Bayesian Hierarchical Modelling for Uncertainty Quantification in Operational Thermal Resistance of LED Systems
Remaining useful life (RUL) prediction is central to prognostics and reliability assessment of light-emitting diode (LED) systems. Their unknown long-term service life remaining when subject to specific operating conditions is affected by various sources of uncertainty stemming from production of in...
Saved in:
| Published in | Applied sciences Vol. 12; no. 19; p. 10063 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
MDPI AG
01.10.2022
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2076-3417 2076-3417 |
| DOI | 10.3390/app121910063 |
Cover
Loading…
| Abstract | Remaining useful life (RUL) prediction is central to prognostics and reliability assessment of light-emitting diode (LED) systems. Their unknown long-term service life remaining when subject to specific operating conditions is affected by various sources of uncertainty stemming from production of individual system components, application of the whole system, measurement and operation. To enhance the reliability of model-based predictions, it is essential to account for all of these uncertainties in a systematic manner. This paper proposes a Bayesian hierarchical modelling framework for inverse uncertainty quantification (UQ) in LED operation under thermal loading. The main focus is on the LED systems’ operational thermal resistances, which are subject to system and application variability. Posterior inference is based on a Markov chain Monte Carlo (MCMC) sampling scheme using the Metropolis–Hastings (MH) algorithm. Performance of the method is investigated for simulated data, which allow to focus on different UQ aspects in applications. Findings from an application scenario in which the impact of disregarded uncertainty on RUL prediction is discussed highlight the need for a comprehensive UQ to allow for reliable predictions. |
|---|---|
| AbstractList | Remaining useful life (RUL) prediction is central to prognostics and reliability assessment of light-emitting diode (LED) systems. Their unknown long-term service life remaining when subject to specific operating conditions is affected by various sources of uncertainty stemming from production of individual system components, application of the whole system, measurement and operation. To enhance the reliability of model-based predictions, it is essential to account for all of these uncertainties in a systematic manner. This paper proposes a Bayesian hierarchical modelling framework for inverse uncertainty quantification (UQ) in LED operation under thermal loading. The main focus is on the LED systems’ operational thermal resistances, which are subject to system and application variability. Posterior inference is based on a Markov chain Monte Carlo (MCMC) sampling scheme using the Metropolis–Hastings (MH) algorithm. Performance of the method is investigated for simulated data, which allow to focus on different UQ aspects in applications. Findings from an application scenario in which the impact of disregarded uncertainty on RUL prediction is discussed highlight the need for a comprehensive UQ to allow for reliable predictions. |
| Author | Mücke, Manfred Dvorzak, Michaela Kleb, Ulrike Magnien, Julien Kraker, Elke |
| Author_xml | – sequence: 1 givenname: Michaela surname: Dvorzak fullname: Dvorzak, Michaela – sequence: 2 givenname: Julien orcidid: 0000-0001-5188-8845 surname: Magnien fullname: Magnien, Julien – sequence: 3 givenname: Ulrike surname: Kleb fullname: Kleb, Ulrike – sequence: 4 givenname: Elke orcidid: 0000-0001-7734-5603 surname: Kraker fullname: Kraker, Elke – sequence: 5 givenname: Manfred orcidid: 0000-0002-3960-4296 surname: Mücke fullname: Mücke, Manfred |
| BookMark | eNptkdlKQzEQhoMouN75AHkAq1lOU3PpbqEiLr0Oc5JJjZwmJYkXfXvjBiLOzSz8388Ms0s2Y4pIyCFnx1JqdgKrFRdcc8aU3CA7gk3USHZ8svmr3iYHpbyyFprLU852SDqHNZYAkd4GzJDtS7Aw0LvkcBhCXFCfMp1Hi7lCiHVNH94g1uCbqoYUaYj0ftXAj6Zxzy-Yly0_Ns9SoXE0eTq7uqRP61JxWfbJloeh4MF33iPz66vni9vR7P5menE2G1mhdB1xhu4UNR8rmDCtgUNnvZBWi94p6NtYWM7RWcnQN4XoUXXOAdcWeuGc3CPTL1-X4NWsclhCXpsEwXwOUl4YyDXYAU0_8dBp5TiwrgMtNIBSY-eZkAgOsXmJLy-bUykZvbGhfl5cM4TBcGY-PmB-f6BBR3-gnyX-lb8DLkKMHQ |
| CitedBy_id | crossref_primary_10_3390_app13031938 crossref_primary_10_1007_s00501_024_01457_5 crossref_primary_10_1016_j_microrel_2024_115399 crossref_primary_10_3389_fsuep_2024_1343339 |
| Cites_doi | 10.1201/b16018 10.1016/j.jmsy.2022.05.010 10.1016/j.sse.2015.05.039 10.1002/9780470684023 10.1016/j.microrel.2011.07.063 10.1080/09506608.2019.1565716 10.1007/978-3-319-23395-6 10.1016/j.eswa.2014.10.021 10.1016/j.ress.2022.108710 10.1109/TDMR.2016.2516044 10.3390/geosciences12010027 10.1093/oso/9780198522195.001.0001 10.1109/RAM.2017.7889736 10.1109/THERMINIC49743.2020.9420536 10.1016/B978-0-12-396502-8.00018-8 10.1016/j.ress.2017.11.020 10.3390/sym14061219 10.1007/978-1-4614-3067-4 10.1016/j.strusafe.2008.06.020 10.1111/j.2517-6161.1968.tb00722.x 10.3390/mi3010078 10.1109/EuroSimE.2015.7103167 10.1016/j.engappai.2020.103678 10.1117/12.2240464 10.1201/9781420011456 10.1177/0049124103257303 10.1063/1.1699114 10.1007/978-3-319-11259-6 10.1007/978-3-319-12385-1 10.1515/9780691214696 10.1080/00224065.2014.11917951 10.1109/TDMR.2012.2190415 10.1007/978-1-4471-4588-2 10.1137/1.9780898717921 10.1002/lpor.202000254 10.1016/j.eswa.2021.115627 10.1016/j.ejor.2010.11.018 10.1137/100788604 10.1080/10618600.2017.1407325 10.1016/j.ress.2015.11.009 10.1093/biomet/57.1.97 10.1007/978-1-4757-4286-2 10.36001/ijphm.2015.v6i4.2289 10.1016/j.probengmech.2015.09.007 10.1076/iaij.4.1.5.16466 10.1016/j.microrel.2018.01.005 10.1109/ICEPT52650.2021.9568181 10.1016/j.ress.2015.05.009 10.1109/TPEL.2020.3024914 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.3390/app121910063 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Sciences (General) |
| EISSN | 2076-3417 |
| ExternalDocumentID | oai_doaj_org_article_b7fa496d1a044a929aa665df023eadee 10_3390_app121910063 |
| GroupedDBID | .4S 2XV 5VS 7XC 8CJ 8FE 8FG 8FH AADQD AAFWJ AAYXX ADBBV ADMLS AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS APEBS ARCSS BCNDV BENPR CCPQU CITATION CZ9 D1I D1J D1K GROUPED_DOAJ IAO IGS ITC K6- K6V KC. KQ8 L6V LK5 LK8 M7R MODMG M~E OK1 P62 PHGZM PHGZT PIMPY PROAC TUS PUEGO |
| ID | FETCH-LOGICAL-c269t-10ed8e9156a7099a1a4cf23c92bd6ab56a2c11edc30ef7092be64dda19cab2dd3 |
| IEDL.DBID | DOA |
| ISSN | 2076-3417 |
| IngestDate | Wed Aug 27 01:23:01 EDT 2025 Tue Jul 01 00:41:38 EDT 2025 Thu Apr 24 23:07:46 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 19 |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c269t-10ed8e9156a7099a1a4cf23c92bd6ab56a2c11edc30ef7092be64dda19cab2dd3 |
| ORCID | 0000-0002-3960-4296 0000-0001-5188-8845 0000-0001-7734-5603 |
| OpenAccessLink | https://doaj.org/article/b7fa496d1a044a929aa665df023eadee |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_b7fa496d1a044a929aa665df023eadee crossref_citationtrail_10_3390_app121910063 crossref_primary_10_3390_app121910063 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2022-10-01 |
| PublicationDateYYYYMMDD | 2022-10-01 |
| PublicationDate_xml | – month: 10 year: 2022 text: 2022-10-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Applied sciences |
| PublicationYear | 2022 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | ref_50 ref_58 Durand (ref_10) 2016; 16 ref_13 ref_56 ref_55 Umlauf (ref_44) 2018; 27 ref_53 ref_51 ref_19 ref_18 ref_15 Ibrahim (ref_42) 2021; 185 Li (ref_38) 2014; 46 Hastings (ref_61) 1970; 57 Bahrami (ref_1) 2020; 65 Mishra (ref_29) 2018; 172 ref_25 Geyer (ref_68) 1992; 7 ref_23 ref_67 ref_22 ref_66 ref_21 ref_65 Vazquez (ref_5) 2015; 111 ref_20 ref_26 Siddique (ref_11) 2022; 12 Dai (ref_28) 2022; 226 Lynch (ref_60) 2004; 32 Ibrahim (ref_33) 2020; 14 Dempster (ref_48) 1968; 30 ref_36 Sutharssan (ref_35) 2012; 3 Fan (ref_34) 2012; 12 ref_30 Qian (ref_8) 2016; 147 Zhao (ref_37) 2021; 36 Kiureghian (ref_14) 2009; 31 Peharz (ref_57) 2014; Volume 1 Si (ref_32) 2011; 213 Lall (ref_39) 2015; 137 (ref_63) 2019; 2019 Allmaras (ref_54) 2013; 55 Ferreira (ref_31) 2022; 63 Nagel (ref_24) 2016; 43 Fan (ref_40) 2015; 42 ref_47 ref_46 ref_45 ref_43 Fink (ref_17) 2020; 92 ref_41 Andrade (ref_27) 2015; 142 Gilks (ref_59) 1994; 43 ref_2 Metropolis (ref_62) 1953; 21 Magnien (ref_52) 2018; 82 ref_49 Chang (ref_3) 2012; 52 ref_9 Walker (ref_12) 2003; 4 Zhang (ref_16) 2020; 2020 ref_4 ref_7 ref_6 Roberts (ref_64) 1997; 7 |
| References_xml | – ident: ref_9 – ident: ref_23 doi: 10.1201/b16018 – volume: 63 start-page: 550 year: 2022 ident: ref_31 article-title: Remaining Useful Life prediction and challenges: A literature review on the use of Machine Learning Methods publication-title: J. Manuf. Syst. doi: 10.1016/j.jmsy.2022.05.010 – ident: ref_55 – volume: 43 start-page: 169 year: 1994 ident: ref_59 article-title: A language and program for complex Bayesian modelling publication-title: J. R. Stat. Soc. Ser. D – volume: 111 start-page: 111 year: 2015 ident: ref_5 article-title: High-power UV-LED degradation: Continuous and cycled working condition influence publication-title: Solid-State Electron. doi: 10.1016/j.sse.2015.05.039 – ident: ref_58 doi: 10.1002/9780470684023 – ident: ref_26 – ident: ref_51 – volume: 52 start-page: 762 year: 2012 ident: ref_3 article-title: Light emitting diodes reliability review publication-title: Microelectron. Reliab. doi: 10.1016/j.microrel.2011.07.063 – volume: 65 start-page: 102 year: 2020 ident: ref_1 article-title: Degradation of optical materials in solid-state lighting systems publication-title: Int. Mater. Rev. doi: 10.1080/09506608.2019.1565716 – ident: ref_15 doi: 10.1007/978-3-319-23395-6 – volume: 42 start-page: 2411 year: 2015 ident: ref_40 article-title: Predicting long-term lumen maintenance life of LED light sources using a particle filter-based prognostic approach publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2014.10.021 – volume: 226 start-page: 108710 year: 2022 ident: ref_28 article-title: Reliability modelling of wheel wear deterioration using conditional bivariate gamma processes and Bayesian hierarchical models publication-title: Reliab. Eng. Syst. Saf. doi: 10.1016/j.ress.2022.108710 – ident: ref_65 – volume: 16 start-page: 80 year: 2016 ident: ref_10 article-title: Power Cycling Reliability of Power Module: A Survey publication-title: IEEE Trans. Device Mater. Reliab. doi: 10.1109/TDMR.2016.2516044 – volume: 137 start-page: 021002:1 year: 2015 ident: ref_39 article-title: Assessment of lumen degradation and remaining life of light-emitting diodes using physics-based indicators and particle filter publication-title: AMSE J. Electron. Packag. – volume: 12 start-page: 27:1 year: 2022 ident: ref_11 article-title: A Survey of Uncertainty Quantification in Machine Learning for Space Weather Prediction publication-title: Geosciences doi: 10.3390/geosciences12010027 – ident: ref_56 doi: 10.1093/oso/9780198522195.001.0001 – ident: ref_30 doi: 10.1109/RAM.2017.7889736 – ident: ref_43 doi: 10.1109/THERMINIC49743.2020.9420536 – volume: Volume 1 start-page: 989 year: 2014 ident: ref_57 article-title: Introduction to probabilistic graphical models publication-title: Academic Press Library in Signal Processing: Signal Processing Theory and Machine Learning doi: 10.1016/B978-0-12-396502-8.00018-8 – volume: 172 start-page: 25 year: 2018 ident: ref_29 article-title: Bayesian hierarchical model-based prognostics for lithium-ion batteries publication-title: Reliab. Eng. Syst. Saf. doi: 10.1016/j.ress.2017.11.020 – ident: ref_47 doi: 10.3390/sym14061219 – ident: ref_2 doi: 10.1007/978-1-4614-3067-4 – volume: 31 start-page: 105 year: 2009 ident: ref_14 article-title: Aleatory or epistemic? Does it matter? publication-title: Struct. Saf. doi: 10.1016/j.strusafe.2008.06.020 – volume: 30 start-page: 205 year: 1968 ident: ref_48 article-title: A generalization of Bayesian inference publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1968.tb00722.x – volume: 3 start-page: 78 year: 2012 ident: ref_35 article-title: Prognostics and Health Monitoring of High Power LED publication-title: Micromachines doi: 10.3390/mi3010078 – volume: 7 start-page: 473 year: 1992 ident: ref_68 article-title: Practical Markov Chain Monte Carlo publication-title: Stat. Sci. – ident: ref_41 doi: 10.1109/EuroSimE.2015.7103167 – volume: 7 start-page: 110 year: 1997 ident: ref_64 article-title: Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms publication-title: Ann. Appl. Probab. – ident: ref_66 – volume: 92 start-page: 103678 year: 2020 ident: ref_17 article-title: Potential, challenges and future directions for deep learning in prognostics and health management applications publication-title: Eng. Appl. Artif. Intell. doi: 10.1016/j.engappai.2020.103678 – ident: ref_7 doi: 10.1117/12.2240464 – volume: 2019 start-page: 8740426 year: 2019 ident: ref_63 article-title: Hierarchical Models and Tuning of Random Walk Metropolis Algorithms publication-title: J. Probab. Stat. – ident: ref_20 – ident: ref_13 doi: 10.1201/9781420011456 – volume: 32 start-page: 301 year: 2004 ident: ref_60 article-title: Bayesian Posterior Predictive Checks for Complex Models publication-title: Sociol. Methods Res. doi: 10.1177/0049124103257303 – volume: 21 start-page: 1087 year: 1953 ident: ref_62 article-title: Equations of state calculations by fast computing machines publication-title: J. Chem. Phys. doi: 10.1063/1.1699114 – ident: ref_25 doi: 10.1007/978-3-319-11259-6 – ident: ref_45 doi: 10.1007/978-3-319-12385-1 – ident: ref_49 doi: 10.1515/9780691214696 – ident: ref_67 – volume: 46 start-page: 1 year: 2014 ident: ref_38 article-title: Application of Bayesian Methods in Reliability Data Analyses publication-title: J. Qual. Technol. doi: 10.1080/00224065.2014.11917951 – volume: 12 start-page: 470 year: 2012 ident: ref_34 article-title: Lifetime estimation of high-power white LED using degradation-data-driven method publication-title: IEEE Trans. Device Mater. Reliab. doi: 10.1109/TDMR.2012.2190415 – ident: ref_46 doi: 10.1007/978-1-4471-4588-2 – ident: ref_53 doi: 10.1137/1.9780898717921 – volume: 14 start-page: 200254:1 year: 2020 ident: ref_33 article-title: Machine Learning and Digital Twin Driven Diagnostics and Prognostics of Light-Emitting Diodes publication-title: Laser Photonics Rev. doi: 10.1002/lpor.202000254 – volume: 185 start-page: 115627:1 year: 2021 ident: ref_42 article-title: Bayesian based lifetime prediction for high-power white LEDs publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2021.115627 – ident: ref_21 – volume: 213 start-page: 1 year: 2011 ident: ref_32 article-title: Remaining useful life estimation - A review on the statistical data driven approaches publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2010.11.018 – volume: 55 start-page: 149 year: 2013 ident: ref_54 article-title: Estimating parameters in physical models through Bayesian inversion: A complete example publication-title: SIAM Rev. doi: 10.1137/100788604 – volume: 27 start-page: 612 year: 2018 ident: ref_44 article-title: BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond) publication-title: J. Comput. Graph. Stat. doi: 10.1080/10618600.2017.1407325 – volume: 147 start-page: 84 year: 2016 ident: ref_8 article-title: An accelerated test method of luminous flux depreciation for LED luminaires and lamps publication-title: Reliab. Eng. Syst. Saf. doi: 10.1016/j.ress.2015.11.009 – volume: 57 start-page: 97 year: 1970 ident: ref_61 article-title: Monte Carlo sampling methods using Markov chains and their applications publication-title: Biometrika doi: 10.1093/biomet/57.1.97 – ident: ref_6 – ident: ref_19 doi: 10.1007/978-1-4757-4286-2 – ident: ref_50 – ident: ref_18 doi: 10.36001/ijphm.2015.v6i4.2289 – volume: 43 start-page: 68 year: 2016 ident: ref_24 article-title: A unified framework for multilevel uncertainty quantification in Bayesian inverse problems publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2015.09.007 – volume: 4 start-page: 5 year: 2003 ident: ref_12 article-title: Defining Uncertainty: A Conceptual Basis for Uncertainty Management in Model-Based Decision Support publication-title: Integr. Assess. doi: 10.1076/iaij.4.1.5.16466 – volume: 82 start-page: 84 year: 2018 ident: ref_52 article-title: Parameter driven monitoring for a flip-chip LED module under power cycling condition publication-title: Microelectron. Reliab. doi: 10.1016/j.microrel.2018.01.005 – volume: 2020 start-page: 6068203:1 year: 2020 ident: ref_16 article-title: Basic Framework and Main Methods of Uncertainty Quantification publication-title: Math. Probl. Eng. – ident: ref_36 doi: 10.1109/ICEPT52650.2021.9568181 – volume: 142 start-page: 169 year: 2015 ident: ref_27 article-title: Statistical modelling of railway track geometry degradation using Hierarchical Bayesian models publication-title: Reliab. Eng. Syst. Saf. doi: 10.1016/j.ress.2015.05.009 – ident: ref_22 – volume: 36 start-page: 4633 year: 2021 ident: ref_37 article-title: An Overview of Artificial Intelligence Applications for Power Electronics publication-title: IEEE Trans. Power Electron. doi: 10.1109/TPEL.2020.3024914 – ident: ref_4 doi: 10.1007/978-1-4614-3067-4 |
| SSID | ssj0000913810 |
| Score | 2.24719 |
| Snippet | Remaining useful life (RUL) prediction is central to prognostics and reliability assessment of light-emitting diode (LED) systems. Their unknown long-term... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| StartPage | 10063 |
| SubjectTerms | Bayesian hierarchical modelling LED system power cycling remaining useful life thermal resistance uncertainty quantification |
| Title | Bayesian Hierarchical Modelling for Uncertainty Quantification in Operational Thermal Resistance of LED Systems |
| URI | https://doaj.org/article/b7fa496d1a044a929aa665df023eadee |
| Volume | 12 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA6iFz2I9YHPkoOCIotNNpvuHq1WivjGgrclj1kolLbo9uC_dya7lvUgXryG2RAmk_lmNpNvGDtGjLXedG2kvIZIpQlExDIVKQ0itYlEd0iJ4v2DHgzV7Vvy1mj1RTVhFT1wpbgL2y2MyrQXpqOUQTA3RuvEF4g1VOsL5H0R8xrJVPDBmSDqqqrSPca8nu6DBZ5OQZj8A4MaVP0BU2422HodDPLLahEttgSTTbbWoAjcZK368H3w05oh-myLTXvmE-j1Ix-M6AFx6Gcy5tTXLFBsc4xE-RC_Ctf95Sd_npuqKCjsAx9N-OMM3uv_gBxNBd3zmL_gnBQsOuDTgt_1r3nNZ77Nhjf916tBVHdOiJzUWYm-FXwKGeZmposhoBFGuULGLpPWa2NxWDohwLu4AwVKSAtaeW9E5oyV3sc7bHkyncAu41YlGUBSQOJAycJZo2Mf21TZzPtO4fbY-bcuc1fTilN3i3GO6QVpPm9qfo-dLKRnFZ3GL3I92paFDJFghwE0jbw2jfwv09j_j0kO2KqkFw-hfu-QLZfvczjCOKS0bbbS6z88vbSD6X0Bg-Dgog |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Bayesian+Hierarchical+Modelling+for+Uncertainty+Quantification+in+Operational+Thermal+Resistance+of+LED+Systems&rft.jtitle=Applied+sciences&rft.au=Dvorzak%2C+Michaela&rft.au=Magnien%2C+Julien&rft.au=Kleb%2C+Ulrike&rft.au=Kraker%2C+Elke&rft.date=2022-10-01&rft.issn=2076-3417&rft.eissn=2076-3417&rft.volume=12&rft.issue=19&rft.spage=10063&rft_id=info:doi/10.3390%2Fapp121910063&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_app121910063 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2076-3417&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2076-3417&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2076-3417&client=summon |