ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Life design method of high-temperature equipment based on dual-scale damage theory
Received date: 2024-12-24
Revised date: 2025-01-17
Accepted date: 2025-02-19
Online published: 2025-02-25
Supported by
National Key Research and Development Project(2022YFB4600019);National Natural Science Foundation of China(U21B2077);China National Postdoctoral Program for Innovative Talents(BX20230120)
The contradiction between the long-term safe operation of high-temperature structures and harsh service environment is becoming increasingly prominent. Creep-fatigue interaction damage has become increasingly prominent， leading to high failure rates of high-temperature components. In addition， the urgent demand for deep peak shaving in power generation units under carbon neutrality targets means that the critical high-temperature components face a lack of accurate life assessment methods. Traditional life design approaches based on single-scale or single-parameter are insufficient to simultaneously account for multi-axial stress effects and microstructural evolution in high-temperature structures， especially for the structures with inhomogeneous microstructures. In this paper， dual-scale modeling approach based on macro-continuum mechanics and micro-crystal plasticity is systematically introduced. Taking hole structure as an example， a life prediction method based on the dual-scale damage theory is presented. To facilitate the engineering application of the dual-scale theoretical framework， a creep-fatigue life prediction software considering surface strengthening effects is developed， enabling rapid damage assessment and life prediction for surface strengthening structures.
Kaishang LI , Haoqi FAN , Runzi WANG , Xiancheng ZHANG , Shantung TU . Life design method of high-temperature equipment based on dual-scale damage theory[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2025 , 46(5) : 531706 -531706 . DOI: 10.7527/S1000-6893.2025.31706
| 1 | 陈波， 李付国， 何敏. 延性金属材料损伤变量的实验表征方法研究［J］. 稀有金属材料与工程， 2011， 40（11）： 2022-2025. |
| CHEN B， LI F G， HE M. Experimental characterization of damage variables of ductile metal［J］. Rare Metal Materials and Engineering， 2011， 40（11）： 2022-2025 （in Chinese）. | |
| 2 | SUN L， ZHANG X C， WANG R Z， et al. Evaluation of fatigue and creep-fatigue damage levels on the basis of engineering damage mechanics approach［J］. International Journal of Fatigue， 2023， 166： 107277. |
| 3 | 涂善东， 王正东， 陈建钧， 等. 基于结构弱点分析的高温构件延寿修复技术［J］. 压力容器， 2004， 21（9）： 1-8. |
| TU S D， WANG Z D， CHEN J J， et al. Structural weakness spotting for life extension repair of high temperature components［J］. Pressure Vessel Technology， 2004， 21（9）： 1-8 （in Chinese）. | |
| 4 | JU Y B， KOYAMA M， SAWAGUCHI T， et al. Effects of ε-martensitic transformation on crack tip deformation， plastic damage accumulation， and slip plane cracking associated with low-cycle fatigue crack growth［J］. International Journal of Fatigue， 2017， 103： 533-545. |
| 5 | LONG X， CHONG K N， SU Y T， et al. Meso-scale low-cycle fatigue damage of polycrystalline nickel-based alloy by crystal plasticity finite element method［J］. International Journal of Fatigue， 2023， 175： 107778. |
| 6 | 孙李刚， 凌超， 陈浩， 等. 结构完整性分析中的多尺度力学方法［J］. 机械工程学报， 2021， 57（16）： 106-121. |
| SUN L G， LING C， CHEN H， et al. Application of multiscale mechanics methods in structural integrity analysis［J］. Journal of Mechanical Engineering， 2021， 57（16）： 106-121 （in Chinese）. | |
| 7 | BRIFFOD F， SHIRAIWA T， ENOKI M. Microstructure modeling and crystal plasticity simulations for the evaluation of fatigue crack initiation in α-iron specimen including an elliptic defect［J］. Materials Science and Engineering： A， 2017， 695： 165-177. |
| 8 | DONG Y W， ZHU Y L， WU F H， et al. A dual-scale elasto-viscoplastic constitutive model of metallic materials to describe thermo-mechanically coupled monotonic and cyclic deformations［J］. International Journal of Mechanical Sciences， 2022， 224： 107332. |
| 9 | MCDOWELL D L， DUNNE F P E. Microstructure-sensitive computational modeling of fatigue crack formation［J］. International Journal of Fatigue， 2010， 32（9）： 1521-1542. |
| 10 | SAJURI Z BIN， MIYASHITA Y， HOSOKAI Y， et al. Effects of Mn content and texture on fatigue properties of as-cast and extruded AZ61 magnesium alloys［J］. International Journal of Mechanical Sciences， 2006， 48（2）： 198-209. |
| 11 | ZHANG Y C， LI X L， YUAN S H， et al. High-cycle-fatigue properties of selective-laser-melted AlSi10Mg with multiple building directions［J］. International Journal of Mechanical Sciences， 2022， 224： 107336. |
| 12 | CHEN B， JIANG J， DUNNE F P E. Is stored energy density the primary meso-scale mechanistic driver for fatigue crack nucleation？［J］. International Journal of Plasticity， 2018， 101： 213-229. |
| 13 | ZHAO N L， WANG W Z， LIU Y Z. Intergranular mechanical behavior in a blade groove-like component by crystal plasticity model with cohesive zone model［J］. Engineering Fracture Mechanics， 2018， 201： 196-213. |
| 14 | TINGA T， BREKELMANS W A M， GEERS M G D. Application of a multiscale constitutive framework to real gas turbine components［J］. Advanced Materials Research， 2011， 278： 253-258. |
| 15 | WANG R Z， GU H H， ZHU S P， et al. A data-driven roadmap for creep-fatigue reliability assessment and its implementation in low-pressure turbine disk at elevated temperatures?［J］. Reliability Engineering & System Safety， 2022， 225： 108523. |
| 16 | GU H H， WANG R Z， ZHU S P， et al. Machine learning assisted probabilistic creep-fatigue damage assessment［J］. International Journal of Fatigue， 2022， 156： 106677. |
| 17 | COFFIN L F， TAVERNELLI J F. The cyclic straining and fatigue of metals［J］. Transactions of the Metallurgical Society of AIME， 1959， 215（5）： 794-807. |
| 18 | MANSON S S， DOLAN T J. Thermal stress and low cycle fatigue［J］. Journal of Applied Mechanics， 1966， 33（4）： 957. |
| 19 | OSTERGREN W J. A damage function and associated failure equations for predicting hold time and frequency effects in elevated temperature， low cycle fatigue?［J］. Journal of Testing and Evaluation， 1976， 4（5）： 327-339. |
| 20 | CHABOCHE J L， LESNE P M. A non-linear continuous fatigue damage model［J］. Fatigue & Fracture of Engineering Materials & Structures， 1988， 11（1）： 1-17. |
| 21 | SHANG D G， YAO W X. A nonlinear damage cumulative model for uniaxial fatigue［J］. International Journal of Fatigue， 1999， 21（2）： 187-194. |
| 22 | NADERI M， KHONSARI M M. An experimental approach to low-cycle fatigue damage based on thermodynamic entropy［J］. International Journal of Solids and Structures， 2010， 47（6）： 875-880. |
| 23 | KACHANOV L M. Rupture time under creep conditions［J］. International Journal of Fracture， 1999， 97（1）： 11-18. |
| 24 | RABOTNOV Y， LECKIE FA， PRAGER W. Creep problems in structural members［J］. Journal of Applied Mechanics， 1970， 37（1）： 249. |
| 25 | BETTEN J， SKLEPUS S， ZOLOCHEVSKY A. A creep damage model for initially isotropic materials with different properties in tension and compression［J］. Engineering Fracture Mechanics， 1998， 59（5）： 623-641. |
| 26 | ZHANG L， LIU Y R， YANG Q. A creep model with damage based on internal variable theory and its fundamental properties［J］. Mechanics of Materials， 2014， 78： 44-55. |
| 27 | SOSNIN O V， GOREV B V， RUBANOV V V. Energy variant of theory of creep?［J］. Strength of Materials， 1976， 8（11）： 1261-1266. |
| 28 | 王润梓. 基于能量密度耗散准则的蠕变—疲劳寿命预测模型及应用［D］. 上海： 华东理工大学， 2019. |
| WANG R Z. Creep-fatigue life prediction model based on energy density dissipation criterion and its application［D］. Shanghai： East China University of Science and Technology， 2019 （in Chinese）. | |
| 29 | WEN J F， TU S T， XUAN F Z， et al. Effects of stress level and stress state on creep ductility： Evaluation of different models［J］. Journal of Materials Science & Technology， 2016， 32（8）： 695-704. |
| 30 | HALES R. The role of cavity growth mechanisms in determining creep-rupture under multiaxial stresses［J］. Fatigue & Fracture of Engineering Materials & Structures， 1994， 17（5）： 579-591. |
| 31 | TAKAHASHI Y. Further evaluation of creep-fatigue life prediction methods for low-carbon nitrogen-added 316 stainless steel［J］. Journal of Pressure Vessel Technology， 1999， 121（2）： 142-148. |
| 32 | WANG R Z， ZHANG X C， TU S T， et al. A modified strain energy density exhaustion model for creep-fatigue life prediction?［J］. International Journal of Fatigue， 2016， 90： 12-22. |
| 33 | WANG R Z， ZHANG X C， GONG J G， et al. Creep-fatigue life prediction and interaction diagram in nickel-based GH4169 superalloy at 650 ℃ based on cycle-by-cycle concept［J］. International Journal of Fatigue， 2017， 97： 114-123. |
| 34 | WANG R Z， WANG J， GONG J G， et al. Creep-fatigue behaviors and life assessments in two nickel-based superalloys［J］. Journal of Pressure Vessel Technology， 2018， 140（3）： 031405. |
| 35 | SANGID M D. The physics of fatigue crack initiation［J］. International Journal of Fatigue， 2013， 57： 58-72. |
| 36 | POLáK J. Role of persistent slip bands and persistent slip markings in fatigue crack initiation in polycrystals［J］. Crystals， 2023， 13（2）： 220. |
| 37 | LUKá? P， KUNZ L. Role of persistent slip bands in fatigue?［J］. Philosophical Magazine， 2004， 84（3-5）： 317-330. |
| 38 | HSIUNG L M， STOLOFF N S. A point defect model for fatigue crack initiation in Ni3Al+B single crystals［J］. Acta Metallurgica et Materialia， 1990， 38（6）： 1191-1200. |
| 39 | SANGID M D， MAIER H J， SEHITOGLU H. A physically based fatigue model for prediction of crack initiation from persistent slip bands in polycrystals［J］. Acta Materialia， 2011， 59（1）： 328-341. |
| 40 | BENNETT V P， MCDOWELL D L. Polycrystal orientation distribution effects on microslip in high cycle fatigue［J］. International Journal of Fatigue， 2003， 25（1）： 27-39. |
| 41 | HALLBERG H， SIGMUND KYRRE ?， SKALLERUD B. Crystal plasticity modeling of microstructure influence on fatigue crack initiation in extruded Al6082-T6 with surface irregularities［J］. International Journal of Fatigue， 2018， 111： 16-32. |
| 42 | GU T， STOPKA K S， XU C， et al. Prediction of maximum fatigue indicator parameters for duplex Ti-6Al-4V using extreme value theory［J］. Acta Materialia， 2020， 188： 504-516. |
| 43 | MCDOWELL D L. Microstructure-sensitive computational fatigue analysis［M］∥Handbook of Materials Modeling. Dordrecht： Springer Netherlands， 2005： 1193-1214. |
| 44 | MANONUKUL A， DUNNE F P E. High-and low-cycle fatigue crack initiation using polycrystal plasticity［J］. Proceedings of the Royal Society of London Series A： Mathematical， Physical and Engineering Sciences， 2004， 460（2047）： 1881-1903. |
| 45 | CRUZADO A， LUCARINI S， LLORCA J， et al. Crystal plasticity simulation of the effect of grain size on the fatigue behavior of polycrystalline Inconel 718［J］. International Journal of Fatigue， 2018， 113： 236-245. |
| 46 | CRUZADO A， LUCARINI S， LLORCA J， et al. Microstructure-based fatigue life model of metallic alloys with bilinear Coffin-Manson behavior［J］. International Journal of Fatigue， 2018， 107： 40-48. |
| 47 | HULL D， RIMMER D E. The growth of grain-boundary voids under stress［J］. Philosophical Magazine， 1959， 4（42）： 673-687. |
| 48 | ROODPOSHTI P S， SARKAR A， MURTY K L， et al. Grain boundary sliding mechanism during high temperature deformation of AZ31 Magnesium alloy［J］. Materials Science and Engineering： A， 2016， 669： 171-177. |
| 49 | NEEDLEMAN A， RICE J R. Plastic creep flow effects in the diffusive cavitation of grain boundaries［M］∥Perspectives in Creep Fracture. Amsterdam： Elsevier， 1983： 107-124. |
| 50 | NEEDLEMAN A， ASARO R J， LEMONDS J， et al. Finite element analysis of crystalline solids［J］. Computer Methods in Applied Mechanics and Engineering， 1985， 52（1-3）： 689-708. |
| 51 | ZHANG W， WANG X， WANG Y Y， et al. Type Ⅳ failure in weldment of creep resistant ferritic alloys： Ⅱ?. Creep fracture and lifetime prediction［J］. Journal of the Mechanics and Physics of Solids， 2020， 134： 103775. |
| 52 | NEEDHAM N G， GLADMAN T. Nucleation and growth of creep cavities in a Type 347 steel［J］. Metal Science， 1980， 14（2）： 64-72. |
| 53 | WEN J F， SRIVASTAVA A， BENZERGA A， et al. Creep crack growth by grain boundary cavitation under monotonic and cyclic loading［J］. Journal of the Mechanics and Physics of Solids， 2017， 108： 68-84. |
| 54 | HOLDSWORTH S. Creep-fatigue failure diagnosis［J］. Materials， 2015， 8（11）： 7757-7769. |
| 55 | QU S， AN X H， YANG H J， et al. Microstructural evolution and mechanical properties of Cu-Al alloys subjected to equal channel angular pressing［J］. Acta Materialia， 2009， 57（5）： 1586-1601. |
| 56 | YANG X F， XI Y Z， HE C Y， et al. Chemical short-range order strengthening mechanism in CoCrNi medium-entropy alloy under nanoindentation［J］. Scripta Materialia， 2022， 209： 114364. |
| 57 | VENKATARAMAN A， SANGID M D. A crystal plasticity model with an atomistically informed description of grain boundary sliding for improved predictions of deformation fields?［J］. Computational Materials Science， 2021， 197： 110589. |
| 58 | ZHAO Y L， SONG Q H， JI H S， et al. Multi-scale modeling method for polycrystalline materials considering grain boundary misorientation angle［J］. Materials & Design， 2022， 221： 110998. |
| 59 | LI D F， BARRETT R A， O’DONOGHUE P E， et al. A multi-scale crystal plasticity model for cyclic plasticity and low-cycle fatigue in a precipitate-strengthened steel at elevated temperature［J］. Journal of the Mechanics and Physics of Solids， 2017， 101： 44-62. |
| 60 | GOH C H， WALLACE J M， NEU R W， et al. Polycrystal plasticity simulations of fretting fatigue［J］. International Journal of Fatigue， 2001， 23： 423-435. |
| 61 | MUSINSKI W D， MCDOWELL D L. Microstructure-sensitive probabilistic modeling of HCF crack initiation and early crack growth in Ni-base superalloy IN100 notched components?［J］. International Journal of Fatigue， 2012， 37： 41-53. |
| 62 | SHANGGUAN W B， LU Z H. Experimental study and simulation of a hydraulic engine mount with fully coupled fluid-structure interaction finite element analysis model［J］. Computers & Structures， 2004， 82（22）： 1751-1771. |
| 63 | ZHU S P， LIU Q， PENG W W， et al. Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks［J］. International Journal of Mechanical Sciences， 2018， 142： 502-517. |
| 64 | LI K S， WANG R Z， WANG J，et al. Investigation of creep-fatigue crack initiation by using an optimal dual-scale modelling approach［J］.International Journal of Fatigue， 2023， 172： 107621. |
| 65 | MEADE E D， SUN F W， TIERNAN P， et al. A multiscale experimentally-based finite element model to predict microstructure and damage evolution in martensitic steels［J］. International Journal of Plasticity， 2021， 139： 102966. |
| 66 | MEADE E D， SUN F， TIERNAN P， et al. Experimental study and multiscale modelling of the high temperature deformation of tempered martensite under multiaxial loading?［J］. Materials Science and Engineering： A， 2018， 737： 383-392. |
| 67 | JACOB A， MEHMANPARAST A. Sensitivity analysis of material microstructure effects on predicted crack paths using finite element simulations［J］. Journal of Multiscale Modelling， 2016， 7（2）： 1650003. |
| 68 | OWOLABI G M， PRASANNAVENKATESAN R， MCDOWELL D L. Probabilistic framework for a microstructure-sensitive fatigue Notch factor［J］. International Journal of Fatigue， 2010， 32（8）： 1378-1388. |
| 69 | ZHAO Q， ABDEL WAHAB M， LING Y， et al. Fatigue crack propagation within Al-Cu-Mg single crystals based on crystal plasticity and XFEM combined with cohesive zone model［J］. Materials & Design， 2021， 210： 110015. |
| 70 | HAN Q N， QIU W H， HE Z W， et al. The effect of crystal orientation on fretting fatigue crack formation in Ni-based single-crystal superalloys： SEM observation and crystal plasticity finite element simulation［J］. Tribology International， 2018， 125： 209-219. |
| 71 | SHANG X Q， ZHANG H M， CUI Z S， et al. A multiscale investigation into the effect of grain size on void evolution and ductile fracture： Experiments and crystal plasticity modeling［J］. International Journal of Plasticity， 2020， 125： 133-149. |
| 72 | ALABORT E， BARBA D， SULZER S， et al. Grain boundary properties of a nickel-based superalloy： Characterisation and modelling［J］. Acta Materialia， 2018， 151： 377-394. |
| 73 | PEI H Q， YANG Y Z， GU S N， et al. Study on oxidation-creep behavior of a Ni-based single crystal superalloy based on crystal plasticity theory?［J］. Materials Science and Engineering： A， 2022， 839： 142834. |
| 74 | CARPINTERI A， PAGGI M. Asymptotic analysis in linear elasticity： From the pioneering studies by wieghardt and Irwin until today?［J］. Engineering Fracture Mechanics， 2009， 76（12）： 1771-1784. |
| 75 | YUAN G J， WANG R Z， GONG C Y， et al. Investigations of micro-Notch effect on small fatigue crack initiation behaviour in nickel-based alloy GH4169： Experiments and simulations?［J］. International Journal of Fatigue， 2020， 136： 105578. |
| 76 | SUN F W， MEADE E D， O′DOWD N P. Microscale modelling of the deformation of a martensitic steel using the Voronoi tessellation method［J］. Journal of the Mechanics and Physics of Solids， 2018， 113： 35-55. |
| 77 | RUIZ C， NOAILLY J， LACROIX D. Material property discontinuities in intervertebral disc porohyperelastic finite element models generate numerical instabilities due to volumetric strain variations［J］. Journal of the Mechanical Behavior of Biomedical Materials， 2013， 26： 1-10. |
| 78 | BAUER S， LACKNER R. Gradient-based adaptive discontinuity layout optimization for the prediction of strength properties in matrix-inclusion materials［J］. International Journal of Solids and Structures， 2015， 63： 82-98. |
| 79 | SKELTON R P. The energy density exhaustion method for assessing the creep-fatigue lives of specimens and components［J］. Materials at High Temperatures， 2013， 30（3）： 183-201. |
| 80 | WANG R Z， GUO S J， CHEN H F， et al. Multi-axial creep-fatigue life prediction considering history-dependent damage evolution： A new numerical procedure and experimental validation［J］. Journal of the Mechanics and Physics of Solids， 2019， 131： 313-336. |
| 81 | HUO J Z， SUN D B， WU H Y， et al. Multi-axis low-cycle creep/fatigue life prediction of high-pressure turbine blades based on a new critical plane damage parameter?［J］. Engineering Failure Analysis， 2019， 106： 104159. |
| 82 | BENEDETTI M， BERTO F， LE BONE L， et al. A novel Strain-Energy-Density based fatigue criterion accounting for mean stress and plasticity effects on the medium-to-high-cycle uniaxial fatigue strength of plain and notched components［J］. International Journal of Fatigue， 2020， 133： 105397. |
| 83 | KIM T W， KANG D H， YEOM J T， et al. Continuum damage mechanics-based creep-fatigue-interacted life prediction of nickel-based superalloy at high temperature［J］. Scripta Materialia， 2007， 57（12）： 1149-1152. |
| 84 | PARK S， JUNG J， CHO W， et al. Predictive dual-scale finite element simulation for hole expansion failure of ferrite-bainite steel［J］. International Journal of Plasticity， 2021， 136： 102900. |
| 85 | WANG R Z， ZHU S P， WANG J， et al. High temperature fatigue and creep-fatigue behaviors in a Ni-based superalloy： Damage mechanisms and life assessment［J］. International Journal of Fatigue， 2019， 118： 8-21. |
| 86 | HILL R， RICE J R. Constitutive analysis of elastic-plastic crystals at arbitrary strain［J］. Journal of the Mechanics and Physics of Solids， 1972， 20（6）： 401-413. |
| 87 | ASARO R J， RICE J R. Strain localization in ductile single crystals［J］. Journal of the Mechanics and Physics of Solids， 1977， 25（5）： 309-338. |
| 88 | YUAN G J， ZHANG X C， CHEN B， et al. Low-cycle fatigue life prediction of a polycrystalline nickel-base superalloy using crystal plasticity modelling approach［J］. Journal of Materials Science & Technology， 2020， 38： 28-38. |
| 89 | LI D F， GOLDEN B J， O’DOWD N P. Multiscale modelling of mechanical response in a martensitic steel： A micromechanical and length-scale-dependent framework for precipitate hardening［J］. Acta Materialia， 2014， 80： 445-456. |
| 90 | FOURNIER B， DALLE F， SAUZAY M， et al. Comparison of various 9-12% Cr steels under fatigue and creep-fatigue loadings at high temperature［J］. Materials Science and Engineering： A， 2011， 528（22-23）： 6934-6945. |
| 91 | CARROLL L J， CABET C， CARROLL M C， et al. The development of microstructural damage during high temperature creep-fatigue of a nickel alloy?［J］. International Journal of Fatigue， 2013， 47： 115-125. |
| 92 | ZHANG S L， XUAN F Z. Interaction of cyclic softening and stress relaxation of 9-12% Cr steel under strain-controlled fatigue-creep condition： Experimental and modeling［J］. International Journal of Plasticity， 2017， 98： 45-64. |
| 93 | FREDERICK C O， ARMSTRONG P J. A mathematical representation of the multiaxial Bauschinger effect［J］. Materials at High Temperatures， 2007， 24（1）： 1-26. |
| 94 | ZHANG K S， JU J W， LI Z H， et al. Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity?［J］. Mechanics of Materials， 2015， 85： 16-37. |
| 95 | LI K S， CHENG L Y， XU Y L， et al. A dual-scale modelling approach for creep-fatigue crack initiation life prediction of holed structure in a nickel-based superalloy［J］. International Journal of Fatigue， 2022， 154： 106522. |
| 96 | RAMULU M， KUNAPORN S， JENKINS M， et al. Fatigue performance of high-pressure waterjet-peened aluminum alloy［J］. Journal of Pressure Vessel Technology， 2002， 124（1）： 118-123. |
| 97 | SOYAMA H， PARK J D， SAKA M. Use of cavitating jet for introducing compressive residual stress［J］. Journal of Manufacturing Science and Engineering， 2000， 122（1）： 83-89. |
| 98 | RAMULU M， KUNAPORN S， AROLA D， et al. Waterjet machining and peening of metals?［J］. Journal of Pressure Vessel Technology， 2000， 122（1）： 90-95. |
| 99 | YAO S L， LI W， WANG J S， et al. Surface strengthening in confined spaces： A novel deflecting abrasive waterjet peening for improving the surface integrity of nickel-based superalloys GH4169［J］. Journal of Manufacturing Processes， 2023， 85： 417-433. |
| 100 | LI K S， YAO S L， CHENG L Y， et al. Creep-fatigue life prediction of notched structure after an advanced surface strengthening treatment in a nickel-based superalloy at 650 ℃［J］. International Journal of Plasticity， 2024， 173： 103861. |
| 101 | LIN Y， PAN J， ZHOU H F， et al. Mechanical properties and optimal grain size distribution profile of gradient grained nickel［J］. Acta Materialia， 2018， 153： 279-289. |
| 102 | SHIELDS M D， ZHANG J X. The generalization of Latin hypercube sampling［J］. Reliability Engineering & System Safety， 2016， 148： 96-108. |
| 103 | MCCLELLAND J L， RUMELHART D E. Explorations in parallel distributed processing：A handbook of models， programs and exercise［M］. Cambridge： The MIT Press， 1989：121-153. |
| 104 | CORTES C， VAPNIK V. Support-vector networks［J］. Machine Learning， 1995， 20（3）： 273-297. |
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