第39卷第2期英文摘要

Application Prospect of Vibration and Shock in Fuze Technology

ZHANG He

（ZNDY of Ministerial Key Laboratory，Nanjing University of Science and Technology Nanjing，210094，China）

Abstract This paper explores different vibration and shock problems existing in ammunition fuze system during service processing，launching，ballistic flight and target penetration．The vibration problems cover the vibration load resulted from transportation and ballistic flight，and the energy conversion of airflow vibration into the electric energy to solve the problem of full ballistic power supply．The shock problems cover the accidental fall during the service process，the recoil during the launch，the inertia overload during the penetration process，and the conversion of the impact overload into the electric energy．A series of measures that must be taken to ensure the reliability of fuze in shock and vibration environment were discussed．Neither structural damage nor premature releasing malfunction should be caused by the harsh impact environment．Also，the measures for converting the energy of vibration and shock energy to electric energy to meet the requirements for the fuze control detonating circuit and full ballistic power supply are discussed．Finally，the development of fuze vibration and shock problems is prospected．

Keywords fuze；vibration；shock；inertial force

Vibration Analysis and Suppression of Robot Joints Based on Flexible Dynamics Model

ZHANGTie1， QIN Binbin1， LIU Xiaogang2

（1．School of Mechanical and Automotive Engineering，South China University of Technology Guangzhou，510641，China）（2．Guangxi Key Laboratory of Robotics and Welding，Guilin University of Aerospace Technology Guilin，541004，China）

Abstract To solve the problems of mechanical resonance caused by flexible transmission in industrial robot system，a vibration suppression method of robot joints based on flexible dynamics model is studied to reduce the vibration of arm in motion．Firstly，the flexible dynamics model of robot joints is established to analyze the causes of vibration by mathematical expressions，for obtaining the modal information of joints by using ABAQUS（a software）．Thus，the measurement point arrangement of the force hammer excitation experiment can be achieved based on the characteristics of the modal information．In order to suppress the vibration of robot joint，the modal information of the joint shaft is obtained by experiment，and then the notch filter is designed by analyzing the influence of resonance frequency on the robot control．The sim

ulation and control experiment of the robot are carried out in the 5th joint．The experimental results on the value of the end residual amplitude indicate that the acceleration of amplitude decreases from 3to 0．5m／s2，the absolute value of the motor rotor offset decreases from 1to 0．5°，embodying the good suppression characteristics of the notch filter．

Keywords flexible－body dynamics；finite element method；force hammer experiment method；notch filter；vibration suppression

Vibratory Synchronization Transmission in the Vibrating System of Three Exciters

LIU Yunshan1，2， GU Dawei1， ZHANG Juqian1， ZHANG Xueliang1， WEN Bangchun1

（1．School of Mechanical Engineering ＆ Automation，Northeastern University Shenyang，110819，China）（2．Department of Mechanical Engineering，Guidaojiaotong Polytechnic Institute Shenyang，110023，China）

Abstract The principle that a non－powered motor rotates synchronously as a powered motor is called vibratory synchronization transmission．A dynamics model is set up for a vibrating bedstand of three homodromy exciters，，and then the steady－state response and average torque equilibrium equations of system are derived．Finally，the synchronization criterion，the stability criterion of vibratory synchronization and the vibratory synchronization transmission state are obtained．Meanwhile，the experiments proceed on the condition of 50Hz power－supply frequency，with the hall sensor measuring system．The image of phase differences is acquired before and after cutting off motor No．2and No．3．The experimental results verify the effectiveness of the theory and method，which provides the basis for the application of multi－exciters vibratory synchronization machines in vibratory synchronization transmission．

Keywords self－synchronization；vibratory synchronization transmission；dimensionless coupling torque；coefficient of synchronization；synchronization；stability

Shaking Table Model Tests of Concrete Gravity Dam with and Without Seismic Reinforcement

LI Jing， CHEN Jianyun， XU Qiang， ZHANG Lingchen

（Infrastructural Department of Engineering，Dalian University of Technology Dalian，116023，China）

Abstract In this paper，agravity dam model with a geometric scale of 1：100is applied．The low elastic modulus and low－strength concrete simulation materials which satisfy the elastic－gravity similarity rate and the metal materials which satisfy the similar relationship of the reinforcement ratio are applied．The comparative shaking table model tests of concrete gravity dam with and without reinforcement are carried out by applying artificial waves and Lijiang waves and Qianan waves respectively，and the effect of seismic reinforcement is verified quantitatively according to the similarity ratio．Experimental results show that although aseismic reinforcement has little effect for the initial crack of dam sections，the fast spreads of the cracks are obviously restricted after the crack occurs in the dam．The results are valuable for engineering in high－intensity seismic regions．

Keywords gravity dam；seismic reinforcement；earthquake；shaking table model test

Quantitative Detection of Small Crack by Nonlinear Laser Ultrasonics

WAN Haibo1， YANG Shixi2， LIU Yongqiang2

（1．School of Mechanical and Automotive Engineering，Zhejiang University of Water Resources and Electric Power Hangzhou，310018，China）（2．School of Mechanical Engineering，Zhejiang University Hangzhou，310027，China）

Abstract The sensitivity of nonlinear ultrasonic features to small crack is recognized much higher thanwhat can be achieved by conventional linear features．However，in most of cases，the conventional nonlinear ultrasonic features can only locate the crack but difficult to quantify．In this paper，a novel technique for the quantification detection of small crack is presented．The structure needing to be detected is radiated by laser to produce a nonlinear ultrasound and its state space predictive model is constructed based on its dynamical responses in time domain．Then the Bhattacharyya Distance is adopted as the quantification metric to detect the crack．Furthermore，the crack is quantified using the feature extracted from the entire scanned area．An example of the approach and experimental measurement is given for alloys with different kinds of cracks．The experimental results show the reliability of the approach．

Keywords state space；small crack；quantitative；detection

Aeroengine Exhaust Gas Temperature Prediction Based on IQPSO－SVR

PI Jun， HUANG Jiangbo， HUANG Lei， GAO Shuwei， LIU Guangcai

（Sino－European Institute of Aviation Engineering，Civil Aviation University of China Tianjin，300300，China）

Abstract In order to reduce the impact of aircraft engine exhaust gas temperature on aircraft safety flight，the IQPSO－SVR（improved quantum－behaved particle swarm optimization support vector regression）model was proposed to predict the aero－engine exhaust gas temperature，Take the V2500engine of A319aircraft as an example，the performance parameter data from condition monitoring are selected as both the training and test samples，The high－pressure rotor speed，low－pressure rotor speed，fuel flow and highpressure compressor outlet temperature of the aero－engine are taken as the inputs of the model，The aeroengine exhaust gas temperature is used as the output of the model，The IQPSO－SVR model is tested under the condition of different training samples，and compared with QPSO－SVR（quantum behaved particle swarm optimization support vector regression）and SVR （support vector regression），experimental results show that the quantum adaptive particle swarm optimization SVR is more accurate than the other two methods in the prediction of aero－engine exhaust gas temperature and the QAPSO－SVR has better prediction ability in noise reduction．

Keywords aeroengine；improved quantum－behaved particle swarm optimization；support vector regression；exhaust gas temperature；prediction

Jet Analysis of Piezoelectric Needleless Syringe Nozzles Based on FLUENT

ZHANG Tiemin， LI Shenghua， LIANG Li， MEI Yuan

（Engineering College，South China Agricultural University Guangzhou，510642，China）

Abstract The effect of nozzle structure of piezoelectric needleless syringes on jet velocity，turbulence intensity and jet morphology on the nozzle cross－section are studied．First，the numerical simulations with the fluid dynamic software Fluent are carried out using the Realizable k－εturbulence model and the VOF multiphase model based on viscous incompressible fluid N－S equations．The results show that the nozzle with a cone－shaped structure can obtain a symmetrical jet with good controllability．Second，the coneshaped contraction angle and the length of the middle cylinder of the cone－shaped nozzle are simulated and analyzed to study effects of structural parameters and their interactions on jetting speed？？and turbulenceintensity of the nozzle by using the orthogonal test method．Third，the results analyzed by the SPSS software show that the cylinder length has a significant impact on the average jet velocity and mean turbulence intensity of the nozzle．The cone angle has no significant effect on the former but has a significant effect on the latter．The interaction between the cylinder length and the cone angle has no significant effect on neither the former nor the latter．When the cone angle is 30（and the middle cylinder length is 0．2mm，the cone－shaped nozzle can obtain the best jet characteristic．The mean velocity of the outlet is 6．56m／s and the mean value of turbulence intensity is 1．04%．This study can provide a reference for nozzle design of piezoelectric needleless syringe．

Keywords needle－free injection；nozzle；piezoelectric effect；jet

Model－Based Identification of Bolt Looseness

WANG Zibin， GUO Qintao， ZHAN Ming

（National Key Laboratory of Science and Technology on Helicopter Transmission，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

Abstract A new two stages method for on－line identification of bolt state is proposed based on the existing model damage identification technology．The first stage to identify whether there is a torque in bolt connection is reduced，at the same time a new damage index based on modal strain energy is set up，and bolt looseness in the nonlinear performance is discussed．The purpose of the second stage is to identify the residual torque，the equivalent stiffness of bolted connection is identified by a sensitivity－based updating based on the first 3order modes，and the relationship between the residual torque and the equivalent stiffness is established．Finally，under laboratory conditions，two rectangular steel plates connected by bolts are used as the experimental object，the looseness of the bolts is represented by changing the relative residual stress．The results show that the purposed method can be used to identify the happening of torque reduction，and estimate whether the residual torque value is lower than the limit value．

Keywords bolt connection；state recognition；sensitivity－based updating；modal strain energy

Model and Experimental Research on the Relation Between Pressure and Impeller Clearance of Magnetic Levitation Compressor

HAN Bangcheng1，2， CUI Bingwei1，2， ZHENG Shiqiang1，2， ZHANG Yin1，2， SONG Xinda1，2

（1．Science and Technology on Inertial Laboratory，Beihang University Beijing，100191，China）（2．Beijing Engineering Research Center of High－Speed Magnetically Suspended Motor Technology and Application Beijing，100191，China）

Abstract The wind pressure disturbance is the direct cause of compressor rotating stall and surge．The magnetic－levitation compressor has the advantage of controlling the axial displacement of the magnetic levitation rotor to achieve the adjustment of compressor wind pressure．The principle of stabilizing suspension and axial displacement of magnetic levitation rotor is analyzed by establishing the dynamic equation of axial active bearing．A mathematical model of clearance and wind pressure is established by using parameters such as speed of direct relation of wind pressure，impeller height and tip clearance of impeller based on theabove analysis．An experiment is carried out on the 30kW magnetic－levitating compressor．Through data mining，it can be found that when the top gap of the impeller changes 0．1mm and 0．2mm respectively，the numerical value of the wind pressure is very similar to that of the mathematical model．The experimental results also show that the tip clearance of impeller has a significant effect on the compressor wind pressure．For different fault states of the magnetic levitation compressor，different tip clearance of impeller can be selected to adjust the compressor according to mathematical model in this thesis．

Keywords magnetic levitation compressor；active magnetic bearing ；tip clearance changes；ventilation pressure adjusting

Fault Diagnosis Method for High－Speed Train Lateral Damper Based on Variational Mode Decomposition and Multiscale Entropy

GOU Xiantai， LI Changxi， JIN Weidong

（School of Electrical Engineering，Southwest Jiaotong University Chengdu，610031，China）

Abstract In the fault period of high－speed train lateral damper，the vibration signal is non－linear and nonstationary，and features extracting is relatively difficult．In order to solve this problem，a method of features extracting based on variational mode decomposition and multiscale entropy is proposed．The original signal is decomposed into several intrinsic mode function components after being processed by the variational mode decomposition method．Then，the best component is selected by the mutual information index．The feature matrix is constructed through the multiscale entropy of the best component，and removed redundant features using feature evaluation algorithm．The fault type of lateral damper is judged by transforming in the best subset of feature matrix in support vector machine．Experimental results show that the proposed method can extract the feature and judge the fault type of lateral damper effectively，which proves the feasibility of this mechanical fault diagnosis method．

Keywords variational mode decomposition；multiscale entropy；high－speed train lateral damper；fault diagnosis

Analysis and Experimental Study on Quasi－Zero－Stiffness Vibration Isolation Characteristics of Rehabilitation Robot

YANG Xuefeng， MENG Qingguo， LI Wei， LU En， SHENG Lianchao， DONG Shi

（School of Mechatronic Engineering，China University of Mining and Technology Xuzhou，221116，China）

Abstract In this paper，a novel type of passive vibration isolation mechanism with quasi－zero－stiffness is proposed and designed，in order to solve the problem of low frequency vibration of rehabilitation robot．It is achieved by two symmetrical tension springs with a negative stiffness characteristic in parallel with a linear positive stiffness spring．Through the study of static characteristics，the relationship between the force displacement and the stiffness displacement of the vibration isolation mechanism is established，it is concluded that the parameters of the mechanism have quasi－zero－stiffness characteristics at the equilibrium position．The dynamic characteristics，nonlinear dynamic equations in harmonic power and the harmonic displacement excitation are studied，respectively．The influence of mechanism parameters and the excitationon the system force transfer rate and the displacement transfer rate are analyzed using a harmonic balance method．Finally，the curves of the input and output are compared with or without the negative stiffness through experiments．The results show that in the case of negative stiffness mechanism，the vibration isolation system has a certain range of quasi－zero－stiffness characteristics and the low frequency vibration isolation performance is better，which can achieve the effect of high static and low dynamic stiffness．It is innovative and instructive for the low frequency vibration isolation of robot．

Keywords low frequency vibration of robot；quasi－zero－stiffness；nonlinear；transfer rate；experimental verification

Experimental Research on Modal Characteristics of a Thermal Post－Buckling Panel

CHENG Hao， QIN Zhaohong， KONG Fanjin， GONG Wenran， WU Zhenqiang

（Science and Technology on Reliability and Environment Engineering Laboratory，Beijing Institute of Structure and Environment Engineering Beijing，100076，China）

Abstract High speed vehicles are exposed to severe aerodynamic heating during flight．The thermal load can affect material properties and induce thermal stress，thermal deformation，even thermal buckling．Therefore，the dynamic stiffness and modal characteristics change．Experiments are carried out on an aluminum alloy panel to investigate the thermal modal characteristics pre－and post－buckling．The panel is heated using aquartz lamp heating system．The thermal buckling characteristics are first experimentally tested，and the critical buckled temperature is obtained．Then，a series of high temperature modal surveys are carried out．The modal frequency，damping and shape are identified at each temperature distribution．It is shown that the modal frequencies reduce firstly as the temperature increases．However，after the critical buckled temperature，the modal frequencies increase with the augment of the temperature．Since the sensitivities of different modal parameters with the same thermal loads are different，the 3rdand 4thmodal shape are swapped during the heating process．The modal damping increases with the raise of temperature．

Keywords thermal buckling；high temperature；mode；panel

Variable Universe Fuzzy Control Strategy for Magneto－Rheological Semi－active Suspension of Cross Country Car

PANG Hui， LIU Fan， WANG Yan

（School of Mechanical and Precision Instrument Engineering，Xi′an University of Technology Xi′an，710048，China）

Abstract In order to solve the problem that the traditional variable universe fuzzy controller for semi－active suspension dependents on empirical rules，an improved variable universe T－S fuzzy control strategy based on fuzzy neural network is proposed．Firstly，according to the testing data of the magneto－rheological（MR）damping force characteristic，the damping force of MR shock absorber based on adaptive fuzzy neural network and the half vehicle MR semi－active suspension system is established．Secondly，the T－S fuzzy controller for suspension system is developed，meanwhile in order to adjust the variables of T－S fuzzy controller in real time，the fuzzy neural network structure is used to describe the change of the scaling factor．Finally，the effectiveness and feasibility of the proposed control method are verified by the simulation results．

Keywords semi－active suspension；magneto－rheological damper；variable universe；T－S fuzzy control；fuzzy neural network

Fault Feature Extraction of Planetary Gearboxes Based on Angle Domain Windowed Synchronous Average of the Envelope Signal

ZHAO Lei， GUO Yu， WU Xing

（Faculty of Mechanical and Electrical Engineering，Kunming University of Science and Technology Kunming，650500，China）

Abstract The vibration response of a planetary gearbox has a time－varying and non－stationarity due to the effect of planet gear passing，the rotation of sun gear and a planet carrier，and other time－varying conditions．However，the traditional synchronous average cannot be directly applied to the planetary gearboxes．In the light of such problem，this paper proposes a fault feature extraction method based on foreign windowed synchronous averaging，which is based on angle domain windowed synchronous average of envelope signal to overcome the time－varying transmission path and non－stationarity．This method using spectral kurtosis to extract the envelope signal of the vibration signal of the planetary gearbox；Then，the enveloping signals are resampled by the calculation order tracking technique．The rotation of each carrier，the appropriate window function and window width are selected for windowed interception of angle domain signals．Finally，the gear meshing tooth sequence feature is verified，and the vibration separation signal is reconstructed by windowed signals according to rearranging tooth sequence，extraction of gear fault characteristics by angle domain synchronous average of vibration separation signals．Fault analysis of planetary gearboxes measured signal shows that the method can effectively extract the planet gearbox fault characteristics．

Keywords planetary gearboxes；envelope analysis；order tracking；angle synchronous average；vibration separation signal

Detection Method of Spur Gear Tooth Root Crack Damage Degree

SUN Qi1， LIU Xinchang2， ZHANG Bing2， CHEN Chunjun1

（1．School of Mechanical Engineering，Southwest Jiaotong University Chengdu，610031，China）（2．State Key Laboratory of Traction Power，Southwest Jiao tong University Chengdu，610031，China）

Abstract In order to achieve the degree detection of the crack damage degree of a spur gear system，a combination analysis method of principal component analysis（PCA），and the gray theory analysis method are adopted in the paper．First，a dynamic model of a spur gear system is established，so that it is possible to obtain the simulation signals under different degrees of crack．The next step is to capture the crack sensitive characteristic parameters of these signals by modern signal analysis methods including time domain，frequency domain，etc．Then the characteristic parameters is optimized by the combined analysis method of the PCA and the gray theory proposed in this paper to reduce its dimensionality．Finally，the degree detection is achieved depending on the parameter of correlation by the method．Through the analysis of the sim－ulation signals from the model，it is proved that the accuracy increased by 16%than the general method of fixed threshold．The method is effective．

Keywords mechanics；damage quantitative detection；grey relational analysis；principal component analysis（PCA）；state recognition

Characteristics of Frequency Veering for Mistuned Bladed Disks Based on the Contribution Degree of Bladed

ZHANGHongyuan1，2， YUAN Huiqun3， YANG Wenjun2， ZHAO Tianyu2

（1．School of Automobile and Traffic，Shenyang Ligong University Shenyang，110159，China）（2．School of Mechanical Engineering ＆ Automation，Northeastern University Shenyang，110819，China）（3．School of Sciences，Northeastern University Shenyang，110819，China）

Abstract A sub－structure model of aero－engine compressor′s bladed disks is established．Considering the non－linear contact problem of tenon and mortise，the frequency veering characteristic of the bladed disks from the perspectives of the strain energy is analyzed．Then，the modal vibration contribution degree factor and localization factor of the mistuned bladed disks are calculated，as well as the forced vibration response contribution degree factor and localization factor on the frequency veering distance of the mistuned bladed disks．The relationship of the frequency veering distance and contribution degree factor for the mistuned bladed disks localization is studied，and the results indicate that the frequency veering had a significant effect on the mistuned bladed disks localization，the degree of the localization is relatively high in the region of frequency veering．The contribution degree of bladed strain energy on the mistuned bladed disks changes along with the frequency veering distance．

Keywords mistuned bladed disks；frequency veering；localization；strain energy；contribution degree

Damage Location Detection Method Based on Lamb Wave Direction Algorithm and Piezoelectric Knot

ZHAOZhujun， LI Cheng， HOU Yuliang， TIE Ying， SONG Chengjie

（School of Mechanical Engineering，Zhengzhou University Zhengzhou，450001，China）

Abstract In this work，based on the propagation properties of Lamb wave，an approach is proposed to detect damage location in composite material．Two piezoelectric knots are utilized in this approach，each knot includes three piezoelectric transducers．Damage scattering signals are collected using piezoelectric knots．In this method，the difference of time and displacement between each transducer is obtained using the propagation speed of Lamb wave．Considering the geometrical position of piezoelectric transducers，the spreading direction of scattering signals is computed with a direction algorithm，in which the arrival time of the wave packet to each transducer is utilized．This direction is the one that the lamb wave occurs scattering from the damage position．By this way，each piezoelectric knot can detect one spreading direction from the damage location．Therefore，the damage location is determined with the intersection of these identified directions．Moreover，the validation of the damage location detection method is given in this work．The fundamental theory of cross correlation is investigated，and the cross－correlation algorithm isused to extract the damage scattering signal．Experimental tests have been performed on carbon fiber reinforced resin matrix composite plates to validate the detection method．The damage location is obtained and compared with the experimental results．It reaches a good agreement，and this scenario indicates the robustness of this method to detect the damage location．

Keywords Lamb wave；direction algorithm；cross correlation；piezoelectric knot

Experimental Study on Random Motion Generated by Ocean Wave Spectrum by Using Horizontal Movement Simulator

XUE Mian1，2， XING Jianjian2， YUAN Xiaoli3，， CHEN Yichao2， LUO Maojun2

（1．Key Laboratory of Coastal Disaster and Defence of Ministry of Education，Hohai University Nanjing，210098，China）（2．College of Harbour Coastal and Offshore Engineering，Hohai University Nanjing，210098，China）（3．College of Science，Hohai University Nanjing，210098，China）

Abstract A horizontal movement simulator is designed in this study．The random motion displacements generated by broad band B spectrum and narrow band J spectrum are studied experimentally by using a horizontal movement simulator．Statistical characteristics such as the maximum／ minimum displacement and standard deviation of random motion displacement generated by ocean wave spectrum and determinate coefficient between corresponding measured power spectrum density and theoretical spectrum are analyzed by varying significant wave height and peak period．The determinate coefficient between measured power spectrum density and theoretical spectrum of B spectrum is greater than that of J spectrum，which is mainly affected by peak period for J spectrum．The standard deviation of the random motion displacement and the variance of power spectrum density of J spectrum are also found to be greater than that of B spectrum．The result indicates that it is difficult to generate random motion displacement exactly by a horizontal movement simulator for more highly dispersed J spectrum compared with broad band Bretschneider spectrum．

Keywords movement simulator；broad band spectrum；narrow band spectrum；statistical characteristic；fast Fourier transform

Rolling Bearing Fault Diagnosis Method Based on EEMD Singular Value Entropy

ZHANG Chen， ZHAO Rongzhen， DENG Linfeng

（School of Mechanical ＆ Electronic Engineering，Lanzhou University of Technology Lanzhou，730050，China）

Abstract In the light of fault identification，a rolling bearing fault diagnosis method is proposed to make full use of the vibration signal．The improvement is based on ensemble empirical mode decomposition（EEMD）singular value entropy criterion．First，the intrinsic mode functions（IMFs）are created based on the EEMD decomposition of the vibration signal of a rolling bearing．The representative fault information is selected from the IMF to reconstruct the original signal in terms of evaluation index，such as kurtosis，mean square error，and Euclidean distance．Then the singular value entropy is obtained by combining the information entropy method to determine the fault category of the rolling．The results show that the proposed method can distinguish the different characteristics of a rolling bearing under different types of work char－acteristics of the interval with a higher fault diagnosis accuracy than the traditional method．

Keywords rolling bearing；ensemble empirical mode decomposition（EEMD）method；singular value entropy；fault diagnosis

Method of Planetary Gearbox Degradation Feature Extraction

NI Xianglong1， ZHAO Jianmin2， CHEN Jichao3， ZHANG Xinghui2， LI Haiping2

（1．Luoyang Electronic Equipment Test Center of China Luoyang，471003，China）（2．Shijiazhuang Campus of Army Engineering University Shijiazhuang，050003，China）（3．Non－Commissoned Officer School of Space Engineering University Beijing，102249，China）

Abstract Planetary transmission system has been widely used in modern industry，and study on planetary gearbox degradation feature analysis method has important significance for mechanical system prognostics and health management（PHM）．In the light of the degradation characteristic of planetary gearbox，root means square（RMS）spectrum is proposed based on the signal processing method and composition way of Kurtogram．RMS is calculated as the characteristic index instead of kurtosis in RMS spectrum．As a result，RMS spectrum presents the RMS changes of every frequency band of time domain and frequency domain in the system degradation process．The principles and applications of RMS spectrum and RMS normalized spectrum are described by bearing experimental data examples．A detailed study of planetary gearbox degradation process characteristics analysis based on the RMS spectrum is expressed in the case study．There are some conclusions obtained from the case study，such as the RMS changes are not the same for different frequency bands；Some frequency bands can stably reflect degradation process，whilst some frequency bands are sensitive to the acceleration of the degradation stage．These conclusions are very meaningful to the extracting planetary gearbox degradation feature index in degradation prediction．

Keywords planetary gearbox；feature index；kurtogram；root mean square spectrum

Investigation of the Multi－dimensional PLS Uncertainty and Dependence

WANG Qiang1，2， WU Ziyan3， LIU Shukui1

（1．State Key Laboratory for Geomechanics and Deep Underground Engineering，China University of Mining and Technology Xuzhou，221116，China）（2．School of Mechanics and Civil Engineering，China University of Mining and Technology Xuzhou，221116，China）（3．School of Mechanics，Civil Engineering and Architecture，Northwestern Polytechnical University Xi′an，710129，China）

Abstract In the light of the uncertainty and dependence of the performance limit state（PLS），a multi－dimensional fragility analysis methodology is proposed．Incremental dynamic analysis（IDA）is carried out to generate PLS threshold sample，and a multi－dimensional PLS formula is constructed．The two－dimensional performance limit state band is proposed to determine the structural failure domain．The upper and lower bound of the band area is identified based on the interval estimation．The correlation coefficient is introduced to describe the PLS dependence level．Multi－dimensional probabilistic seismic demand model（PSDM）is obtained through nonlinear dynamic time history analysis．An RC－bridge is used as an example to illustrate the methodology，and the multi－dimensional fragility confidence interval is calculated．The sensi－tivity of the fragility is carried out．Results show that limit state band can better solve the PLS uncertainty problem．The fragility confidence interval length becomes narrow with the decrease of confidence level．As the PLS correlation coefficient increases，the PLS dependence reduces．Non－conservative fragility estimation will be generated，which is adverse for risk control．

Keywords multi－dimensional fragility；incremental dynamic analysis；limit state band；probabilistic seismic demand model；confidence interval

Nonlinear Ultrasonic Characterization of Pitting Corrosion Damage of 304Stainless Steel

LI Ping， CHEN Lei， WANG Tengteng， ZHAO Jie

（School of Materials Science and Engineering，Dalian University of Technology Dalian，116024，China）

Abstract The nondestructive characterization of pitting corrosion of 304austenitic stainless sheets of steel is realized by nonlinear ultrasonic surface wave detection technique．The solid solution 304austenitic stainless sheets of steel are soaked in the FeCl3of 6．0%，10．0%and 14．0%for 6，12，and 18hrespectively．The surface morphology of the samples soaked is observed by OLS4000laser confocal microscope，and the three－dimensional morphology and size of the steady－state pitting holes are measured．The nonlinear coefficient of the ultrasonic surface wave is measured by RAM－5000．The normalized nonlinear coefficient is analyzed based on the morphology and dimensional change of the pits．The results show that the normalized nonlinear coefficient rises gradually with the increasing ultrasonic surface wave spreading distance．When the surface wave spreading distance is constant，the normalized nonlinear coefficient is significantly increased with the increase of soaking time and the mass fraction of the solution．It is concluded that the stress－strain nonlinear effect resulted from the interaction of ultrasonic wave and discontinuous interface around pits tends to be remarkable with the increasingly serious pitting damage．

Keywords stainless steel；pitting corrosion；ultrasonic surface wave；nonlinear coefficient

Experimental Study on Effect of Rail Corrugation on Structure Vibration in Egg Fastener Zone

CAI Xiaopei， ZHONG Yanglong， GUO Liangwu， TAN Xi

（School of Civil Engineering，Beijing Jiaotong University Beijing，100044，China）

Abstract Rail corrugation usually appears in the subway operation，especially in the egg fastener zone．In order to reveal the vibration character of structure that is caused by rail corrugation，the rail corrugation is measured in the subway typical sections of straight and curve lines and the common and egg fastener zone．The vibration accelerations of the track，tunnel，and ground are tested．The vibration magnitude and transmission characteristics of the structure are compared in the time domain and frequency domain．The influence of rail corrugation on acceleration vibration level and the vibration reduction effect of egg fastener is analyzed．The results show that：1）the corrugation in the egg fastener zones increases the dynamic impact between wheel rail and the vibration acceleration of rail－track bed－tunnel－ground；2）the rail corrugation inthe egg fastener areas makes the vibration level of the structure under rail larger than that of the common fastener sections，and the vibration reduction effect is difficult to achieve；3）the rail corrugation in the egg fastener areas is more serious than the common fastener sections，especially in the lines of smaller radius curve，larger capacity and faster speed．The influence of rail corrugation should be taken into account in the selection of track．

Keywords rail corrugation；egg fastener；vibration acceleration；1／3octave value；field test

Sensor Fault Diagnosis for ECAS System Based on Extended Kalman Filter Bank

CHEN Long1， SHAN Haiqiang1， XU Xing1， CUI Xiaoli2

（1．School of Automotive and Traffic Engineering，Jiangsu University Zhenjiang，212013，China）（2．School of Mechanical Engineering，Hunan Institute of Technology Henyang，421002，China）

Abstract In the light of worse control caused by sensor faults in the process of adjusting the ride height for electronically controlled air suspension（ECAS）system，a method that can diagnose the sensor faults for ECAS system is presented．A physical model of the ECAS system is built by AMESim in order to describe accurately the air spring characteristics．Meanwhile，mathematical models of road excitation and sensor faults are constructed by Matlab／Simulink．For the nonlinear characteristics of the ECAS system，extended Kalman filters，which are designed by extended Kalman estimation algorithm，are used to establish the residual observer bank of the sensor fault．According to the state estimations achieved by extended Kalman filter bank，output residuals are obtained and could be compared with a threshold to detect and isolate the sensor faults．Then，the co－simulation of different sensors with different faults is carried out．Finally，the test bench of 1／4ECAS system is built to perform experiments of sensor fault diagnosis during the process of height adjustment．Simulation and test results show that the proposed approach accurately detect typical sensor faults of the ECAS system and preferably isolated different sensors with faults to ensure the accurate and reliable operation of the ECAS system．

Keywords electronically controlled air suspension；vehicle height adjustment；sensor fault；extended kalman filter；fault diagnosis

Damage Degree Recognition of Bearing Based on Correlation Analysis and Lempel－Ziv Index

YINJiancheng， XU Minqiang

（Deep Space Exploration Research Center，Harbin Institute of Technology Harbin，150001，China）

Abstract For the damage degree recognition of bearing inner and outer ring under the single failure mode，an evaluation method based on the Lempel－Ziv index and correlation analysis is proposed．The influence of noise on Lempel－Ziv index is reduced by correlation analysis on the basis of retaining frequency components in the signal．Firstly，the autocorrelation analysis of the original signal is used to reduce the noise component of the signal．Secondly，the coding sequence of the original signal is obtained by 0－1encoding of thenoise reduction signal．Finally the sequence after coding is used to calculate the Lempel－Ziv index to get the signal complexity．The effectiveness of the proposed method is verified by simulation and experimental data．Compared with the traditional Lempel－Ziv complexity and the Lempel－Ziv complexity after filtering，the proposed method can identify the bearing fault signal complexity in the noise environment，which can effectively distinguish the damage degree of the bearing inner and outer ring under the single failure mode．

Keywords bearing；correlation analysis；damage degree；inner ring；outer ring

Measurement of free Velocities from Resiliently Mounted Machines in Situ

WANG Zhen1，2， ZHAO Zhigao3

（1．School of Mechanical Engineering and Automation，Wuhan Textile University Wuhan，430200，China）（2．Hubei Key Laboratory of Digital Textile Equipment Wuhan Textile University Wuhan，430200，China）（3．Wuhan 2nd Ship Design ＆ Research Institute Wuhan，430205，China）

Abstract This paper presents an indirect measurement method of free velocities from resiliently mounted machines in situ．First，the dynamic equation of the coupled isolation system is established using impedance synthesis analysis．Second，the effective point mobility is utilized to convert the multi－input and multi－output system to a single－input and single－output system．The relationships between the free velocities and the velocities of mounting points of the machine are analyzed．Accordingly，the measurement method of free velocities is obtained．Finally，the errors and adaptive frequency ranges of this method are analyzed respectively．Besides，the accuracy of the proposed method is proved by a numerical simulation example．The results of a test also verify the theory deduction．This study thus provides theoretical references for the measurement of free velocities in practical engineering．

Keywords vibration isolation；source characterization；free velocity；impedance synthesis analysis；effective point mobility

Research on Improved Wavelet Packet Threshold Denoising Algorithm Based on Sample Entropy

XIANG Beiping， ZHOU Jian， NI Lei， AI Panhua

（Manufacturing Process Testing Technology Key Laboratory of the Ministry of Education，Southwest University of Science and Technology Mianyang，621000，China）

Abstract In the light of eliminating the interference of noise，the limitation of traditional wavelet packet threshold denoising method is analyzed and an improved wavelet packet threshold denoising algorithm based on sample entropy is proposed．At the aspect of threshold function，the method takes sample entropy as a characteristic parameter to represent noise distribution of noisy signal wavelet packet coefficients，and improves the threshold function according to the parameter value，so that it can adjust adaptively based on the noise distribution of signal wavelet packet coefficients．In terms of threshold selection，define the difference between denoised signal and original signal as the estimation of the noise signal，and use sample entropy as the determination criterion to choose the optimal threshold which makes the noise esti－mation sample entropy maximum．Finally，the method is used to denoise rolling bearing vibration．Comparison with the traditional method shows that the method removed noise effectively and restored signal frequency characteristic better，it′s a greater denoising algorithm．

Keywords sample entropy；wavelet packet coefficients；threshold denoising；vibration signal；fault diagnosis

Method Integrate EWT Multi－scale Permutation Entropy with GG Clustering for Bearing Fault Diagnosis

ZHAO Rongzhen， LI Jipu， DENG Linfeng

（School of Mechanical and Electrical Engineering，Lanzhou University of Technology Lanzhou，730050，China）

Abstract In the light of the identification of the faults type of rolling bearing，which is hard due to the non－linear and non－stationary characteristics of the fault signals，a method of fault identification is proposed．It consists of the experience wavelet transform （EWT），multi－scale permutation entropy （MPE）and GG （Gath－Geva）clustering algorithm．First of all，the original signals of rolling bearing are decomposed into many intrinsic mode components based on the EWT decomposition．Then，the state features of the rolling bearing are preliminary extracted；the optimal modal component is selected with correlation analysis，and the permutation entropy is calculated in multiple scales．Finally，the principal component analysis（PCA）is used to reduce the dimension of the entropy feature vector for visualization，and low features subset is introduced into the GG clustering algorithm to realize the fault diagnosis of the rolling bearing．Comparisons with other mode combination method show that the proposed fault diagnosis method has certainly advantages，which better fault recognition effect．

Keywords empirical wavelet transform；multi－scale permutation entropy；correlation analysis；GG clustering

Failure Control Device for Bridges During Earthquake

SUN Guangjun， WANG Seng， LI Hongjing

（College of Civil Engineering，Nanjing University of Technology Nanjing，211816，China）

Abstract In order to enhance the unseating prevention capacity of bridge and reduce the seismic loss of transportation lifeline system，a new control device for the seismic unseating prevention of bridges is developed according to the conceptions of energy dissipation，multi－failure and damage reduction．The device provides two different control types of performance including energy dissipation－based displacement restriction and unseating prevention，and these two level control types can be automatically transformed．Firstly，the composition，characteristics and the working mechanism of the device are analyzed．Then，a quasi－static experiment is conducted to examine the hysteretic curve of the energy dissipation－based displacement restriction unit of the first－level control．Then，a static tensile experiment is conducted to investigate the deformation characteristics，the failure mode and the anchoring capacity of the cable restrainer unit on the second－level control．In addition，a bolt shear experiment is conducted to examine the controlconversion function．Finally，our finite element simulation method is verified by the experimental results．The results indicate that the two－level control device for seismic unseating failure has an effective displacement constraint capacity，a reasonable energy dissipation mechanism and a distinct structure of damage－reduction fuse．The device achieves complementary advantages between its girder－girder connection and piergirder connection control mode，providing a reliable guarantee for unseating prevention and a safety protection of bridge pier in strong earthquake．

Keywords bridge；earthquake；unseating；control；energy dissipation－based displacement restriction；girder－girder connection；structural fuse

Estimation of Fluctuating Wind Amplitude and Phase Spectrum Using APES Algorithm Based on Field Monitored Data

WANG Xiangjie1， DAN Danhui1， YAN Xingfei2， CHENG Wei1

（1．College of Civil Enginerring，Tongji University Shanghai，200092，China）（2．Shanghai Urban Construction Design Research Institute Shanghai，200215，China）

Abstract For super－tall and long－span structures，wind－induced vibration possesses a threat to the structural safety．It is important to model and analysis the wind load．The fluctuating wind power spectra in given specifications could only reflect the second－order probabilistic characteristic，which indicates that it is not capable of fully expressing the stochastic wind field．Besides，the popular Fourier transfer algorithm cannot achieve a high estimation accuracy and high resolution．In view of this problem，a high－resolution nonparametric spectral estimation algorithm－amplitude and phase estimation （APES）is used to estimate the fluctuating wind amplitude and phase spectrum，using the field measured wind velocity data of a certain cable stayed bridge．Through statistical analysis，the mean value of the amplitude spectrum and phase spectrum，as well as the distribution type at different frequency points，are obtained，thus to improve the modeling accuracy of the fluctuating wind spectrum，which is important in anti－wind design and safety assessment．

Keywords fluctuating wind；amplitude spectrum；phase spectrum；structural wind resistance