通常会造成系统互连的情况可能会破坏一些连接，这些连接甚至没有直接参与实际发生故障的系统。而这又可能导致看似不相关的节点出现问题，从而导致另一个级联失效的发生。
此外，在这种情况下，相关系统也会受到影响。例如，DNS解析可能会失败，那些通常会造成系统互连的情况可能会破坏一些连接，这些连接甚至没有直接参与实际发生故障的系统。而这又可能导致看似不相关的节点出现问题，从而导致另一个级联失效的发生。
2012年12月，Gmail服务在全球范围内出现了部分损失(40%)，持续了18分钟。这次服务损失是由包含错误逻辑的负载平衡软件的例行更新引起的——在这种情况下，该错误是由使用[https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ 不合适的all而不是更合适的some]的逻辑引起的。通过完全更新网络中的一个节点，而不是部分更新所有节点，修复了级联失效。
2012年12月，Gmail服务在全球范围内出现了部分损失(40%)，持续了18分钟。这次服务损失是由包含错误逻辑的负载平衡软件的例行更新引起的——在这种情况下，该错误是由使用[https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ 不合适的all而不是更合适的some]的逻辑引起的。通过完全更新网络中的一个节点，而不是部分更新所有节点，修复了级联失效。
== Cascading structural failure ==
== 级联结构失效 ==
级联结构失效
某些具有离散结构构件的承重结构可能会出现 "拉链效应"，即单个结构构件的失效会增加相邻构件的荷载。 在凯悦酒店人行道坍塌事件中，当单根垂直悬杆失效时，悬空的人行道（由于施工中的错误，人行道已经过度受力）倒塌，使相邻的悬杆超载，相邻的悬杆依次失效（像拉链一样）。一座可能发生这种倒塌的桥梁被称为断裂临界桥梁，许多桥梁的坍塌都是由单一部件的故障引起的。正确设计的结构使用足够安全系数的和/或交替的荷载路径来防止这种类型的机械级联失效。<ref name="petroski">{{cite book| title=To Engineer Is Human: The Role of Failure in Structural Design| first=Henry| last=Petroski| year=1992| isbn=978-0-679-73416-1| publisher=Vintage| place=| url-access=registration| url=https://archive.org/details/toengineerishuma00petr}}</ref>
某些具有离散结构构件的承重结构可能会出现 "拉链效应"，即单个结构构件的失效会增加相邻构件的荷载。 在凯悦酒店人行道坍塌事件中，当单根垂直悬杆失效时，悬空的人行道（由于施工中的错误，人行道已经过度受力）倒塌，使相邻的悬杆超载，相邻的悬杆依次失效（像拉链一样）。一座可能发生这种倒塌的桥梁被称为断裂临界桥梁，许多桥梁的坍塌都是由单一部件的故障引起的。正确设计的结构使用足够安全系数的和/或交替的荷载路径来防止这种类型的机械级联失效。<ref name="petroski">{{cite book| title=To Engineer Is Human: The Role of Failure in Structural Design| first=Henry| last=Petroski| year=1992| isbn=978-0-679-73416-1| publisher=Vintage| place=| url-access=registration| url=https://archive.org/details/toengineerishuma00petr}}</ref>
== Other examples ==
== 其他例子 ==
===生物===
=== Biology ===
生物学中存在着生化级联，一个小的反应就会对整个系统产生影响。一个负面的例子是缺血性级联反应，在这种反应中，一个小的脑缺血发作释放出的毒素比最初的损伤杀死更多的细胞，导致更多的毒素被释放。目前的研究正在寻找一种方法来阻断中风患者的这种级联反应，以最大限度地减少损伤。
生物学中存在着生化级联，一个小的反应就会对整个系统产生影响。一个负面的例子是缺血性级联反应，在这种反应中，一个小的脑缺血发作释放出的毒素比最初的损伤杀死更多的细胞，导致更多的毒素被释放。目前的研究正在寻找一种方法来阻断中风患者的这种级联反应，以最大限度地减少损伤。
在物种灭绝的研究中，有时一个物种的灭绝会导致许多其他物种的灭绝。这样的物种被称为<font color="#ff8000"> 关键种 keystone species</font>。
在物种灭绝的研究中，有时一个物种的灭绝会导致许多其他物种的灭绝。这样的物种被称为<font color="#ff8000"> 关键种 keystone species</font>。
=== 电子学 ===
=== Electronics ===
另一个例子是Cockcroft-Walton发电机，它也会发生级联失效，其中一个故障的二极管会导致所有二极管在顷刻间发生故障。
另一个例子是Cockcroft-Walton发电机，它也会发生级联失效，其中一个故障的二极管会导致所有二极管在顷刻间发生故障。
在科学实验中，这种效应的另一个例子是2001年用于超级神冈探测器实验中的几千支易碎的玻璃光电倍增管发生内爆，其中一个探测器的故障造成的冲击波似乎引发了其他探测器的内爆，形成了连锁反应。
在科学实验中，这种效应的另一个例子是2001年用于超级神冈探测器实验中的几千支易碎的玻璃光电倍增管发生内爆，其中一个探测器的故障造成的冲击波似乎引发了其他探测器的内爆，形成了连锁反应。
=== Finance ===
=== 金融 ===
金融
在金融领域，金融机构连锁倒闭的风险被称为系统性风险：一家金融机构的倒闭可能会引起其他金融机构（其交易对手）的倒闭，在整个系统中连锁倒闭。<ref name="HuangVodenska2013">{{cite journal|last1=Huang|first1=Xuqing|last2=Vodenska|first2=Irena|last3=Havlin|first3=Shlomo|last4=Stanley|first4=H. Eugene|title=Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation|journal=Scientific Reports|volume=3|pages=1219|year=2013|issn=2045-2322|doi=10.1038/srep01219|pmid=23386974|pmc=3564037|arxiv=1210.4973|bibcode=2013NatSR...3E1219H}}</ref>
在金融领域，金融机构连锁倒闭的风险被称为系统性风险：一家金融机构的倒闭可能会引起其他金融机构（其交易对手）的倒闭，在整个系统中连锁倒闭。<ref name="HuangVodenska2013">{{cite journal|last1=Huang|first1=Xuqing|last2=Vodenska|first2=Irena|last3=Havlin|first3=Shlomo|last4=Stanley|first4=H. Eugene|title=Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation|journal=Scientific Reports|volume=3|pages=1219|year=2013|issn=2045-2322|doi=10.1038/srep01219|pmid=23386974|pmc=3564037|arxiv=1210.4973|bibcode=2013NatSR...3E1219H}}</ref>
那些被认为构成系统性风险的机构要么被视为“太大而不能倒”(TBTF) ，要么被视为“太相关而不能倒闭”(TICTF) ，这取决于它们为什么会构成威胁。
那些被认为构成系统性风险的机构要么被视为“太大而不能倒”(TBTF) ，要么被视为“太相关而不能倒闭”(TICTF) ，这取决于它们为什么会构成威胁。
但请注意，系统性风险不是由于单个机构本身造成的，而是由于它们相互之间的联系。关于经济学和金融学的详细模型，请参阅艾略特 Elliott等人（2014）和阿西莫格鲁 Acemoglu等人（2015）的文章。<ref name="Acemoglu Ozdaglar Tahbaz-Salehi 2015 pp. 564–608">{{cite journal | last=Acemoglu | first=Daron | last2=Ozdaglar | first2=Asuman | last3=Tahbaz-Salehi | first3=Alireza | title=Systemic Risk and Stability in Financial Networks | journal=American Economic Review | publisher=American Economic Association | volume=105 | issue=2 | year=2015 | issn=0002-8282 | doi=10.1257/aer.20130456 | pages=564–608| hdl=1721.1/100979 | hdl-access=free }}</ref><ref name="Elliott Golub Jackson 2014 pp. 3115–3153">{{cite journal | last=Elliott | first=Matthew | last2=Golub | first2=Benjamin | last3=Jackson | first3=Matthew O. | title=Financial Networks and Contagion | journal=American Economic Review | publisher=American Economic Association | volume=104 | issue=10 | year=2014 | issn=0002-8282 | doi=10.1257/aer.104.10.3115 | pages=3115–3153}}</ref>
但请注意，系统性风险不是由于单个机构本身造成的，而是由于它们相互之间的联系。关于经济学和金融学的详细模型，请参阅艾略特 Elliott等人（2014）和阿西莫格鲁 Acemoglu等人（2015）的文章。<ref name="Acemoglu Ozdaglar Tahbaz-Salehi 2015 pp. 564–608">{{cite journal | last=Acemoglu | first=Daron | last2=Ozdaglar | first2=Asuman | last3=Tahbaz-Salehi | first3=Alireza | title=Systemic Risk and Stability in Financial Networks | journal=American Economic Review | publisher=American Economic Association | volume=105 | issue=2 | year=2015 | issn=0002-8282 | doi=10.1257/aer.20130456 | pages=564–608| hdl=1721.1/100979 | hdl-access=free }}</ref><ref name="Elliott Golub Jackson 2014 pp. 3115–3153">{{cite journal | last=Elliott | first=Matthew | last2=Golub | first2=Benjamin | last3=Jackson | first3=Matthew O. | title=Financial Networks and Contagion | journal=American Economic Review | publisher=American Economic Association | volume=104 | issue=10 | year=2014 | issn=0002-8282 | doi=10.1257/aer.104.10.3115 | pages=3115–3153}}</ref>
金融领域的一种相关的（但不同的）级联失效发生在股票市场，2010年的闪电崩盘就是一个例子。
金融领域的一种相关的（但不同的）级联失效发生在股票市场，2010年的闪电崩盘就是一个例子。
有关研究和预测金融连锁反应影响的另一个框架，请参见<ref>{{cite journal|last1=Li|first1=W|last2=Kenett|first2=DY|last3=Yamasaki|first3=K|last4=Stanley|first4=HE|last5=Havlin|first5=S|title=Ranking the economic importance of countries and industries|journal=Journal of Network Theory in Finance|volume=3|pages=1–17|year=2017|issn=2055-7795|doi=10.21314/JNTF.2017.031|arxiv=1408.0443}}</ref><ref name="HuangVodenska2013"/>
有关研究和预测金融连锁反应影响的另一个框架，请参见<ref>{{cite journal|last1=Li|first1=W|last2=Kenett|first2=DY|last3=Yamasaki|first3=K|last4=Stanley|first4=HE|last5=Havlin|first5=S|title=Ranking the economic importance of countries and industries|journal=Journal of Network Theory in Finance|volume=3|pages=1–17|year=2017|issn=2055-7795|doi=10.21314/JNTF.2017.031|arxiv=1408.0443}}</ref><ref name="HuangVodenska2013"/>
== 相互依赖的级联失效 ==
== Interdependent cascading failures ==
[[File:Interdependent_relationship_among_different_infrastructures.tif|thumb|right|图1: 不同基础设施之间的相互依存关系的说明]]
[[File:Schematic_demonstration_of_first-_and_second-order_percolation_transitions.tif|thumb|right|图2： 一阶和二阶渗流过渡的示意图。在二阶情况下，'''最大连通分支 giant component'''在渗流阈值p=p_c时不断接近零。在一阶情况下，最大连通分支不连续地接近零。]]
[[File:Interdependent_relationship_among_different_infrastructures.tif|thumb|right|Fig. 1: Illustration of the interdependent relationship among different infrastructures]]
[[File:Schematic_demonstration_of_first-_and_second-order_percolation_transitions.tif|thumb|right|Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = p_c. In the first-order case, the giant component approaches zero discontinuously]]
图2： 一阶和二阶渗流过渡的示意图。在二阶情况下，'''<font color="ff8000">最大连通分支giant component</font>'''在渗流阈值p=p_c时不断接近零。在一阶情况下，最大连通分支不连续地接近零。
诸如供水、运输、燃料和发电站等多种基础设施都是耦合在一起的，并相互依赖着运行，见图1。由于这种耦合，相互依存的网络对随机故障，特别是对有针对性的攻击极为敏感，因此，一个网络中一小部分节点的故障就会导致几个相互依存的网络中出现一连串的故障。<ref>{{cite web|title=Report of the Commission to Assess the Threat to the United States from Electromagnetic Pulse (EMP) Attack|url=http://empcommission.org/docs/A2473-EMP_Commission-7MB.pdf}}</ref><ref>{{Cite journal|last=Rinaldi|first=S.M.|last2=Peerenboom|first2=J.P.|last3=Kelly|first3=T.K.|date=2001|title=Identifying, understanding, and analyzing critical infrastructure interdependencies|url=|journal= IEEE Control Systems Magazine|volume=21|pages=11–25|via=}}</ref> 电气停电经常是由相互依赖的网络之间的故障级联造成的，近年来发生的几次大规模停电事件就极大地说明了这个问题。停电是网络之间的依存关系所起的重要作用的一个很好的证明。例如，2003年意大利大停电导致铁路网、医疗系统、金融服务大面积瘫痪，此外，还严重影响了电信网络。通信系统的部分故障又进一步损害了电网管理系统，从而对电网产生了正反馈。<ref>{{cite journal|last=V. Rosato |first=Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S.D., & Setola, R. |title=Modelling interdependent infrastructures using interacting dynamical models |journal=International Journal of Critical Infrastructures |year=2008 |volume=4 |pages=63–79 |doi=10.1504/IJCIS.2008.016092 }}</ref>这个例子强调了在一个相互影响的网络系统中，相互依赖是如何显著放大损害的。基于'''<font color="#ff8000"> 渗流理论 Percolation Theory</font>'''，最近发展了一个研究耦合网络之间级联失效的框架。<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> 与连续崩溃的单一网络的渗流相比，级联失效会导致网络的突然崩溃，见图2。空间嵌入式系统中的级联失效已经被证明会导致系统特别脆弱。<ref name="BashanBerezin2013">{{cite journal|last1=Bashan|first1=Amir|last2=Berezin|first2=Yehiel|last3=Buldyrev|first3=Sergey V.|last4=Havlin|first4=Shlomo|title=The extreme vulnerability of interdependent spatially embedded networks|journal=Nature Physics|year=2013|issn=1745-2473|doi=10.1038/nphys2727|volume=9|issue=10|pages=667–672|arxiv=1206.2062|bibcode=2013NatPh...9..667B}}</ref>关于级联失效的动态过程见参考文献。<ref>{{Cite journal|last=Zhou|first=D.|last2=Bashan|first2=A.|last3=Cohen|first3=R.|last4=Berezin|first4=Y.|last5=Shnerb|first5=N.|last6=Havlin|first6=S.|date=2014|title=Simultaneous first- and second-order percolation transitions in interdependent networks|url=|journal=Phys. Rev. E|volume=90|issue=1|pages=012803|bibcode=2014PhRvE..90a2803Z|doi=10.1103/PhysRevE.90.012803|pmid=25122338|arxiv=1211.2330}}</ref>迪•姆洛 Di Muro等人开发了一个修复故障的模型，以避免级联失效。<ref>{{Cite journal|last=Di Muro|first=M. A.|last2=La Rocca|first2=C. E.|last3=Stanley|first3=H. E.|last4=Havlin|first4=S.|last5=Braunstein|first5=L. A.|date=2016-03-09|title=Recovery of Interdependent Networks|journal=Scientific Reports|language=En|volume=6|issue=1|pages=22834|doi=10.1038/srep22834|pmid=26956773|pmc=4783785|issn=2045-2322|arxiv=1512.02555|bibcode=2016NatSR...622834D}}</ref>
诸如供水、运输、燃料和发电站等多种基础设施都是耦合在一起的，并相互依赖着运行，见图1。由于这种耦合，相互依存的网络对随机故障，特别是对有针对性的攻击极为敏感，因此，一个网络中一小部分节点的故障就会导致几个相互依存的网络中出现一连串的故障。<ref>{{cite web|title=Report of the Commission to Assess the Threat to the United States from Electromagnetic Pulse (EMP) Attack|url=http://empcommission.org/docs/A2473-EMP_Commission-7MB.pdf}}</ref><ref>{{Cite journal|last=Rinaldi|first=S.M.|last2=Peerenboom|first2=J.P.|last3=Kelly|first3=T.K.|date=2001|title=Identifying, understanding, and analyzing critical infrastructure interdependencies|url=|journal= IEEE Control Systems Magazine|volume=21|pages=11–25|via=}}</ref> 电气停电经常是由相互依赖的网络之间的故障级联造成的，近年来发生的几次大规模停电事件就极大地说明了这个问题。停电是网络之间的依存关系所起的重要作用的一个很好的证明。例如，2003年意大利大停电导致铁路网、医疗系统、金融服务大面积瘫痪，此外，还严重影响了电信网络。通信系统的部分故障又进一步损害了电网管理系统，从而对电网产生了正反馈。<ref>{{cite journal|last=V. Rosato |first=Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S.D., & Setola, R. |title=Modelling interdependent infrastructures using interacting dynamical models |journal=International Journal of Critical Infrastructures |year=2008 |volume=4 |pages=63–79 |doi=10.1504/IJCIS.2008.016092 }}</ref>这个例子强调了在一个相互影响的网络系统中，相互依赖是如何显著放大损害的。基于'''<font color="#ff8000"> 渗流理论 Percolation Theory</font>'''，最近发展了一个研究耦合网络之间级联失效的框架。<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> 与连续崩溃的单一网络的渗流相比，级联失效会导致网络的突然崩溃，见图2。空间嵌入式系统中的级联失效已经被证明会导致系统特别脆弱。<ref name="BashanBerezin2013">{{cite journal|last1=Bashan|first1=Amir|last2=Berezin|first2=Yehiel|last3=Buldyrev|first3=Sergey V.|last4=Havlin|first4=Shlomo|title=The extreme vulnerability of interdependent spatially embedded networks|journal=Nature Physics|year=2013|issn=1745-2473|doi=10.1038/nphys2727|volume=9|issue=10|pages=667–672|arxiv=1206.2062|bibcode=2013NatPh...9..667B}}</ref>关于级联失效的动态过程见参考文献。<ref>{{Cite journal|last=Zhou|first=D.|last2=Bashan|first2=A.|last3=Cohen|first3=R.|last4=Berezin|first4=Y.|last5=Shnerb|first5=N.|last6=Havlin|first6=S.|date=2014|title=Simultaneous first- and second-order percolation transitions in interdependent networks|url=|journal=Phys. Rev. E|volume=90|issue=1|pages=012803|bibcode=2014PhRvE..90a2803Z|doi=10.1103/PhysRevE.90.012803|pmid=25122338|arxiv=1211.2330}}</ref>迪•姆洛 Di Muro等人开发了一个修复故障的模型，以避免级联失效。<ref>{{Cite journal|last=Di Muro|first=M. A.|last2=La Rocca|first2=C. E.|last3=Stanley|first3=H. E.|last4=Havlin|first4=S.|last5=Braunstein|first5=L. A.|date=2016-03-09|title=Recovery of Interdependent Networks|journal=Scientific Reports|language=En|volume=6|issue=1|pages=22834|doi=10.1038/srep22834|pmid=26956773|pmc=4783785|issn=2045-2322|arxiv=1512.02555|bibcode=2016NatSR...622834D}}</ref>
此外，研究表明，当这种系统嵌入空间时，极易受到局部攻击或故障的影响。超过临界损伤半径，故障可能扩散到整个系统。<ref>{{Cite journal|last=Berezin|first=Yehiel|last2=Bashan|first2=Amir|last3=Danziger|first3=Michael M.|last4=Li|first4=Daqing|last5=Havlin|first5=Shlomo|date=2015-03-11|title=Localized attacks on spatially embedded networks with dependencies|journal=Scientific Reports|language=en|volume=5|issue=1|pages=8934|doi=10.1038/srep08934|pmid=25757572|pmc=4355725|issn=2045-2322|bibcode=2015NatSR...5E8934B}}</ref>
此外，研究表明，当这种系统嵌入空间时，极易受到局部攻击或故障的影响。超过临界损伤半径，故障可能扩散到整个系统。<ref>{{Cite journal|last=Berezin|first=Yehiel|last2=Bashan|first2=Amir|last3=Danziger|first3=Michael M.|last4=Li|first4=Daqing|last5=Havlin|first5=Shlomo|date=2015-03-11|title=Localized attacks on spatially embedded networks with dependencies|journal=Scientific Reports|language=en|volume=5|issue=1|pages=8934|doi=10.1038/srep08934|pmid=25757572|pmc=4355725|issn=2045-2322|bibcode=2015NatSR...5E8934B}}</ref>
== 过载级联失效模型 ==
过载传播导致的级联失效的模型是Motter-Lai模型。<ref>{{Cite journal|last=Motter|first=A. E.|last2=Lai|first2=Y. C.|date=2002|title=Cascade-based attacks on complex networks|url=|journal=Phys. Rev. E|volume=66|issue=6 Pt 2|pages=065102|doi=10.1103/PhysRevE.66.065102|pmid=12513335|bibcode=2002PhRvE..66f5102M|arxiv=cond-mat/0301086}}</ref>赵继昌 Jichang Zhao等人对这种故障的时空传播进行了研究。<ref>{{Cite journal|last=Zhao|first=J.|last2=Li|first2=D.|last3=Sanhedrai|first3=H.|last4=Cohen|first4=R.|last5=Havlin|first5=S.|date=2016|title=Spatio-temporal propagation of cascading overload failures in spatially embedded networks|url=|journal=Nature Communications|volume=7|pages=10094|bibcode=2016NatCo...710094Z|doi=10.1038/ncomms10094|pmid=26754065|pmc=4729926}}</ref>
随着网络科学的研究进展，复杂网络特别是相互依存的网络就可以帮助我们认识不同经济金融子系统之间的相互连接方式，并可以设计不同的级联失效机制展示风险、破产等失败事件的传播过程。本课程中，将从经济金融系统的网络建模出发，讨论如何设计级联失效机制，并介绍相关最新研究成果。
随着网络科学的研究进展，复杂网络特别是相互依存的网络就可以帮助我们认识不同经济金融子系统之间的相互连接方式，并可以设计不同的级联失效机制展示风险、破产等失败事件的传播过程。本课程中，将从经济金融系统的网络建模出发，讨论如何设计级联失效机制，并介绍相关最新研究成果。