(劳伦斯柏克莱国家实验室2011)PerformanceandDegradationModelingofBatteries

A review of advanced and practical lithium battery materialsRotem Marom,*S.Francis Amalraj,Nicole Leifer,David Jacob and Doron AurbachReceived 3rd December 2010,Accepted 31st January 2011DOI:10.1039/c0jm04225kPresented herein is a discussion of the forefront in research and development of advanced electrode materials and electrolyte solutions for the next generation of lithium ion batteries.The main challenge of the field today is in meeting the demands necessary to make the electric vehicle fully commercially viable.This requires high energy and power densities with no compromise in safety.Three families of advanced cathode materials (the limiting factor for energy density in the Li battery systems)are discussed in detail:LiMn 1.5Ni 0.5O 4high voltage spinel compounds,Li 2MnO 3–LiMO 2high capacity composite layered compounds,and LiMPO 4,where M ¼Fe,Mn.Graphite,Si,Li x TO y ,and MO (conversion reactions)are discussed as anode materials.The electrolyte is a key component that determines the ability to use high voltage cathodes and low voltage anodes in the same system.Electrode–solution interactions and passivation phenomena on both electrodes in Li-ion batteries also play significant roles in determining stability,cycle life and safety features.This presentation is aimed at providing an overall picture of the road map necessary for the future development of advanced high energy density Li-ion batteries for EV applications.IntroductionOne of the greatest challenges of modern society is to stabilize a consistent energy supply that will meet our growing energy demands.A consideration of the facts at hand related to the energy sources on earth reveals that we are not encountering an energy crisis related to a shortage in total resources.For instancethe earth’s crust contains enough coal for the production of electricity for hundreds of years.1However the continued unbridled usage of this resource as it is currently employed may potentially bring about catastrophic climatological effects.As far as the availability of crude oil,however,it in fact appears that we are already beyond ‘peak’production.2As a result,increasing oil shortages in the near future seem inevitable.Therefore it is of critical importance to considerably decrease our use of oil for propulsion by developing effective electric vehicles (EVs).EV applications require high energy density energy storage devices that can enable a reasonable driving range betweenDepartment of Chemistry,Bar-Ilan University,Ramat-Gan,52900,Israel;Web:http://www.ch.biu.ac.il/people/aurbach.E-mail:rotem.marom@live.biu.ac.il;aurbach@mail.biu.ac.ilRotem MaromRotem Marom received her BS degree in organic chemistry (2005)and MS degree in poly-mer chemistry (2007)from Bar-Ilan University,Ramat Gan,Israel.She started a PhD in electrochemistry under the supervision of Prof.D.Aurbach in 2010.She is currently con-ducting research on a variety of lithium ion battery materials for electric vehicles,with a focus on electrolyte solutions,salts andadditives.S :Francis AmalrajFrancis Amalraj hails from Tamil Nadu,India.He received his MSc in Applied Chemistry from Anna University.He then carried out his doctoral studies at National Chemical Laboratory,Pune and obtained his PhD in Chemistry from Pune University (2008).He is currently a postdoctoral fellow in Prof.Doron Aurbach’s group at Bar-Ilan University,Israel.His current research interest focuses on the synthesis,electrochemical and transport properties of high ener-getic electrode materials for energy conversion and storage systems.Dynamic Article Links CJournal ofMaterials ChemistryCite this:DOI:10.1039/c0jm04225k /materialsFEATURE ARTICLED o w n l o a d e d b y B e i j i n g U n i v e r s i t y o f C h e m i c a l T e c h n o l o g y o n 24 F e b r u a r y 2011P u b l i s h e d o n 23 F e b r u a r y 2011 o n h t t p ://p u b s .r s c .o r g | d o i :10.1039/C 0J M 04225KView Onlinecharges and maintain acceptable speeds.3Other important requirements are high power density and acceptable safety features.The energy storage field faces a second critical chal-lenge:namely,the development of rechargeable systems for load leveling applications (e.g.storing solar and wind energy,and reducing the massive wasted electricity from conventional fossil fuel combustion plants).4Here the main requirements are a very prolonged cycle life,components (i.e.,relevant elements)abun-dant in high quantities in the earth’s crust,and environmentally friendly systems.Since it is not clear whether Li-ion battery technology can contribute significantly to this application,battery-centered solutions for this application are not discussedherein.In fact,even for electrical propulsion,the non-petroleum power source with the highest energy density is the H 2/O 2fuel cell (FC).5However,despite impressive developments in recent years in the field,there are intrinsic problems related to electrocatalysis in the FCs and the storage of hydrogen 6that will need many years of R&D to solve.Hence,for the foreseeable future,rechargeable batteries appear to be the most practically viable power source for EVs.Among the available battery technologies to date,only Li-ion batteries may possess the power and energy densities necessary for EV applications.The commonly used Li-ion batteries that power almost all portable electronic equipment today are comprised of a graphite anode and a LiCoO 2cathode (3.6V system)and can reach a practical energy density of 150W h kg À1in single cells.This battery technology is not very useful for EV application due to its limited cycle life (especially at elevated temperatures)and prob-lematic safety features (especially for large,multi-cell modules).7While there are ongoing developments in the hybrid EV field,including practical ones in which only part of the propulsion of the car is driven by an electrical motor and batteries,8the main goal of the battery community is to be able to develop full EV applications.This necessitates the development of Li-ion batteries with much higher energy densities compared to the practical state-of-the-art.The biggest challenge is that Li-ion batteries are complicated devices whose components never reach thermodynamic stability.The surface chemistry that occurs within these systems is very complicated,as described briefly below,and continues to be the main factor that determines their performance.9Nicole Leifer Nicole Leifer received a BS degree in chemistry from MIT in 1998.After teaching high school chemistry and physics for several years at Stuyvesant High School in New York City,she began work towards her PhD in solid state physics from the City University of New York Grad-uate Center.Her research con-sisted primarily of employing solid state NMR in the study of lithium ion electrode materialsand electrode surfacephenomena with Prof.Green-baum at Hunter College andProf.Grey at Stony Brook University.After completing her PhD she joined Prof.Doron Aurbach for a postdoctorate at Bar-Ilan University to continue work in lithium ion battery research.There she continues her work in using NMR to study lithium materials in addition to new forays into carbon materials’research for super-capacitor applications with a focus on enhancement of electro-chemical performance through the incorporation of carbonnanotubes.David Jacob David Jacob earned a BSc from Amravati University in 1998,an MSc from Pune University in 2000,and completed his PhD at Bar-Ilan University in 2007under the tutelage of Professor Aharon Gedanken.As part of his PhD research,he developed novel methods of synthesizing metal fluoride nano-material structures in ionic liquids.Upon finishing his PhD he joined Prof.Doron Aurbach’s lithium ionbattery group at Bar-Ilan in2007as a post-doctorate and during that time developed newformulations of electrolyte solutions for Li-ion batteries.He has a great interest in nanotechnology and as of 2011,has become the CEO of IsraZion Ltd.,a company dedicated to the manufacturing of novelnano-materials.Doron Aurbach Dr Doron Aurbach is a full Professor in the Department of Chemistry at Bar-Ilan Univer-sity (BIU)in Ramat Gan,Israel and a senate member at BIU since 1996.He chaired the chemistry department there during the years 2001–2005.He is also the chairman of the Israeli Labs Accreditation Authority.He founded the elec-trochemistry group at BIU at the end of 1985.His groupconducts research in thefollowing fields:Li ion batteries for electric vehicles and for otherportable uses (new cathodes,anodes,electrolyte solutions,elec-trodes–solution interactions,practical systems),rechargeable magnesium batteries,electronically conducting polymers,super-capacitors,engineering of new carbonaceous materials,develop-ment of devices for storage and conversion of sustainable energy (solar,wind)sensors and water desalination.The group currently collaborates with several prominent research groups in Europe and the US and with several commercial companies in Israel and abroad.He is also a fellow of the ECS and ISE as well as an associate editor of Electrochemical and Solid State Letters and the Journal of Solid State Electrochemistry.Prof.Aurbach has more than 350journals publications.D o w n l o a d e d b y B e i j i n g U n i v e r s i t y o f C h e m i c a l T e c h n o l o g y o n 24 F e b r u a r y 2011P u b l i s h e d o n 23 F e b r u a r y 2011 o n h t t p ://p u b s .r s c .o r g | d o i :10.1039/C 0J M 04225KAll electrodes,excluding 1.5V systems such as LiTiO x anodes,are surface-film controlled (SFC)systems.At the anode side,all conventional electrolyte systems can be reduced in the presence of Li ions below 1.5V,thus forming insoluble Li-ion salts that comprise a passivating surface layer of particles referred to as the solid electrolyte interphase (SEI).10The cathode side is less trivial.Alkyl carbonates can be oxidized at potentials below 4V.11These reactions are inhibited on the passivated aluminium current collectors (Al CC)and on the composite cathodes.There is a rich surface chemistry on the cathode surface as well.In their lithiated state,nucleophilic oxygen anions in the surface layer of the cathode particles attack electrophilic RO(CO)OR solvents,forming different combinations of surface components (e.g.ROCO 2Li,ROCO 2M,ROLi,ROM etc.)depending on the electrolytes used.12The polymerization of solvent molecules such as EC by cationic stimulation results in the formation of poly-carbonates.13The dissolution of transition metal cations forms surface inactive Li x MO y phases.14Their precipitation on the anode side destroys the passivation of the negative electrodes.15Red-ox reactions with solution species form inactive LiMO y with the transition metal M at a lower oxidation state.14LiMO y compounds are spontaneously delithiated in air due to reactions with CO 2.16Acid–base reactions occur in the LiPF 6solutions (trace HF,water)that are commonly used in Li-ion batteries.Finally,LiCoO 2itself has a rich surface chemistry that influences its performance:4LiCo III O 2 !Co IV O 2þCo II Co III 2O 4þ2Li 2O !4HF4LiF þ2H 2O Co III compounds oxidize alkyl carbonates;CO 2is one of the products,Co III /Co II /Co 2+dissolution.14Interestingly,this process seems to be self-limiting,as the presence of Co 2+ions in solution itself stabilizes the LiCoO 2electrodes,17However,Co metal in turn appears to deposit on the negative electrodes,destroying their passivation.Hence the performance of many types of electrodes depends on their surface chemistry.Unfortunately surface studies provide more ambiguous results than bulk studies,therefore there are still many open questions related to the surface chemistry of Li-ion battery systems.It is for these reasons that proper R&D of advanced materials for Li-ion batteries has to include bulk structural and perfor-mance studies,electrode–solution interactions,and possible reflections between the anode and cathode.These studies require the use of the most advanced electrochemical,18structural (XRD,HR microscopy),spectroscopic and surface sensitive analytical techniques (SS NMR,19FTIR,20XPS,21Raman,22X-ray based spectroscopies 23).This presentation provides a review of the forefront of the study of advanced materials—electrolyte systems,current collectors,anode materials,and finally advanced cathodes materials used in Li-ion batteries,with the emphasis on contributions from the authors’group.ExperimentalMany of the materials reviewed were studied in this laboratory,therefore the experimental details have been provided as follows.The LiMO 2compounds studied were prepared via self-combus-tion reactions (SCRs).24Li[MnNiCo]O 2and Li 2MnO 3$Li/MnNiCo]O 2materials were produced in nano-andsubmicrometric particles both produced by SCR with different annealing stages (700 C for 1hour in air,900 C or 1000 C for 22hours in air,respectively).LiMn 1.5Ni 0.5O 4spinel particles were also synthesized using SCR.Li 4T 5O 12nanoparticles were obtained from NEI Inc.,USA.Graphitic material was obtained from Superior Graphite (USA),Timcal (Switzerland),and Conoco-Philips.LiMn 0.8Fe 0.2PO 4was obtained from HPL Switzerland.Standard electrolyte solutions (alkyl carbonates/LiPF 6),ready to use,were obtained from UBE,Japan.Ionic liquids were obtained from Merck KGaA (Germany and Toyo Gosie Ltd.,(Japan)).The surface chemistry of the various electrodes was charac-terized by the following techniques:Fourier transform infrared (FTIR)spectroscopy using a Magna 860Spectrometer from Nicolet Inc.,placed in a homemade glove box purged with H 2O and CO 2(Balson Inc.air purification system)and carried out in diffuse reflectance mode;high-resolution transmission electron microscopy (HR-TEM)and scanning electron microscopy (SEM),using a JEOL-JEM-2011(200kV)and JEOL-JSM-7000F electron microscopes,respectively,both equipped with an energy dispersive X-ray microanalysis system from Oxford Inc.;X-ray photoelectron spectroscopy (XPS)using an HX Axis spectrom-eter from Kratos,Inc.(England)with monochromic Al K a (1486.6eV)X-ray beam radiation;solid state 7Li magic angle spinning (MAS)NMR performed at 194.34MHz on a Bruker Avance 500MHz spectrometer in 3.2mm rotors at spinning speeds of 18–22kHz;single pulse and rotor synchronized Hahn echo sequences were used,and the spectra were referenced to 1M LiCl at 0ppm;MicroRaman spectroscopy with a spectrometerfrom Jobin-Yvon Inc.,France.We also used M €ossbauer spec-troscopy for studying the stability of LiMPO 4compounds (conventional constant-acceleration spectrometer,room temperature,50mC:57Co:Rh source,the absorbers were put in Perspex holders.In situ AFM measurements were carried out using the system described in ref.25.The following electrochemical measurements were posite electrodes were prepared by spreading slurries comprising the active mass,carbon powder and poly-vinylidene difluoride (PVdF)binder (ratio of 75%:15%:10%by weight,mixed into N -methyl pyrrolidone (NMP),and deposited onto aluminium foil current collectors,followed by drying in a vacuum oven.The average load was around 2.5mg active mass per cm 2.These electrodes were tested in two-electrode,coin-type cells (Model 2032from NRC Canada)with Li foil serving as the counter electrode,and various electrolyte puter-ized multi-channel battery analyzers from Maccor Inc.(USA)and Arbin Inc.were used for galvanostatic measurements (voltage vs.time/capacity,measured at constant currents).Results and discussionOur road map for materials developmentFig.1indicates a suggested road map for the direction of Li-ion research.The axes are voltage and capacity,and a variety of electrode materials are marked therein according to their respective values.As is clear,the main limiting factor is the cathode material (in voltage and capacity).The electrode mate-rials currently used in today’s practical batteries allow forD o w n l o a d e d b y B e i j i n g U n i v e r s i t y o f C h e m i c a l T e c h n o l o g y o n 24 F e b r u a r y 2011P u b l i s h e d o n 23 F e b r u a r y 2011 o n h t t p ://p u b s .r s c .o r g | d o i :10.1039/C 0J M 04225Ka nominal voltage of below 4V.The lower limit of the electro-chemical window of the currently used electrolyte solutions (alkyl carbonates/LiPF 6)is approximately 1.5V vs.Li 26(see later discussion about the passivation phenomena that allow for the operation of lower voltage electrodes,such as Li and Li–graphite).The anodic limit of the electrochemical window of the alkyl carbonate/LiPF 6solutions has not been specifically determined but practical accepted values are between 4.2and 5V vs.Li 26(see further discussion).With some systems which will be discussed later,meta-stability up to 4.9V can be achieved in these standard electrolyte solutions.Electrolyte solutionsThe anodic stability limits of electrolyte solutions for Li-ion batteries (and those of polar aprotic solutions in general)demand ongoing research in this subfield as well.It is hard to define the onset of oxidation reactions of nonaqueous electrolyte solutions because these strongly depend on the level of purity,the presence of contaminants,and the types of electrodes used.Alkyl carbonates are still the solutions of choice with little competition (except by ionic liquids,as discussed below)because of the high oxidation state of their central carbon (+4).Within this class of compounds EC and DMC have the highest anodic stability,due to their small alkyl groups.An additional benefit is that,as discussed above,all kinds of negative electrodes,Li,Li–graphite,Li–Si,etc.,develop excellent passivation in these solutions at low potentials.The potentiodynamic behavior of polar aprotic solutions based on alkyl carbonates and inert electrodes (Pt,glassy carbon,Au)shows an impressive anodic stability and an irreversible cathodic wave whose onset is $1.5vs.Li,which does not appear in consequent cycles due to passivation of the anode surface bythe SEI.The onset of these oxidation reactions is not well defined (>4/5V vs.Li).An important discovery was the fact that in the presence of Li salts,EC,one of the most reactive alkyl carbonates (in terms of reduction),forms a variety of semi-organic Li-con-taining salts that serve as passivation agents on Li,Li–carbon,Li–Si,and inert metal electrodes polarized to low potentials.Fig.2and Scheme 1indicates the most significant reduction schemes for EC,as elucidated through spectroscopic measure-ments (FTIR,XPS,NMR,Raman).27–29It is important to note (as reflected in Scheme 1)that the nature of the Li salts present greatly affects the electrode surface chemistry.When the pres-ence of the salt does not induce the formation of acidic species in solutions (e.g.,LiClO 4,LiN(SO 2CF 3)2),alkyl carbonates are reduced to ROCO 2Li and ROLi compounds,as presented in Fig. 2.In LiPF 6solutions acidic species are formed:LiPF 6decomposes thermally to LiF and PF 5.The latter moiety is a Lewis acid which further reacts with any protic contaminants (e.g.unavoidably present traces of water)to form HF.The presence of such acidic species in solution strongly affects the surface chemistry in two ways.One way is that PF 5interactswithFig.1The road map for R&D of new electrode materials,compared to today’s state-of-the-art.The y and x axes are voltage and specific capacity,respectively.Fig.2A schematic presentation of the CV behavior of inert (Pt)elec-trodes in various families of polar aprotic solvents with Li salts.26D o w n l o a d e d b y B e i j i n g U n i v e r s i t y o f C h e m i c a l T e c h n o l o g y o n 24 F e b r u a r y 2011P u b l i s h e d o n 23 F e b r u a r y 2011 o n h t t p ://p u b s .r s c .o r g | d o i :10.1039/C 0J M 04225Kthe carbonyl group and channels the reduction process of EC to form ethylene di-alkoxide species along with more complicated alkoxy compounds such as binary and tertiary ethers,rather than Li-ethylene dicarbonates (see schemes in Fig.2);the other way is that HF reacts with ROLi and ROCO 2Li to form ROH,ROCO 2H (which further decomposes to ROH and CO 2),and surface LiF.Other species formed from the reduction of EC are Li-oxalate and moieties with Li–C and C–F bonds (see Scheme 1).27–31Efforts have been made to enhance the formation of the passivation layer (on graphite electrodes in particular)in the presence of these solutions through the use of surface-active additives such as vinylene carbonate (VC)and lithium bi-oxalato borate (LiBOB).27At this point there are hundreds of publica-tions and patents on various passivating agents,particularly for graphite electrodes;their further discussion is beyond the scope of this paper.Readers may instead be referred to the excellent review by Xu 32on this subject.Ionic liquids (ILs)have excellent qualities that could render them very relevant for use in advanced Li-ion batteries,including high anodic stability,low volatility and low flammability.Their main drawbacks are their high viscosities,problems in wetting particle pores in composite structures,and low ionic conductivity at low temperatures.Recent years have seen increasing efforts to test ILs as solvents or additives in Li-ion battery systems.33Fig.3shows the cyclic voltammetric response (Pt working electrodes)of imidazolium-,piperidinium-,and pyrrolidinium-based ILs with N(SO 2CF 3)2Àanions containing LiN(SO 2CF 3)2salt.34This figure reflects the very wide electrochemical window and impressive anodic stability (>5V)of piperidium-and pyr-rolidium-based ILs.Imidazolium-based IL solutions have a much lower cathodic stability than the above cyclic quaternary ammonium cation-based IL solutions,as demonstrated in Fig.3.The cyclic voltammograms of several common electrode mate-rials measured in IL-based solutions are also included in the figure.It is clearly demonstrated that the Li,Li–Si,LiCoO 2,andLiMn 1.5Ni 0.5O 4electrodes behave reversibly in piperidium-and pyrrolidium-based ILs with N(SO 2CF 3)2Àand LiN(SO 2CF 3)2salts.This figure demonstrates the main advantage of the above IL systems:namely,the wide electrochemical window with exceptionally high anodic stability.It was demonstrated that aluminium electrodes are fully passivated in solutions based on derivatives of pyrrolidium with a N(SO 2CF 3)2Àanion and LiN(SO 2CF 3)2.35Hence,in contrast to alkyl carbonate-based solutions in which LiN(SO 2CF 3)2has limited usefulness as a salt due to the poor passivation of aluminium in its solutions in the above IL-based systems,the use of N(SO 2CF 3)2Àas the anion doesn’t limit their anodic stability at all.In fact it was possible to demonstrate prototype graphite/LiMn 1.5Ni 0.5O 4and Li/L-iMn 1.5Ni 0.5O 4cells operating even at 60 C insolutionsScheme 1A reaction scheme for all possible reduction paths of EC that form passivating surface species (detected by FTIR,XPS,Raman,and SSNMR 28–31,49).Fig.3Steady-state CV response of a Pt electrode in three IL solutions,as indicated.(See structure formulae presented therein.)The CV presentations include insets of steady-state CVs of four electrodes,as indicated:Li,Li–Si,LiCoO 2,and LiMn 1.5Ni 0.5O 4.34D o w n l o a d e d b y B e i j i n g U n i v e r s i t y o f C h e m i c a l T e c h n o l o g y o n 24 F e b r u a r y 2011P u b l i s h e d o n 23 F e b r u a r y 2011 o n h t t p ://p u b s .r s c .o r g | d o i :10.1039/C 0J M 04225Kcomprising alkyl piperidium-N(SO2CF3)2as the IL solvent and Li(SO2CF3)2as the electrolyte.34Challenges remain in as far as the use of these IL-based solutions with graphite electrodes.22Fig.4shows the typical steady state of the CV of graphite electrodes in the IL without Li salts.The response in this graph reflects the reversible behavior of these electrodes which involves the insertion of the IL cations into the graphite lattice and their subsequent reduction at very low potentials.However when the IL contains Li salt,the nature of the reduction processes drastically changes.It was recently found that in the presence of Li ions the N(SO2CF3)2Àanion is reduced to insoluble ionic compounds such as LiF,LiCF3, LiSO2CF3,Li2S2O4etc.,which passivate graphite electrodes to different extents,depending on their morphology(Fig.4).22 Fig.4b shows a typical SEM image of a natural graphite(NG) particle with a schematic view of its edge planes.Fig.4c shows thefirst CVs of composite electrodes comprising NG particles in the Li(SO2CF3)2/IL solution.These voltammograms reflect an irreversible cathodic wave at thefirst cycle that belongs to the reduction and passivation processes and their highly reversible repeated Li insertion into the electrodes comprising NG. Reversible capacities close to the theoretical ones have been measured.Fig.4d and e reflect the structure and behavior of synthetic graphiteflakes.The edge planes of these particles are assumed to be much rougher than those of the NG particles,and so their passivation in the same IL solutions is not reached easily. Their voltammetric response reflects the co-insertion of the IL cations(peaks at0.5V vs.Li)together with Li insertion at the lower potentials(<0.3V vs.Li).Passivation of this type of graphite is obtained gradually upon repeated cycling(Fig.4e), and the steady-state capacity that can be obtained is much lower than the theoretical one(372mA h gÀ1).Hence it seems that using graphite particles with suitable morphologies can enable their highly reversible and stable operation in cyclic ammonium-based ILs.This would make it possible to operate high voltage Li-ion batteries even at elevated temperatures(e.g. 4.7–4.8V graphite/LiMn1.5Ni0.5O4cells).34 The main challenge in thisfield is to demonstrate the reasonable performance of cells with IL-based electrolytes at high rates and low temperatures.To this end,the use of different blends of ILs may lead to future breakthroughs.Current collectorsThe current collectors used in Li-ion systems for the cathodes can also affect the anodic stability of the electrolyte solutions.Many common metals will dissolve in aprotic solutions in the potential ranges used with advanced cathode materials(up to5V vs.Li). Inert metals such as Pt and Au are also irrelevant due to cost considerations.Aluminium,however,is both abundantand Fig.4A collection of data related to the behavior of graphite electrodes in butyl,methyl piperidinium IL solutions.22(a)The behavior of natural graphite electrodes in pure IL without Li salt(steady-state CV is presented).(b)The schematic morphology and a SEM image of natural graphite(NG)flakes.(c)The CV response(3first consecutive cycles)of NG electrodes in IL/0.5lithium trifluoromethanesulfonimide(LiTFSI)solution.(d and e)Same as(b and c)but for synthetic graphiteflakes.DownloadedbyBeijingUniversityofChemicalTechnologyon24February211Publishedon23February211onhttp://pubs.rsc.org|doi:1.139/CJM4225Kcheap and functions very well as a current collector due to its excellent passivation properties which allow it a high anodic stability.The question remains as to what extent Al surfaces can maintain the stability required for advanced cathode materials (up to 5V vs.Li),especially at elevated temperatures.Fig.5presents the potentiodynamic response of Al electrodes in various EC–DMC solutions,considered the alkyl carbonate solvent mixture with the highest anodic stability,at 30and 60 C.37The inset to this picture shows several images in which it is demonstrated that Al surfaces are indeed active and develop unique morphologies in the various solutions due to their obvious anodic processes in solutions,some of which lead to their effective passivation.The electrolyte used has a critical impact on the anodic stability of the Al.In general,LiPF 6solutions demonstrate the highest stability even at elevated temperatures due to the formation of surface AlF 3and even Al(PF 6)3.Al CCs in EC–DMC/LiPF 6solutions provide the highest anodic stability possible for conventional electrode/solution systems.This was demonstrated for Li/LiMn 1.5Ni 0.5O 4spinel (4.8V)cells,even at 60 C.36This was also confirmed using bare Al electrodes polarized up to 5V at 60 C;the anodic currents were seen to decay to negligible values due to passivation,mostly by surface AlF 3.37Passivation can also be reached in Li(SO 2CF 3),LiClO 4and LiBOB solutions (Fig.5).Above 4V (vs.Li),the formation of a successful passivation layer on Al CCs is highly dependent on the electrolyte formula used.The anodic stability of EC–DMC/LiPF 6solutions and Al current collectors may be further enhanced by the use of additives,but a review of additives in itself deserves an article of its own and for this readers are again referred to the review by Xu.32When discussing the topic of current collectors for Li ion battery electrodes,it is important to note the highly innovative work on (particularly anodic)current collectors by Taberna et al.on nano-architectured Cu CCs 47and Hu et al.who assembled CCs based on carbon nano-tubes for flexible paper-like batteries,38both of whom demonstrated suberb rate capabilities.39AnodesThe anode section in Fig.1indicates four of the most promising groups of materials whose Li-ion chemistry is elaborated as follows:1.Carbonaceous materials/graphite:Li ++e À+C 6#LiC 62.Sn and Si-based alloys and composites:40,41Si(Sn)+x Li ++x e À#Li x Si(Sn),X max ¼4.4.3.Metal oxides (i.e.conversion reactions):nano-MO +2Li ++2e À#nano-MO +Li 2O(in a composite structure).424.Li x TiO y electrodes (most importantly,the Li 4Ti 5O 12spinel structure).43Li 4Ti 5O 12+x Li ++x e À#Li 4+x Ti 5O 12(where x is between 2and 3).Conversion reactions,while they demonstrate capacities much higher than that of graphite,are,practically speaking,not very well-suited for use as anodes in Li-ion batteries as they generally take place below the thermodynamic limit of most developed electrolyte solutions.42In addition,as the reactions require a nanostructuring of the materials,their stability at elevated temperatures will necessarily be an issue because of the higher reactivity (due to the 1000-fold increase in surface area).As per the published research on this topic,only a limited meta-stability has been demonstrated.Practically speaking,it does not seem likely that Li batteries comprising nano-MO anodes will ever reach the prolonged cycle life and stability required for EV applications.Tin and silicon behave similarly upon alloying with Li,with similar stoichiometries and >300%volume changes upon lith-iation,44but the latter remain more popular,as Si is much more abundant than Sn,and Li–Si electrodes indicate a 4-fold higher capacity.The main approaches for attaining a workable revers-ibility in the Si(Sn)–Li alloying reactions have been through the use of both nanoparticles (e.g.,a Si–C nanocomposites 45)and composite structures (Si/Sn–M1–M2inter-metalliccompounds 44),both of which can better accommodate these huge volume changes.The type of binder used in composite electrodes containing Si particles is very important.Extensive work has been conducted to determine suitable binders for these systems that can improve the stability and cycle life of composite silicon electrodes.46As the practical usage of these systems for EV applications is far from maturity,these electrodes are not dis-cussed in depth in this paper.However it is important to note that there have been several recent demonstrations of how silica wires and carpets of Si nano-rods can act as much improved anode materials for Li battery systems in that they can serveasFig.5The potentiodynamic behavior of Al electrodes (current density measured vs.E during linear potential scanning)in various solutions at 30and 60 C,as indicated.The inset shows SEM micrographs of passivated Al surfaces by the anodic polarization to 5V in the solutions indicated therein.37D o w n l o a d e d b y B e i j i n g U n i v e r s i t y o f C h e m i c a l T e c h n o l o g y o n 24 F e b r u a r y 2011P u b l i s h e d o n 23 F e b r u a r y 2011 o n h t t p ://p u b s .r s c .o r g | d o i :10.1039/C 0J M 04225K。

劳伦斯伯克利国家实验室(Lawrence BerkeleyNational Laboratory)联系方式：网址：电话：510-486-4000简介：Berkeley Lab is a multidisciplinary national laboratory located in Berkeley, California on a hillside directly above the campus of the University of California at Berkeley. The site consists of 76 buildings located on 183 acres, which overlook both the campus and the San Francisco Bay. The Lab, which conducts unclassified research, employs about 4,300 people, including nearly 1,000 staff scientists, 1,000 undergraduate, graduate students and postdoctoral fellows, and more than 1,500 technical and support personnel. In addition, each year the Lab hosts more than 2,000 participating guests.美国很多著名大学都为政府代管国家实验室，这些实验室的名字也就和大学连在一起了。

最著名的如。

劳伦斯伯克利国家实验室位于美国加州大学伯克利分校，占地81公顷，毗邻旧金山湾。

它隶属于美国能源部，由伯克利代管。

劳伦斯伯克利实验室是1939年诺贝尔物理学奖得主欧内斯特.奥兰多.伯克利先生建立的，早期关注于高能物理领域的研究。

利用可调谐纳米尺度激光器探测细胞特性作者：HassaunA.Jones-Bey美国劳伦斯伯克利国家实验室和加州大学伯克利分校的研究人员发明了一种纳米尺度生物光源，该光源在整个可见光谱区域能够发射可调谐激光。

该项发明最终将有可能推动亚波长光学的发展。

亚波长激光器在物理、信息、生物科学等领域具有广泛应用，并且具有室温运行稳定，以及与细胞层次的液体环境相容的特性。

[1]研究人员PeidongYang表示：“这项发明借鉴了劳伦斯伯克利国家实验室以前的成果：在空气和无源亚波作者：Hassaun A. Jones-Bey美国劳伦斯伯克利国家实验室和加州大学伯克利分校的研究人员发明了一种纳米尺度生物光源，该光源在整个可见光谱区域能够发射可调谐激光。

该项发明最终将有可能推动亚波长光学的发展。

亚波长激光器在物理、信息、生物科学等领域具有广泛应用，并且具有室温运行稳定，以及与细胞层次的液体环境相容的特性。

[1]研究人员Peidong Yang表示：“这项发明借鉴了劳伦斯伯克利国家实验室以前的成果：在空气和无源亚波长波导中实现纳米尺寸光源。

” 该项发明的创新之处在于在铌酸钾纳线上实现了非线性光学转换。

铌酸钾具有毒性低、化学稳定性好、室温下有效非线性系数大和折射率高等特性，并且它在较宽的波段（包括可见光波段）内都是透明的。

纳线先在一个热水溶液中合成，然后采用超声分离。

红外激光辐射用于控制单个纳线，同时作为泵浦光，通过谐波产生和波混频，使纳线发射可调谐可见激光。

研究人员使用纳米尺度光源在液体中进行光学成像以及近场扫描，获得了高达200nm的分辨率。

荧光当纳线光源与荧光微球接触时可以产生荧光，其发光机理为：纳线光源接触荧光微球时，微球在接触点释放出橙色荧光。

当纳线移开后，橙色荧光的强度随即降低80倍，说明纳线是荧光的主要激发源。

该项发明的另一位研究人员Jan Liphardt认为：“显微镜成像时，对样本进行成像和操作是两个独立的过程，在纳线光源技术中，我们将这两种功能融融合在一个器件中，对样本进行成像的同时也可以对样本进行操作。

Bull Earthquake Eng(2008)6:645–675DOI10.1007/s10518-008-9078-1ORIGINAL RESEARCH PAPERNumerical analyses of fault–foundation interactionI.Anastasopoulos·A.Callerio·M.F.Bransby·M.C.R.Davies·A.El Nahas·E.Faccioli·G.Gazetas·A.Masella·R.Paolucci·A.Pecker·E.RossignolReceived:22October2007/Accepted:14July2008/Published online:17September2008©Springer Science+Business Media B.V.2008Abstract Field evidence from recent earthquakes has shown that structures can be designed to survive major surface dislocations.This paper:(i)Describes three differentfinite element(FE)methods of analysis,that were developed to simulate dip slip fault rupture propagation through soil and its interaction with foundation–structure systems;(ii)Validates the developed FE methodologies against centrifuge model tests that were conducted at the University of Dundee,Scotland;and(iii)Utilises one of these analysis methods to conduct a short parametric study on the interaction of idealised2-and5-story residential structures lying on slab foundations subjected to normal fault rupture.The comparison between nume-rical and centrifuge model test results shows that reliable predictions can be achieved with reasonably sophisticated constitutive soil models that take account of soil softening after failure.A prerequisite is an adequately refined FE mesh,combined with interface elements with tension cut-off between the soil and the structure.The results of the parametric study reveal that the increase of the surcharge load q of the structure leads to larger fault rupture diversion and“smoothing”of the settlement profile,allowing reduction of its stressing.Soil compliance is shown to be beneficial to the stressing of a structure.For a given soil depthH and imposed dislocation h,the rotation θof the structure is shown to be a function of:I.Anastasopoulos(B)·G.GazetasNational Technical University,Athens,Greecee-mail:ianast@civil.ntua.grA.Callerio·E.Faccioli·A.Masella·R.PaolucciStudio Geotecnico Italiano,Milan,ItalyM.F.BransbyUniversity of Auckland,Auckland,New ZealandM.C.R.Davies·A.El NahasUniversity of Dundee,Dundee,UKA.Pecker·E.RossignolGeodynamique et Structure,Paris,France123(a)its location relative to the fault rupture;(b)the surcharge load q;and(c)soil compliance.Keywords Fault rupture propagation·Soil–structure-interaction·Centrifuge model tests·Strip foundation1IntroductionNumerous cases of devastating effects of earthquake surface fault rupture on structures were observed in the1999earthquakes of Kocaeli,Düzce,and Chi-Chi.However,examples of satisfactory,even spectacular,performance of a variety of structures also emerged(Youd et al.2000;Erdik2001;Bray2001;Ural2001;Ulusay et al.2002;Pamuk et al.2005).In some cases the foundation and structure were quite strong and thus either forced the rupture to deviate or withstood the tectonic movements with some rigid-body rotation and translation but without damage(Anastasopoulos and Gazetas2007a,b;Faccioli et al.2008).In other cases structures were quite ductile and deformed without failing.Thus,the idea(Duncan and Lefebvre1973;Niccum et al.1976;Youd1989;Berill1983)that a structure can be designed to survive with minimal damage a surface fault rupture re-emerged.The work presented herein was motivated by the need to develop quantitative understan-ding of the interaction between a rupturing dip-slip(normal or reverse)fault and a variety of foundation types.In the framework of the QUAKER research project,an integrated approach was employed,comprising three interrelated steps:•Field studies(Anastasopoulos and Gazetas2007a;Faccioli et al.2008)of documented case histories motivated our investigation and offered material for calibration of the theoretical methods and analyses,•Carefully controlled geotechnical centrifuge model tests(Bransby et al.2008a,b)hel-ped in developing an improved understanding of mechanisms and in acquiring a reliable experimental data base for validating the theoretical simulations,and•Analytical numerical methods calibrated against the abovefield and experimental data offered additional insight into the nature of the interaction,and were used in developing parametric results and design aids.This paper summarises the methods and the results of the third step.More specifically: (i)Three differentfinite element(FE)analysis methods are presented and calibratedthrough available soil data.(ii)The three FE analysis methods are validated against four centrifuge experiments con-ducted at the University of Dundee,Scotland.Two experiments are used as a benchmark for the“free-field”part of the problem,and two more for the interaction of the outcrop-ping dislocation with rigid strip foundations.(iii)One of these analysis methods is utilised in conducting a short parametric study on the interaction of typical residential structures with a normal fault rupture.The problem studied in this paper is portrayed in Fig.1.It refers to a uniform cohesionless soil deposit of thickness H at the base of which a dip-slip fault,dipping at angle a(measured from the horizontal),produces downward or upward displacement,of vertical component h.The offset(i.e.,the differential displacement)is applied to the right part of the model quasi-statically in small consecutive steps.123hx O:“f o c u s ”O ’:“e p i c e n t e r ”Hanging wallFootwallyLW –LW hx O:“fo c u s ”O ’:“e p i c e n t e r ”Hanging wallFootwallyL W –LWq BStrip Foundation s(a )(b)Fig.1Definition and geometry of the studied problem:(a )Propagation of the fault rupture in the free field,and (b )Interaction with strip foundation of width B subjected to uniform load q .The left edge of the foundation is at distance s from the free-field fault outcrop2Centrifuge model testingA series of centrifuge model tests have been conducted in the beam centrifuge of the University of Dundee (Fig.2a)to investigate fault rupture propagation through sand and its in-teraction with strip footings (Bransby et al.2008a ,b ).The tests modelled soil deposits of depth H ranging from 15to 25m.They were conducted at accelerations ranging from 50to 115g.A special apparatus was developed in the University of Dundee to simulate normal and reverse faulting.A central guidance system and three aluminum wedges were installed to impose displacement at the desired dip angle.Two hydraulic actuators were used to push on the side of a split shear box (Fig.2a)up or down,simulating reverse or normal faulting,respectively.The apparatus was installed in one of the University of Dundee’s centrifuge strongboxes (Fig.2b).The strongbox contains a front and a back transparent Perspex plate,through which the models are monitored in flight.More details on the experimental setup can be found in Bransby et al.(2008a ).Displacements (vertical and horizontal)at different123Fig.2(a)The geotechnicalcentrifuge of the University ofDundee;(b)the apparatus for theexperimental simulation of faultrupture propagation through sandpositions within the soil specimen were computed through the analysis of a series of digital images captured as faulting progressed using the Geo-PIV software(White et al.2003).Soil specimens were prepared within the split box apparatus by pluviating dry Fontainebleau sand from a specific height with controllable massflow rate.Dry sand samples were prepared at relative densities of60%.Fontainebleau sand was used so that previously published laboratory element test data(e.g Gaudin2002)could be used to select drained soil parameters for thefinite element analyses.The experimental simulation was conducted in two steps.First,fault rupture propagation though soil was modelled in the absence of a structure(Fig.1a),representing the free-field part of the problem.Then,strip foundations were placed at a pre-specified distance s from the free-field fault outcrop(Fig.1b),and new tests were conducted to simulate the interaction of the fault rupture with strip foundations.3Methods of numerical analysisThree different numerical analysis approaches were developed,calibrated,and tested.Three different numerical codes were used,in combination with soil constitutive models ranging from simplified to more sophisticated.This way,three methods were developed,each one corresponding to a different level of sophistication:(a)Method1,using the commercial FE code PLAXIS(2006),in combination with a simplenon-associated elastic-perfectly plastic Mohr-Coulomb constitutive model for soil; 123Foundation : 2-D Elastic Solid Elements Elastic BeamElementsInterfaceElements hFig.3Method 1(Plaxis)finite element diecretisation(b)Method 2,utilising the commercial FE code ABAQUS (2004),combined with a modifiedMohr-Coulomb constitutive soil model taking account of strain softening;and(c)Method 3,making use of the FE code DYNAFLOW (Prevost 1981),along with thesophisticated multi-yield constitutive model of Prevost (1989,1993).Centrifuge model tests that were conducted in the University of Dundee were used to validate the effectiveness of the three different numerical methodologies.The main features,the soil constitutive models,and the calibration procedure for each one of the three analysis methodologies are discussed in the following sections.3.1Method 13.1.1Finite element modeling approachThe first method uses PLAXIS (2006),a commercial geotechnical FE code,capable of 2D plane strain,plane stress,or axisymmetric analyses.As shown in Fig.3,the finite element mesh consists of 6-node triangular plane strain elements.The characteristic length of the elements was reduced below the footing and in the region where the fault rapture is expected to propagate.Since a remeshing technique (probably the best approach when dealing with large deformation problems)is not available in PLAXIS ,at the base of the model and near the fault starting point,larger elements were introduced to avoid numerical inaccuracies and instability caused by ill conditioning of the element geometry during the displacement application (i.e.node overlapping and element distortion).The foundation system was modeled using a two-layer compound system,consisting of (see Fig.3):•The footing itself,discretised by very stiff 2D elements with linear elastic behaviour.The pressure applied by the overlying building structure has been imposed to the models through the self weight of the foundation elements.123Fig.4Method1:Calibration of constitutive model parameters utilising the FE code Tochnog;(a)oedometer test;(b)Triaxial test,p=90kPa•Beam elements attached to the nodes at the bottom of the foundation,with stiffness para-meters lower than those of the footing to avoid a major stiffness discontinuity between the underlying soil and the foundation structure.•The beam elements are connected to soil elements through an interface with a purely frictional behaviour and the same friction angleϕwith the soil.The interface has a tension cut-off,which causes a gap to develop between soil and foundation in case of detachment. Due to the large imposed displacement reached during the centrifuge tests(more than3m in several cases),with a relative displacement of the order of10%of the modeled soil height, the large displacement Lagrangian description was adopted.After an initial phase in which the geostatic stresses were allowed to develop,the fault displacement has been monotonically imposed both on the right side and the right bottom boundaries,while the remaining boundaries of the model have beenfixed in the direction perpendicular to the side(Fig.3),so as to reproduce the centrifuge test boundary conditions.3.1.2Soil constitutive model and calibrationThe constitutive model adopted for all of the analyses is the standard Mohr-Coulomb for-mulation implemented in PLAXIS.The calibration of the elastic and strength parameters of the soil had been conducted during the earlier phases of the project by means of the FEM code Tochnog(see the developer’s home page ),adopting a rather refined and user-defined constitutive model for sand.This model was calibrated with a set of experimental data available on Fontainebleau sand(Gaudin2002).Oedometer tests (Fig.4a)and drained triaxial compression tests(Fig.4b)have been simulated,and sand model parameters were calibrated to reproduce the experimental results.The user-defined model implemented in Tochnog included a yielding function at the critical state,which corresponds to the Mohr-Coulomb failure criterion.A subset of those parameters was then utilised in the analysis conducted using the simpler Mohr-Coulomb model of PLAXIS:•Angle of frictionϕ=37◦•Young’s Modulus E=675MPa•Poisson’s ratioν=0.35•Angle of Dilationψ=0◦123hFoundation : Elastic Beam ElementsGap Elements Fig.5Method 2(Abaqus)finite element diecretisationThe assumption of ψ=0and ν=0.35,although not intuitively reasonable,was proven to provide the best fit to experimental data,both for normal and reverse faulting.3.2Method 23.2.1Finite element modeling approachThe FE mesh used for the analyses is depicted in Fig.5(for the reverse fault case).The soil is now modelled with quadrilateral plane strain elements of width d FE =1m.The foun-dation,of width B ,is modelled with beam elements.It is placed on top of the soil model and connected through special contact (gap)elements.Such elements are infinitely stiff in compression,but offer no resistance in tension.In shear,their behaviour follows Coulomb’s friction law.3.2.2Soil constitutive modelEarlier studies have shown that soil behaviour after failure plays a major role in problems related to shear-band formation (Bray 1990;Bray et al.1994a ,b ).Relatively simple elasto-plastic constitutive models,with Mohr-Coulomb failure criterion,in combination with strain softening have been shown to be effective in the simulation of fault rupture propagation through soil (Roth et al.1981,1982;Loukidis 1999;Erickson et al.2001),as well as for modelling the failure of embankments and slopes (Potts et al.1990,1997).In this study,we apply a similar elastoplastic constitutive model with Mohr-Coulomb failure criterion and isotropic strain softening (Anastasopoulos 2005).Softening is introduced by reducing the mobilised friction angle ϕmob and the mobilised dilation angle ψmob with the increase of plastic octahedral shear strain:123ϕmob=ϕp−ϕp−ϕresγP fγP oct,for0≤γP oct<γP fϕres,forγP oct≥γP f(1)ψmob=⎧⎨⎩ψp1−γP octγP f,for0≤γP oct<γP fψres,forγP oct≥γP f⎫⎬⎭(2)whereϕp andϕres the ultimate mobilised friction angle and its residual value;ψp the ultimate dilation angle;γP f the plastic octahedral shear strain at the end of softening.3.2.3Constitutive model calibrationConstitutive model parameters are calibrated through the results of direct shear tests.Soil response can be divided in four characteristic phases(Anastasopoulos et al.2007):(a)Quasi-elastic behavior:The soil deforms quasi-elastically(Jewell and Roth1987),upto a horizontal displacementδx y.(b)Plastic behavior:The soil enters the plastic region and dilates,reaching peak conditionsat horizontal displacementδx p.(c)Softening behavior:Right after the peak,a single horizontal shear band develops(Jewelland Roth1987;Gerolymos et al.2007).(d)Residual behavior:Softening is completed at horizontal displacementδx f(δy/δx≈0).Then,deformation is accumulated along the developed shear band.Quasi-elastic behaviour is modelled as linear elastic,with secant modulus G S linearly incre-asing with depth:G S=τyγy(3)whereτy andγy:the shear stress and strain atfirst yield,directly measured from test data.After peak conditions are reached,it is assumed that plastic shear deformation takes placewithin the shear band,while the rest of the specimen remains elastic(Shibuya et al.1997).Scale effects have been shown to play a major role in shear localisation problems(Stone andMuir Wood1992;Muir Wood and Stone1994;Muir Wood2002).Given the unavoidableshortcomings of the FE method,an approximate simplified scaling method(Anastasopouloset al.2007)is employed.The constitutive model was encoded in the FE code ABAQUS(2004).Its capability toreproduce soil behaviour has been validated through a series of FE simulations of the directshear test(Anastasopoulos2005).Figure6depicts the results of such a simulation of denseFontainebleau sand(D r≈80%),and its comparison with experimental data by Gaudin (2002).Despite its simplicity and(perhaps)lack of generality,the employed constitutivemodel captures the predominant mode of deformation of the problem studied herein,provi-ding a reasonable simplification of complex soil behaviour.3.3Method33.3.1Finite element modeling approachThefinite element model used for the analyses is shown for the normal fault case in Fig.7.The soil is modeled with square,quadrilateral,plane strain elements,of width d FE=0.5m. 123Fig.6Method 2:Calibration ofconstitutive model—comparisonbetween laboratory direct sheartests on Fontainebleau sand(Gaudin 2002)and the results ofthe constitutive modelx D v3.3.2Soil constitutive ModelThe constitutive model is the multi-yield constitutive model developed by Prevost (1989,1993).It is a kinematic hardening model,based on a relatively simple plasticity theory (Prevost 1985)and is applicable to both cohesive and cohesionless soils.The concept of a “field of work-hardening moduli”(Iwan 1967;Mróz 1967;Prevost 1977),is used by defining a collection f 0,f 1,...,f n of nested yield surfaces in the stress space.V on Mises type surfaces are employed for cohesive materials,and Drucker-Prager/Mohr-Coulomb type surfaces are employed for frictional materials (sands).The yield surfaces define regions of constant shear moduli in the stress space,and in this manner the model discretises the smooth elastic-plastic stress–strain curve into n linear segments.The outermost surface f n represents a failure surface.In addition,accounting for experimental evidence from tests on frictional materials (de 1987),a non-associative plastic flow rule is used for the dilatational component of the plastic potential.Finally,the material hysteretic behavior and shear stress-induced anisotropic effects are simulated by a kinematic rule .Upon contact,the yield surfaces are translated in the stress space by the stress point,and the direction of translation is selected such that the yield surfaces do not overlap,but remain tangent to each other at the stress point.3.3.3Constitutive model parametersThe required constitutive parameters of the multi-yield constitutive soil model are summari-sed as follows (Popescu and Prevost 1995):a.Initial state parameters :mass density of the solid phase ρs ,and for the case of porous saturated media,porosity n w and permeability k .b.Low strain elastic parameters :low strain moduli G 0and B 0.The dependence of the moduli on the mean effective normal stress p ,is assumed to be of the following form:G =G 0 p p 0 n B =B 0 p p 0n (4)and is accounted for,by introducing two more parameters:the power exponent n and the reference effective mean normal stress p 0.c.Yield and failure parameters :these parameters describe the position a i ,size M i and plastic modulus H i ,corresponding to each yield surface f i ,i =0,1,...n .For the case of pressure sensitive materials,a modified hyperbolic expression proposed by Prevost (1989)and Griffiths and Prévost (1990)is used to simulate soil stress–strain relations.The necessary parameters are:(i)the initial gradient,given by the small strain shear modulus G 0,and (ii)the stress (function of the friction angle at failure ϕand the stress path)and strain,εmax de v ,levels at failure.Hayashi et al.(1992)improved the modified hyperbolic model by introducing a new parameter—a —depending on the maximum grain size D max and uniformity coefficient C u .Finally,the coefficient of lateral stress K 0is necessary to evaluate the initial positions a i of the yield surfaces.d.Dilation parameters :these are used to evaluate the volumetric part of the plastic potentialand consist of:(i)the dilation (or phase transformation)angle ¯ϕ,and (ii)the dilation parameter X pp ,which is the scale parameter for the plastic dilation,and depends basically on relative density and sand type (fabric,grain size).With the exception of the dilation parameter,all the required constitutive model parameters are traditional soil properties,and can be derived from the results of conventional laboratory 123Table1Constitutive model parameters used in method3Number of yield surfaces20Power exponent n0.5Shear modulus G at stress p1 (kPa)75,000Bulk modulus at stress p1(kPa)200,000Unit massρ(t.m−3) 1.63Cohesion0 Reference mean normal stressp1(kPa)100Lateral stress coefficient(K0)0.5Dilation angle in compression (◦)31Dilation angle in extension(◦)31Ultimate friction angle in compression(◦)41.8Ultimate friction angle inextension(◦)41.8Dilation parameter X pp 1.65Max shear strain incompression0.08Max shear strain in extension0.08Generation coefficient in compressionαc 0.098Generation coefficient inextensionαe0.095Generation coefficient in compressionαlc 0.66Generation coefficient inextensionαle0.66Generation coefficient in compressionαuc 1.16Generation coefficient inextensionαue1.16(e.g.triaxial,simple shear)and in situ(e.g.cone penetration,standard penetration,wave velocity)soil tests.The dilational parameter can be evaluated on the basis of results of liquefaction strength analysis,when available;further details can be found in Popescu and Prevost(1995)and Popescu(1995).Since in the present study the sand material is dry,the cohesionless material was modeled as a one-phase material.Therefore neither the soil porosity,n w,nor the permeability,k,are needed.For the shear stress–strain curve generation,given the maximum shear modulus G1,the maximum shear stressτmax and the maximum shear strainγmax,the following functional relationship has been chosen:For y=τ/τmax and x=γ/γr,withγr=τmax/G1,then:y=exp(−ax)f(x,x l)+(1−exp(−ax))f(x,x u)where:f(x,x i)=(2x/x i+1)x i−1/(2x/x i+1)x i+1(5)where a,x l and x u are material parameters.For further details,the reader is referred to Hayashi et al.(1992).The constitutive model is implemented in the computer code DYNAFLOW(Prevost1981) that has been used for the numerical analyses.3.3.4Calibration of model constitutive parametersTo calibrate the values of the constitutive parameters,numerical triaxial tests were simulated with DYNAFLOW at three different confining pressures(30,60,90kPa)and compared with the results of available physical tests conducted on the same material at the same confining pressures.The parameters are defined based on the shear stress versus axial strain curve and volumetric strain versus axial strain curve.Figure8illustrates the comparisons between numerical simulations and physical tests in terms of volumetric strain and shear stress versus123Table2Summary of main attributes of the centrifuge model testsTest Faulting B(m)q(kPa)s(m)g-Level a D r(%)H(m)L(m)W(m)h max(m) 12Normal Free—field11560.224.775.723.53.1528Reverse Free—field11560.815.175.723.52.5914Normal10912.911562.524.675.723.52.4929Reverse10919.211564.115.175.723.53.30a Centrifugal accelerationFig.9Test12—Free-field faultD r=60%Fontainebleau sand(α=60◦):Comparison ofnumerical with experimentalvertical displacement of thesurface for bedrock dislocationh=3.0m(Method1)and2.5m(Method2)[all displacements aregiven in prototype scale]Structure Interaction(FR-SFSI):(i)Test14,normal faulting at60◦;and(ii)Test29,reverse faulting at60◦.In this case,the comparison is conducted for all of the developed numerical analysis approaches.The main attributes of the four centrifuge model tests used for the comparisons are syn-opsised in Table2,while more details can be found in Bransby et al.(2008a,b).4.1Free-field fault rupture propagation4.1.1Test12—normal60◦This test was conducted at115g on medium-loose(D r=60%)Fontainebleau sand,simu-lating normal fault rupture propagation through an H=25m soil deposit.The comparison between analytical predictions and experimental data is depicted in Fig.9in terms of vertical displacement y at the ground surface.All displacements are given in prototype scale.While the analytical prediction of Method1is compared with test data for h=3.0m,in the case of Method2the comparison is conducted at slightly lower imposed bedrock displacement: h=2.5m.This is due to the fact that the numerical analysis with Method2was conducted without knowing the test results,and at that time it had been agreed to set the maximum displacement equal to h max=2.5m.However,when test results were publicised,the actually attained maximum displacement was larger,something that was taken into account in the analyses with Method1.As illustrated in Fig.9,Method2predicts almost correctly the location of fault out-cropping,at about—10m from the“epicenter”,with discrepancies limited to1or2m.The deformation can be seen to be slightly more localised in the centrifuge test,but the comparison between analytical and experimental shear zone thickness is quite satisfactory.The vertical displacement profile predicted by Method1is also qualitatively acceptable.However,the123Method 2Centrifuge Model TestR1S1Method 1(a )(b)(c)Fig.10Test 12—-Normal free-field fault rupture propagation through H =25m D r =60%Fontainebleau sand:Comparison of (a )Centrifuge model test image,compared to FE deformed mesh with shear strain contours of Method 1(b ),and Method 2(c ),for h =2.5mlocation of fault rupture emergence is a few meters to the left compared with the experimen-tal:at about 15m from the “epicenter”(instead of about 10m).In addition,the deformation predicted by Method 1at the ground surface computed using method 1is widespread,instead of localised at a narrow band.FE deformed meshes with superimposed shear strain contours are compared with an image from the experiment in Fig.10,for h =2.5m.In the case of Method 2,the comparison can be seen to be quite satisfactory.However,it is noted that the secondary rupture (S 1)that forms in the experiment to the right of the main shear plane (R 1)is not predicted by Method 2.Also,experimental shear strain contours (not shown herein)are a little more diffuse than the FE prediction.Overall,the comparison is quite satisfactory.In the case of Method 1,the quantitative details are not in satisfactory agreement,but the calculation reveals a secondary rupture to the right of the main shear zone,consistent with the experimental image.4.1.2Test 28—reverse 60◦This test was also conducted at 115g and the sand was of practically the same relative density (D r =61%).Given that reverse fault ruptures require larger normalised bedrock123Fig.11Test28—Reversepropagation through H=15mD r=60%Fontainebleau sand:Comparison of numerical withexperimental verticaldisplacement of the surface forbedrock dislocation h=2.0m(all displacements are given inprototype scale)displacement h/H to propagate all the way to the surface(e.g.Cole and Lade1984;Lade et al.1984;Anastasopoulos et al.2007;Bransby et al.2008b),the soil depth was set at H=15m.This way,a larger h/H could be achieved with the same actuator.Figure11compares the vertical displacement y at the ground surface predicted by the numerical analysis to experimental data,for h=2.0m.This time,both models predict correctly the location of fault outcropping(defined as the point where the steepest gradient is observed).In particular,Method1achieves a slightly better prediction of the outcropping location:−10m from the epicentre(i.e.,a difference of1m only,to the other direction). Method2predicts the fault outbreak at about−7m from the“epicenter”,as opposed to about −9m of the centrifuge model test(i.e.,a discrepancy of about2m).Figure12compares FE deformed meshes with superimposed shear strain contours with an image from the experiment,for h=2.5m.In the case of Method2,the numerical analysis seems to predict a distinct fault scarp,with most of the deformation localised within it.In contrast,the localisation in the experiment is clearly more intense,but the fault scarp at the surface is much less pronounced:the deformation is widespread over a larger area.The analysis with Method1is successful in terms of the outcropping location.However,instead of a single rupture,it predicts the development of two main ruptures(R1and R2),accompanied by a third shear plane in between.Although such soil response has also been demonstrated by other researchers(e.g.Loukidis and Bouckovalas2001),in this case the predicted multiple rupture planes are not consistent with experimental results.4.2Interaction with strip footingsHaving validated the effectiveness of the developed numerical analysis methodologies in simulating fault rupture propagation in the free-field,we proceed to the comparisons of experiments with strip foundations:one for normal(Test14),and one for reverse(Test29) faulting.This time,the comparison is extended to all three methods.4.2.1Test14—normal60◦This test is practically the same with the free-field Test12,with the only difference being the presence of a B=10m strip foundation subjected to a bearing pressure q=90kPa.The foundation is positioned so that the free-field fault rupture would emerge at distance s=2.9m from the left edge of the foundation.123。

The Annals of Statistics2011,V ol.39,No.1,174–200DOI:10.1214/10-AOS832©Institute of Mathematical Statistics,2011FOCUSED INFORMATION CRITERION AND MODEL A VERAGING FOR GENERALIZED ADDITIVE PARTIAL LINEAR MODELSB Y X INYU Z HANG1AND H UA L IANG2Chinese Academy of Sciences and University of RochesterWe study model selection and model averaging in generalized additive partial linear models(GAPLMs).Polynomial spline is used to approximatenonparametric functions.The corresponding estimators of the linear para-meters are shown to be asymptotically normal.We then develop a focusedinformation criterion(FIC)and a frequentist model average(FMA)estimatoron the basis of the quasi-likelihood principle and examine theoretical proper-ties of the FIC and FMA.The major advantages of the proposed proceduresover the existing ones are their computational expediency and theoretical re-liability.Simulation experiments have provided evidence of the superiority ofthe proposed procedures.The approach is further applied to a real-world dataexample.1.Introduction.Generalized additive models,which are a generalization of the generalized models and involve a summand of one-dimensional nonparamet-ric functions instead of a summand of linear components,have been widely used to explore the complicated relationships between a response to treatment and pre-dictors of interest[Hastie and Tibshirani(1990)].Various attempts are still being made to balance the interpretation of generalized linear models and theflexibility of generalized additive models such as generalized additive partial linear models (GAPLMs),in which some of the additive component functions are linear,while the remaining ones are modeled nonparametrically[Härdle et al.(2004a,2004b)].A special case of a GAPLM with a single nonparametric component,the gener-alized partial linear model(GPLM),has been well studied in the literature;see, for example,Severini and Staniswalis(1994),Lin and Carroll(2001),Hunsberger (1994),Hunsberger et al.(2002)and Liang(2008).The profile quasi-likelihood procedure has generally been used,that is,the estimation of GPLM is made com-putationally feasible by the idea that estimates of the parameters can be found for a known nonparametric function,and an estimate of the nonparametric function can Received February2010;revised May2010.1Supported in part by the National Natural Science Foundation of China Grants70625004and 70933003.2Supported in part by NSF Grant DMS-08-06097.AMS2000subject classifications.Primary62G08;secondary62G20,62G99.Key words and phrases.Additive models,backfitting,focus parameter,generalized partially lin-ear models,marginal integration,model average,model selection,polynomial spline,shrinkage methods.174GENERALIZED ADDITIVE PARTIALLY LINEAR MODELS175 be found for the estimated parameters.Severini and Staniswalis(1994)showed that the resulting estimators of the parameter are asymptotically normal and that estimators of the nonparametric functions are consistent in supremum norm.The computational algorithm involves searching for maxima of global and local likeli-hoods simultaneously.It is worthwhile to point out that studying GPLM is easier than studying GAPLMs,partly because there is only one nonparametric term in GPLM.Correspondingly,implementation of the estimation for GPLM is simpler than for GAPLMs.Nevertheless,the GAPLMs are moreflexible and useful than GPLM because the former allow several nonparametric terms for some covariates and parametric terms for others,and thus it is possible to explore more complex re-lationships between the response variables and covariates.For example,Shiboski (1998)used a GAPLM to study AIDS clinical trial data and Müller and Rönz (2000)used a GAPLM to carry out credit scoring.However,few theoretical re-sults are available for GAPLMs,due to their generalflexibility.In this article,we shall study estimation of GAPLMs using polynomial spline,establish asymptotic normality for the estimators of the linear parameters and develop a focused in-formation criterion(FIC)for model selection and a frequentist model averaging (FMA)procedure in construction of the confidence intervals for the focus parame-ters with improved coverage probability.We know that traditional model selection methods such as the Akaike informa-tion criterion[AIC,Akaike(1973)]and the Bayesian information criterion[BIC, Schwarz(1978)]aim to select a model with good overall properties,but the se-lected model is not necessarily good for estimating a specific parameter under consideration,which may be a function of the model parameters;see an inspiring example in Section4.4of Claeskens and Hjort(2003).Exploring the data set from the Wisconsin epidemiologic study of diabetic retinopathy,Claeskens,Croux and van Kerckhoven(2006)also noted that different models are suitable for different patient groups.This occurrence has been confirmed by Hand and Vinciotti(2003) and Hansen(2005).Motivated by this concern,Claeskens and Hjort(2003)pro-posed a new model selection criterion,FIC,which is an unbiased estimate of the limiting risk for the limit distribution of an estimator of the focus parameter,and systematically developed a general asymptotic theory for the proposed criterion. More recently,FIC has been studied in several models.Hjort and Claeskens(2006) developed the FIC for the Cox hazard regression model and applied it to a study of skin cancer;Claeskens,Croux and van Kerckhoven(2007)introduced the FIC for autoregressive models and used it to predict the net number of new personal life insurance policies for a large insurance company.The existing model selection methods may arrive at a model which is thought to be able to capture the main information of the data,and to be decided in advance in data analysis.Such an approach may lead to the ignoring of uncertainty intro-duced by model selection.Thus,the reported confidence intervals are too narrow or shift away from the correct location,and the corresponding coverage probabili-ties of the resulting confidence intervals can substantially deviate from the nominal176X.ZHANG AND H.LIANGlevel[Danilov and Magnus(2004)and Shen,Huang and Ye(2004)].Model aver-aging,as an alternative to model selection,not only provides a kind of insurance against selecting a very poor model,but can also avoid model selection instability [Yang(2001)and Leung and Barron(2006)]by weighting/smoothing estimators across several models,instead of relying entirely on a single model selected by some model selection criterion.As a consequence,analysis of the distribution of model averaging estimators can improve coverage probabilities.This strategy has been adopted and studied in the literature,for example,Draper(1995),Buckland, Burnham and Augustin(1997),Burnham and Anderson(2002),Danilov and Mag-nus(2004)and Leeb and Pöstcher(2006).A seminal work,Hjort and Claeskens (2003),developed asymptotic distribution theories for estimation and inference af-ter model selection and model averaging across parametric models.See Claeskens and Hjort(2008)for a comprehensive survey on FIC and model averaging.FIC and FMA have been well studied for parametric models.However,few ef-forts have been made to study FIC and FMA for semiparametric models.To the best of our knowledge,only Claeskens and Carroll(2007)studied FMA in semi-parametric partial linear models with a univariate nonparametric component.The existing results are hard to extend directly to GAPLMs,for the following reasons: (i)there exist nonparametric components in GAPLMs,so the ordinary likelihood method cannot be directly used in estimation for GAPLMs;(ii)unlike the semi-parametric partial linear models in Claeskens and Carroll(2007),GAPLMs allow for multivariate covariate consideration in nonparametric components and also al-low for the mean of the response variable to be connected to the covariates by a link function,which means that the binary/count response variable can be consid-ered in the model.Thus,to develop FIC and FMA procedures for GAPLMs and to establish asymptotic properties for these procedures are by no means straightfor-ward to achieve.Aiming at these two goals,wefirst need to appropriately estimate the coefficients of the parametric components(hereafter,we call these coefficients “linear parameters”).There are two commonly used estimation approaches for GAPLMs:thefirst is local scoring backfitting,proposed by Buja,Hastie and Tibshirani(1989);the second is an application of the marginal integration approach on the nonparamet-ric component[Linton and Nielsen(1995)].However,theoretical properties of the former are not well understood since it is only defined implicitly as the limit of a complicated iterative algorithm,while the latter suffers from the curse of dimen-sionality[Härdle et al.(2004a)],which may lead to an increase in the computa-tional burden and which also conflicts with the purpose of using a GAPLM,that is,dimension reduction.Therefore,in this article,we apply polynomial spline to approximate nonparametric functions in GAPLMs.After the spline basis is cho-sen,the nonparametric components are replaced by a linear combination of spline basis,then the coefficients can be estimated by an efficient one-step maximizing procedure.Since the polynomial-spline-based method solves much smaller sys-tems of equations than kernel-based methods that solve larger systems(which mayGENERALIZED ADDITIVE PARTIALLY LINEAR MODELS177 lead to identifiability problems),our polynomial-spline-based procedures can sub-stantially reduce the computational burden.See a similar discussion about this computational issue in Yu,Park and Mammen(2008),in the generalized additive models context.The use of polynomial spline in generalized nonparametric models can be traced back to Stone(1986),where the rate of convergence of the polynomial spline es-timates for the generalized additive model werefirst obtained.Stone(1994)and Huang(1998)investigated the polynomial spline estimation for the generalized functional ANOV A model.In a widely discussed paper,Stone et al.(1997)pre-sented a completely theoretical setting of polynomial spline approximation,with applications to a wide array of statistical problems,ranging from least-squares re-gression,density and conditional density estimation,and generalized regression such as logistic and Poisson regression,to polychotomous regression and hazard regression.Recently,Xue and Yang(2006)studied estimation in the additive coef-ficient model with continuous response using polynomial spline to approximate the coefficient functions.Sun,Kopciuk and Lu(2008)used polynomial spline in par-tially linear single-index proportional hazards regression models.Fan,Feng and Song(2009)applied polynomial spline to develop nonparametric independence screening in sparse ultra-high-dimensional additive models.Few attempts have been made to study polynomial spline for GAPLMs,due to the extreme technical difficulties involved.The remainder of this article is organized as follows.Section2sets out the model framework and provides the polynomial spline estimation and asymptotic normality of estimators.Section3introduces the FIC and FMA procedures and constructs confidence intervals for the focus parameters on a basis of FMA esti-mators.A simulation study and real-world data analysis are presented in Sections 4and5,respectively.Regularity conditions and technical proofs are presented in the Appendix.2.Model framework and estimation.We consider a GAPLM where the response Y is related to covariates X=(X1,...,X p)T∈R p and Z=(Z1,..., Z d)T∈R d.Let the unknown mean response u(x,z)=E(Y|X=x,Z=z)and the conditional variance function be defined by a known positive function V, var(Y|X=x,Z=z)=V{u(x,z)}.In this article,the mean function u is defined via a known link function g by an additive linear functiong{u(x,z)}=pα=1ηα(xα)+z Tβ,(2.1)where xαis theαth element of x,βis a d-dimensional regression parameter and theηα’s are unknown smooth functions.To ensure identifiability,we assume that E{ηα(Xα)}=0for1≤α≤p.Letβ=(βT c,βT u)T be a vector with d=d c+d u components,whereβc con-sists of thefirst d c parameters ofβ(which we certainly wish to be in the selected178X.ZHANG AND H.LIANGmodel)and βu consists of the remaining d u parameters (for which we are unsure whether or not they should be included in the selected model).In what follows,we call the elements of z corresponding to βc and βu the certain and exploratory vari-ables,respectively.As in the literature on FIC,we consider a local misspecification framework where the true value of the parameter vector βis β0=(βT c,0,δT /√n)T ,with δbeing a d u ×1vector;that is,the true model is away from the deduced model with a distance O(1/√n).This framework indicates that squared model biases and estimator variances are both of size O(1/n),the most possible large-sample approximations.Some arguments related to this framework appear in Hjort and Claeskens (2003,2006).Denote by βS =(βT c ,βT u,S )T the parameter vector in the S th submodel,in the same sense as β,with βu,S being a d u,S -subvector of βu .Let πS be the projec-tion matrix of size d u,S ×d u mapping βu to βu,S .With d u exploratory covariates,our setup allows 2d u extended models to choose among.However,it is not nec-essary to deal with all 2d u possible models and one is free to consider only a few relevant submodels (unnecessarily nested or ordered)to be used in the model se-lection or averaging.A special example is the James–Stein-type estimator studied by Kim and White (2001),which is a weighted summand of the estimators based on the reduced model (d u,S =0)and the full model (d u,S =d u ).So,the covariates in the S th submodel are X and S Z ,where S =diag (I d c ,πS ).To save space,we generally ignore the dimensions of zero vectors/matrices and identity matrices,simply denoting them by 0and I,respectively.If necessary,we will write their dimensions explicitly.In the remainder of this section,we shall investigate poly-nomial spline estimation for (βT c,0,0)based on the S th submodel and establish a theoretical property for the resulting estimators.Let η0= p α=1η0,α(x α)be the true additive function and the covariate X αbe distributed on a compact interval [a α,b α].Without loss of generality,we take all intervals [a α,b α]=[0,1]for α=1,...,p .Noting (A.7)in Appendix A.2,under some smoothness assumptions in Appendix A.1,η0can be well approximated by spline functions.Let S n be the space of polynomial splines on [0,1]of degree ≥1.We introduce a knot sequence with J interior knots,k − =···=k −1=k 0=0<k 1<···<k J <1=k J +1=···=k J + +1,where J ≡J n increases when sample size n increases and the precise order is given in condition (C6).Then,S n consists of functions ςsatisfying the following:(i)ςis a polynomial of degree on each of the subintervals [k j ,k j +1),j =0,...,J n −1,and the last subinterval is [k J n ,1];(ii)for ≥2,ςis ( −1)-times continuously differentiable on [0,1].For simplicity of proof,equally spaced knots are used.Let h =1/(J n +1)be the distance between two consecutive knots.Let (Y i ,X i ,Z i ),i =1,...,n ,be independent copies of (Y,X ,Z ).In the S th submodel,we consider the additive spline estimates of η0based on the independent random sample (Y i ,X i , S Z i ),i =1,...,n .Let G n be the collection of functionsGENERALIZED ADDITIVE PARTIALLY LINEAR MODELS179ηwith the additive formη(x)= pα=1ηα(xα),where each component functionηα∈S n.We would like tofind a functionη∈G n and a value ofβS that maximize the quasi-likelihood functionL(η,βS)=1nni=1Q[g−1{η(X i)+( S Z i)TβS},Y i],η∈G n,(2.2)where Q(m,y)is the quasi-likelihood function satisfying∂Q(m,y)∂m =y−mV(m).For theαth covariate xα,let b j,α(xα)be the B-spline basis function of de-gree .For anyη∈G n,one can writeη(x)=γT b(x),where b(x)={b j,α(xα),j=− ,...,J n,α=1,...,p}T are the spline basis functions andγ={γj,α,j=− ,...,J n,α=1,...,p}T is the spline coefficient vector.Thus,the maximiza-tion problem in(2.2)is equivalent tofinding values ofβ∗S andγ∗that maximize1 nni=1Q[g−1{γ∗T b(X i)+( S Z i)Tβ∗S},Y i].(2.3)We denote the maximizers as β∗S and γ∗S={ γ∗S,j,α,j=− ,...,J n,α=1,..., p}T.The spline estimator ofη0is then η∗S= γ∗T S b(x)and the centered spline esti-mators of each component function areη∗S,α(xα)=J nj=−γ∗S,j,αb j,α(xα)−1nni=1J nj=−γ∗S,j,αb j,α(X iα),α=1,...,p.The above estimation approach can be easily implemented with commonly used statistical software since the resulting model is a generalized linear model.For any measurable functionsϕ1,ϕ2on[0,1]p,define the empirical inner prod-uct and the corresponding norm asϕ1,ϕ2 n=n−1ni=1{ϕ1(X i)ϕ2(X i)}, ϕ 2n=n−1ni=1ϕ2(X i).Ifϕ1andϕ2are L2-integrable,define the theoretical inner product and the corre-sponding norm as ϕ1,ϕ2 =E{ϕ1(X)ϕ2(X)}, ϕ 22=Eϕ2(X),respectively.Let ϕ 2nαand ϕ 22αbe the empirical and theoretical norms,respectively,of a func-tionϕon[0,1],that is,ϕ 2nα=n−1ni=1ϕ2(X iα), ϕ 22α=Eϕ2(Xα)=1ϕ2(xα)fα(xα)dxα,where fα(xα)is the density function of Xα.180X.ZHANG AND H.LIANGDefine the centered version spline basis for anyα=1,...,p and j=− + 1,...,J n,b∗j,α(xα)=b j,α(xα)− b j,α 2α/ b j−1,α 2αb j−1,α(xα),with the stan-dardized version given byB j,α(xα)=b∗j,α(xα) b∗j,α 2α.(2.4)Note that tofind(γ∗,β∗S)that maximizes(2.3)is mathematically equivalent to finding(γ,βS)that maximizes(γ,βS)=1nni=1Q[g−1{γT B(X i)+( S Z i)TβS},Y i],(2.5)where B(x)={B j,α(xα),j=− +1,...,J n,α=1,...,p}T.Similarly to β∗S, γ∗S, η∗S and η∗S,α,we can define βS, γS, ηS and the centered spline estima-tors of each component function ηS,α(xα).In practice,the basis{b j,α(xα),j=− ,...,J n,α=1,...,p}T is used for data analytic implementation and the math-ematically equivalent expression(2.4)is convenient for asymptotic derivation.Letρl(m)={dg−1(m)dm }l/V{g−1(m)},l=1,2.Write T=(X T,Z T)T,m0(T)=η0(X)+Z Tβ0andε=Y−g−1{m0(T)}.T i,m0(T i)andεi are defined in the same way after replacing X,Z and T by X i,Z i and T i,respectively.Write(x)=E[Zρ1{m0(T)}|X=x]E[ρ1{m0(T)}|X=x],ψ(T)=Z− (X),G n=1√nni=1εiρ1{m0(T i)}ψ(T i),D=E[ρ1{m0(T)}ψ(T){ψ(T)}T]and =E[ρ21{m0(T)}ε2ψ(T){ψ(T)}T].The following theorem shows that the estimators βS on the basis of the S th submodel are asymptotically normal.T HEOREM1.Under the local misspecification framework and conditions (C1)–(C11)in the Appendix,√n{ βS−(βT c,0,0)T}=−( S D T S)−1 S G n+( S D T S)−1 S Dδ+o p(1)d−→−( S D T S)−1 S G+( S D T S)−1 S D0δwith G n d−→G∼N(0, ),where“d−→”denotes convergence in distribution.GENERALIZED ADDITIVE PARTIALLY LINEAR MODELS181 R EMARK1.If the link function g is identical and there is only one nonpara-metric component(i.e.,p=1),then the result of Theorem1will simplify to those of Theorems3.1–3.4of Claeskens and Carroll(2007)under the corresponding submodels.R EMARK2.Assume that d u=0.Theorem1indicates that the polynomial-spline-based estimators of the linear parameters are asymptotically normal.This is thefirst explicitly theoretical result on asymptotic normality for estimation of the linear parameters in GAPLMs and is of independent interest and importance. This theorem also indicates that although there are several nonparametric functions and their polynomial approximation deduces biases for the estimators of each non-parametric component,these biases do not make the estimators ofβbiased under condition(C6)imposed on the number of knots.3.Focused information criterion and frequentist model averaging.In this section,based on the asymptotic result in Section2,we develop an FIC model se-lection for GAPLMs,an FMA estimator,and propose a proper confidence interval for the focus parameters.3.1.Focused information criterion.Letμ0=μ(β0)=μ(βc,0,δ/√n)be afocus parameter.Assume that the partial derivatives ofμ(β0)are continuous in a neighborhood ofβc,0.Note that,in the S th submodel,μ0can be estimated by μS=μ([I d c,0d c×d u] T S βS,[0d u×d c,I d u] T S βS).We now show the asymptoticnormality of μS.Write R S= T S( S D T S)−1 S,μc=∂μ(βc,βu)∂βc |βc=βc,0,βu=0,μu=∂μ(βc,βu)∂βu |βc=βc,0,βu=0andμβ=(μT c,μT u)T.T HEOREM2.Under the local misspecification framework and conditions (C1)–(C11)in the Appendix,we have√n( μS−μ0)=−μTβR S G n+μTβ(R S D−I)δ+o p(1)d−→ S≡−μTβR S G+μTβ(R S D−I)0δ.Recall G∼N(0, ).A direct calculation yieldsE( 2S)=μTβR S R S+(R S D−I)δδT(R S D−I)Tμβ.(3.1)Let δbe the estimator ofδby the full model.Then,from Theorem1,we know thatδ=−[0,I]D−1Gn+δ+o p(1).182X.ZHANG AND H.LIANGIf we define =−[0,I ]D −1G +δ∼N(δ,[0,I ]D −1 D −1[0,I ]T ),then δd −→ .Following Claeskens and Hjort (2003)and (3.1),we define the FIC of the S thsubmodel asFIC S =μT β R S R S +(R S D −I ) 0 δ 0 δT (R S D −I )T (3.2)−(R S D −I ) 000I d u D −1 D −1 000I d u(R S D −I )T μβ,which is an approximately unbiased estimator of the mean squared error when √nμ0is estimated by √n μS .This FIC can be used for choosing a proper sub-model relying on the parameter of interest.3.2.Frequentist model averaging .As mentioned previously,an average esti-mator is an alternative to a model selection estimator.There are at least two advan-tages to the use of an average estimator.First,an average estimator often reduces mean square error in estimation because it avoids ignoring useful information from the form of the relationship between response and covariates and it provides a kind of insurance against selecting a very poor submodel.Second,model averaging pro-cedures can be more stable than model selection,for which small changes in the data often lead to a significant change in model choice.Similar discussions of this issue appear in Bates and Granger (1969)and Leung and Barron (2006).By choosing a submodel with the minimum value of FIC,the FIC estimators ofμcan be written as μFIC = S I (FIC selects the S th submodel) μS ,where I (·),an indicator function,can be thought of as a weight function depending on the dataviaδ,yet it just takes value either 0or 1.To smooth estimators across submodels,we may formulate the model average estimator of μasμ=S w(S | δ) μS ,(3.3)where the weights w(S |δ)take values in the interval [0,1]and their sum equals 1.It is readily seen that smoothed AIC,BIC and FIC estimators investigated in Hjort and Claeskens (2003)and Claeskens and Carroll (2007)share this form.The fol-lowing theorem shows an asymptotic property for the general model average esti-mators μdefined in (3.3)under certain conditions.T HEOREM 3.Under the local misspecification framework and conditions (C1)–(C11)in the Appendix ,if the weight functions have at most a countable num-ber of discontinuities ,then √n( μ−μ0)=−μT βD −1G n +μT β Q( δ) 0 δ − 0 δ+o p (1)d −→ ≡−μT βD −1G +μT β Q( ) 0 − 0 ,GENERALIZED ADDITIVE PARTIALLY LINEAR MODELS183where Q(·)=Sw(s|·)R S D and is defined in Section3.1.Referring to the above theorems,we construct a confidence interval forμbased on the model average estimatorˆμ,as follows.Assume that κ2is a consistent esti-mator ofμTβD−1 D−1μβ.It is easily seen that√n( μ−μ0)−μTβQ( δ)δ−δκd−→N(0,1).If we define the lower bound(low n)and upper bound(up n)byμ−μTβQ( δ)δ−δ√n∓z j κ/√n,(3.4)where z j is the j th standard normal quantile,then we have Pr{μ0∈(low n,up n)}→2 (z j)−1,where (·)is a standard normal distribution function.Therefore,the interval(low n,up n)can be used as a confidence interval forμ0with asymptotic level2 (z j)−1.R EMARK3.Note that the limit distribution of √n( μ−μ0)is a nonlinearmixture of several normal variables.As argued in Hjort and Claeskens(2006),a direct construction of a confidence interval based on Theorem3may not be easy. The confidence interval based on(3.4)is better in terms of coverage probability and computational simplicity,as promoted in Hjort and Claeskens(2003)and ad-vocated by Claeskens and Carroll(2007).R EMARK4.A referee has asked whether the focus parameter can depend on the nonparametric functionη0.Our answer is“yes.”For instance,we consider a general focus parameter,η0(x)+μ0,a summand ofμ0,which we have studied,and a nonparametric value at x.We may continue to get an estimator ofη0(x)+μ0by minimizing(3.2)and then model-averaging estimators by weighting the estimators ofμ0andη0as in(3.3).However,the underlying FMA estimators are not root-n consistent because the bias of these estimators is proportional to the bias of the estimators ofη0,which is larger than n−1/2,whereas we can establish their rates of convergence using easier arguments than those employed in the proof of Theorem3.Even though the focus parameters generally depend onμ0andη0 of form H(μ0,η0)for a given function H(·,·),the proposed method can be still applied.However,to develop asymptotic properties for the corresponding FMA estimators depends on the form of H(·,·)and will require further investigation. We omit the details.Our numerical studies below follow these proposals when the focus parameters are related to the nonparametric functions.184X.ZHANG AND H.LIANG4.Simulation study.We generated 1000data sets consisting of n =200and 400observations from the GAPLMlogit {Pr (Y i =1)}=η1(X i,1)+η2(X i,2)+Z T i β=sin (2πX i,1)+5X 4i,2+3X 2i,2−2+Z Ti β,i =1,...,n,where:the true parameter β={1.5,2,r 0(2,1,3)/√n }T ;X i,1and X i,2are inde-pendently uniformly distributed on [0,1];Z i,1,...,Z i,5are normally distributed with mean 0and variance 1;when 1= 2,the correlation between Z i, 1and Z i, 2is | 1− 2|with =0or =0.5;Z i is independent of X i,1and X i,2.We set the first two components of βto be in all submodels.The other three may or may not be present,so we have 23=8submodels to be selected or av-eraged across.r 0varies from 1or 4to 7.Our focus parameters are (i)μ1=β1,(ii)μ2=β2,(iii)μ3=0.75β1+0.05β2−0.3β3+0.1β4−0.06β5and (iv)μ4=η1(0.86)+η2(0.53)+0.32β1−0.87β2−0.33β3−0.15β4+0.13β5.The cubic B-splines have been used to approximate the two nonparametric func-tions.We propose to select J n using a BIC procedure.Based on condition (C6),the optimal order of J n can be found in the range (n 1/(2υ),n 1/3).Thus,we propose to choose the optimal knot number,J n ,from a neighborhood of n 1/5.5.For our nu-merical examples,we have used [2/3N r ,4/3N r ],where N r =ceiling (n 1/5.5)and the function ceiling (·)returns the smallest integer not less than the correspond-ing element.Under the full model,let the log-likelihood function be l n (N n ).Theoptimal knot number,N optn ,is then the one which minimizes the BIC value.That is,N optn=arg min N n ∈[2/3N r ,4/3N r ]{−2l n (N n )+q n log n },(4.1)where q n is the total number of parameters.Four model selection or model averaging methods are compared in this simu-lation:AIC,BIC,FIC and the smoothed FIC (S-FIC).The smoothed FIC weights we have used arew(S |ˆδ)=exp −FIC S μT βD −1 D −1μβ all S exp −FIC SμT βD −1 D −1μβ,a case of expression (5.4)in Hjort and Claeskens (2003).When using the FICor S-FIC method,we estimate D −1 D −1by the covariance matrix of βfull andestimate D by its sample mean,as advocated by Hjort and Claeskens (2003)and Claeskens and Carroll (2007).Thus, can be calculated straightforwardly.Note that the subscript “full ”denotes the estimator using the full model.In this simulation,one of our purposes is to see whether the traditional selection methods like AIC and BIC lead to an overly optimistic coverage probability (CP)of a claimed confidence interval (CI).We consider a claimed 95%confidence in-terval.The other purpose is to check the accuracy of estimators in terms of their。

美国国家实验室的科研评估和启示--以美国劳伦斯伯克利国家实验室为例徐志玮【摘要】This article assesses the level of scientific research at the US Lawrence Berkeley National Laboratory ,in comparison with the top three domestic state key Laboratories. The US national laboratories have published a great number of research papers and have high international influence. They are not only getting huge financial support from the US government ,but also attracting a great amount of funding from many other countries ,undertaking a lot of major internationalprojects ,increasing international research cooperation and correspondingly improving the level of scientific research and international influence. Our domestic state key laboratories need to increase the international cooperation ,to attract the support of the international funds .%对美国劳伦斯伯克利国家实验室的科研水平进行了评估，并且与国内3家国家重点实验室进行了比较分析。

1. 2008年: 哈利波特作者J.K.罗琳在哈佛大学2008年毕业典礼上的演讲Yes, it was a magical talk2. 2007年: 比尔.盖茨在哈佛大学2007年毕业典礼上的演讲Remarks of Bill Gates3. 2006年:著名记者Jim Lehrer在哈佛大学2006年毕业典礼上的演讲4. 2005年: 著名演员约翰.利特高在哈佛大学2005年毕业典礼上的演讲5. 2004年: 前联合国秘书长安南在哈佛大学2004年毕业典礼上的演讲'Three crises, and the need for American leadership'6. 2003年: 前墨西哥总统Ernesto Zedillo在哈佛大学2003年毕业典礼上的演讲7. 2002年: 前美国参议员Daniel Patrick Moynihan在哈佛大学2002年毕业典礼上的演讲8. 2001年: 前美国财政部长Robert E. Rubin在哈佛大学2001年毕业典礼上的演讲9. 2000年: 哈佛大学教授,诺贝尔经济学奖获得者Amartya Sen在哈佛大学2000年毕业典礼上的演讲2009朱棣文：哈佛毕业典礼演讲【演讲人介绍】朱棣文（Steven Chu，1948年2月28日－），美国物理学家，生于美国圣路易斯；华人血统，祖籍中国江苏太仓，曾获得诺贝尔物理学奖（1997年）。

现任美国能源部部长。

1970年，获罗彻斯特大学数学学士和物理学学士。

1976年，获加州大学伯克利分校物理学博士。

1987年，任斯坦福大学物理学教授，是该校第一位华裔教授。

1993年，当选美国国家科学院院士。

1997年，获诺贝尔物理学奖。

2004年，任劳伦斯?伯克利国家实验室主任，是首位掌管这个美国能源部下属国家实验室的亚裔人士。

2009年，出任奥巴马政府能源部长。

【正文】Madam President Faust, members of the Harvard Corporation and the Board of Overseers, faculty, family, friends, and, most importantly, today‟s graduates,尊敬的Faust校长，哈佛集团的各位成员，监管理事会的各位理事，各位老师，各位家长，各位朋友，以及最重要的各位毕业生同学，Thank you for letting me share this wonderful day with you.感谢你们，让我有机会同你们一起分享这个美妙的日子。

LBNL-50934E RNEST O RLANDO L AWRENCEB ERKELEY N ATIONAL L ABORATORY劳伦斯伯克利国家实验室啤酒厂改善能效和节约成本的机会向能源和工厂管理人员提供的能源之星®指南Christina Galitsky, Nathan Martin, Ernst Worrell and Bryan Lehman能源分析处环境能源技术部劳伦斯伯克利国家实验室2003年9月本报告由美国环保局的气候保护合作处资助，为‖能源之星计划‖的一部分，。

能源之星是一个由政府支持、以帮助企业通过优越的能效来保护环境的计划。

这项工作是由环保局合同DW-89-93934401-1通过美国能源部合同 DE-AC03-76SF00098所支持的。

.免责声明本文是对美国政府所赞助项目的记述。

尽管我们相信本文所含的信息是准确的,但是美国政府和各有关部门、加州大学校务委员会以及它们的雇员并不对本文所披露的资讯、设备、产品、工艺的准确性、完整性、实用性作任何保证、表述、暗示及承担任何法律责任,而且并非代表它们的使用将不会侵犯任何私人权益。

本文所引证的任何具体商业产品、加工工艺和服务的商业名称、商标、制造厂商等并非构成或暗示获得美国政府和各有关部门、加州大学校务委员会的认可、推荐或者赞赏。

本文作者所表达的观点并非代表美国政府和各有关部门以及加州大学校务委员会。

劳伦斯・伯克利国家实验室是一个提供平等就业机会的雇主。

目录1.介绍 (2)2.啤酒厂的市场 (3)3.工艺过程介绍 (6)4.能源使用 (10)4.1 能源的消耗和开支 (10)4.2能源强度 (12)5.能效的选择 (14)6.具体生产过程的措施 (20)6.1糖化和过滤槽工艺 (20)6.2 麦汁煮沸和冷却 (20)6.3 发酵 (24)6.4 啤酒处理技术 (25)6.5 包装技术 (26)7.跨工艺的措施 (28)7.1锅炉和蒸汽输配 (28)7.2电机和使用电机的系统 (30)7.3 制冷和冷却 (32)7.4其他的公用设施 (33)8.提高材料效率的机会 (37)9.未来的技术 (41)10.总结和结论 (42)11.鸣谢 (45)12.参考文献 (46)附录I. 大型啤酒厂的地点和产能 (53)附录II. 职工在能效中的任务 (54)附录III. 能效最佳实践的能源管理系统评估 (55)附录IV. 改善工业能效的支持计划 (56)图表表1. 1997年主要啤酒厂的产品和发货价值 (4)表2. 1994年麦牙酒饮料业主要的能源消耗和开支 (10)表3. 1994年啤酒厂行业用电和来源 (11)表4. 估计各种酿造过程用能的百分比 (11)表5. 啤洒工业具体工艺的节能措施 (15)表6. 啤洒工业跨工艺和公用设施的节能措施 (16)表8.具体工艺的能效措施的主要节能和归本的估计 (43)表9.公用设施的能效措施的具体主要节能和归本的估计 (44)图1.1980-1999 年美国的啤酒产量(百万桶) (3)图2. 美国啤酒厂的产量 (百万桶) 1987-1999年 (5)图3. 啤酒生产的工艺过程 (8)图4. 所选择的国家和公司啤酒生产的初级能源强度 (12)图5. 1998 年德国按规模统计的啤酒厂耗能量 (13)图6. 战略性能源管理体系的主要组成部分 (18)啤酒厂改善能效和节约成本的机会向能源和工厂管理人员提供的能源之星®指南Christina Galitsky, Nathan Martin, Ernst Worrell and Bryan Lehman能源分析处环境能源技术部劳伦斯伯克利国家实验室2003年9月摘要在美国的啤酒厂每年的能源开支超过$2亿美元（约16.5亿人民币）1。

LBNL-63807 美国劳伦斯・伯克利国家实验室工业能源效率或温室气体减排目标设定项目的国际经验及成功的关键要素Lynn Price, Christina Galitsky, Klaas Jan Kramer, Aimee McKane环境能源技术处2008年3月此项工作通过美国能源部得到能源基金会和和陶氏化学公司的支持合同号 No. DE-AC02-05CH11231免责声明本报告受美国政府资助而编写。

尽管作者认为本报告所含的信息是正确的，但美国政府及其任何机构，加利福尼亚大学董事及其任何雇员对本报告提及的任何信息、设备、产品或工艺的准确性、全面性、或有效性，以及提及这些信息不侵犯私有权，均不承诺，不表达，不暗示，不承担任何法律责任。

对本报告参考文献中引用的任何具体商品、工艺或服务的商品名、商标、制造商等，不表示或隐含任何认可和推荐，也不表示或隐含得到美国政府及其任何机构、加利福尼亚大学董事的赞同。

本报告作者所持的观点和主张未必表达和反映美国政府及其任何机构，加利福尼亚大学董事的观点和主张。

劳伦斯・伯克利国家实验室是一个提供平等就业机会的雇主。

摘要目标设定协议，通常也称为自愿或协商协议，已被作为促进工业领域能源效率的机制之一应用于许多国家。

最近一份关于目标设定协议的报告给出了18个国家和地区中23个关于能源效率或温室气体减排的自愿协议项目。

国际最佳实践经验表明，成功的项目需要建立一套可以相互配套协调的政策，对参与企业给予强有力的经济激励，并提供技术上和资本上的支持。

目标设定项目的关键要素是：目标制定过程，利用能效指导手册和对标工具确定节能技术和措施，进行能源效率审计，开展节能行动计划，建立并落实能源管理条例，发展激励措施和支持政策，对目标进展情况进行监测，并对项目进行评估。

这份报告首先对三个主要的目标设定项目作简要描述，然后介绍了来自这三个主要项目，以及其他工业能效或减少温室气体排放的国际项目中的关键要素与国际经验。