{"id":"https://openalex.org/W4288447647","doi":"https://doi.org/10.3390/en15155483","title":"Shannon Entropy in Stochastic Analysis of Some Mems","display_name":"Shannon Entropy in Stochastic Analysis of Some Mems","publication_year":2022,"publication_date":"2022-07-28","ids":{"openalex":"https://openalex.org/W4288447647","doi":"https://doi.org/10.3390/en15155483"},"language":"en","primary_location":{"id":"doi:10.3390/en15155483","doi":"https://doi.org/10.3390/en15155483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en15155483","pdf_url":"https://www.mdpi.com/1996-1073/15/15/5483/pdf?version=1659098995","source":{"id":"https://openalex.org/S198098182","display_name":"Energies","issn_l":"1996-1073","issn":["1996-1073"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Energies","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1996-1073/15/15/5483/pdf?version=1659098995","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011646983","display_name":"Marcin Kami\u0144ski","orcid":"https://orcid.org/0000-0002-8180-6991","observed_orcids":["https://orcid.org/0000-0002-8180-6991"]},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Marcin Kami\u0144ski","raw_affiliation_strings":["Department of Structural Mechanics, \u0141\u00f3d\u017a University of Technology, 90-924 \u0141\u00f3d\u017a, Poland"],"raw_orcid":"https://orcid.org/0000-0002-8180-6991","affiliations":[{"raw_affiliation_string":"Department of Structural Mechanics, \u0141\u00f3d\u017a University of Technology, 90-924 \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I188884621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078762562","display_name":"Alberto Corigliano","orcid":"https://orcid.org/0000-0002-1285-2724","observed_orcids":["https://orcid.org/0000-0002-1285-2724"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Corigliano","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-1285-2724","affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011646983"],"corresponding_institution_ids":["https://openalex.org/I188884621"],"apc_list":{"value":2200,"currency":"CHF","value_usd":2303},"apc_paid":{"value":2200,"currency":"CHF","value_usd":2303},"fwci":0.2609,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.34545298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"15","issue":"15","first_page":"5483","last_page":"5483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10369","display_name":"Advanced MEMS and NEMS Technologies","score":0.0027000000700354576,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shannon-entropy","display_name":"Shannon entropy","score":0.9990000128746033},{"id":"https://openalex.org/keywords/mems-devices","display_name":"MEMS devices","score":0.8709999918937683},{"id":"https://openalex.org/keywords/error-propagation","display_name":"error propagation","score":0.8240000009536743},{"id":"https://openalex.org/keywords/forced-vibration","display_name":"forced vibration","score":0.6710000038146973},{"id":"https://openalex.org/keywords/microresonators","display_name":"microresonators","score":0.7990000247955322},{"id":"https://openalex.org/keywords/duffing-equation","display_name":"Duffing equation","score":0.9179999828338623},{"id":"https://openalex.org/keywords/polynomial-chaos-expansion","display_name":"polynomial chaos expansion","score":0.5009999871253967},{"id":"https://openalex.org/keywords/interval-algorithm","display_name":"interval algorithm","score":0.5109999775886536},{"id":"https://openalex.org/keywords/structural-parameter-uncertainty","display_name":"structural parameter uncertainty","score":0.527999997138977}],"concepts":[{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.7769577503204346},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6229240298271179},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.6201901435852051},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5542991757392883},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5515440106391907},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5265947580337524},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5213664770126343},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5196717381477356},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4741208851337433},{"id":"https://openalex.org/C37977207","wikidata":"https://www.wikidata.org/wiki/Q175561","display_name":"Microelectromechanical systems","level":2,"score":0.4426899254322052},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.4417647421360016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40996110439300537},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.382395476102829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3527050018310547},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.340493768453598},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22176894545555115},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.1496138572692871},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08845612406730652},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/en15155483","doi":"https://doi.org/10.3390/en15155483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en15155483","pdf_url":"https://www.mdpi.com/1996-1073/15/15/5483/pdf?version=1659098995","source":{"id":"https://openalex.org/S198098182","display_name":"Energies","issn_l":"1996-1073","issn":["1996-1073"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Energies","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1234267","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11311/1234267","pdf_url":"https://re.public.polimi.it/bitstream/11311/1234267/1/energies-15-05483.pdf","source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:gam:jeners:v:15:y:2022:i:15:p:5483-:d:874559","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/1996-1073/15/15/5483/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:fa47d659aac145d38372a6e3a4aaccf2","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/fa47d659aac145d38372a6e3a4aaccf2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Energies, Vol 15, Iss 15, p 5483 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/en15155483","doi":"https://doi.org/10.3390/en15155483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/en15155483","pdf_url":"https://www.mdpi.com/1996-1073/15/15/5483/pdf?version=1659098995","source":{"id":"https://openalex.org/S198098182","display_name":"Energies","issn_l":"1996-1073","issn":["1996-1073"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Energies","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322650","display_name":"Narodowym Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4288447647.pdf","grobid_xml":"https://content.openalex.org/works/W4288447647.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W74194533","https://openalex.org/W186513846","https://openalex.org/W593256384","https://openalex.org/W1540596182","https://openalex.org/W1627581343","https://openalex.org/W1965555277","https://openalex.org/W1978747989","https://openalex.org/W1980388378","https://openalex.org/W1983378807","https://openalex.org/W1983874169","https://openalex.org/W1986466153","https://openalex.org/W1991610061","https://openalex.org/W1995875735","https://openalex.org/W1999094429","https://openalex.org/W1999851267","https://openalex.org/W2005914283","https://openalex.org/W2009443625","https://openalex.org/W2018985144","https://openalex.org/W2031724906","https://openalex.org/W2039208639","https://openalex.org/W2041404167","https://openalex.org/W2042587503","https://openalex.org/W2044894268","https://openalex.org/W2045656688","https://openalex.org/W2055963033","https://openalex.org/W2065257344","https://openalex.org/W2074265648","https://openalex.org/W2122882636","https://openalex.org/W2336509789","https://openalex.org/W2746805505","https://openalex.org/W2792309381","https://openalex.org/W2920283078","https://openalex.org/W3000457639","https://openalex.org/W3110683067","https://openalex.org/W3172914334","https://openalex.org/W4213103663","https://openalex.org/W4255338393","https://openalex.org/W4302564868"],"related_works":["https://openalex.org/W3172914334","https://openalex.org/W1999851267","https://openalex.org/W1980388378","https://openalex.org/W2390576498","https://openalex.org/W2897326134","https://openalex.org/W7118069841","https://openalex.org/W4242372815","https://openalex.org/W1986286822","https://openalex.org/W2484071773","https://openalex.org/W2103984515"],"abstract_inverted_index":{"This":[0,22],"work":[1],"is":[2,24,43,102],"focused":[3],"on":[4],"the":[5,76,93],"numerical":[6],"determination":[7],"of":[8,28,39,52,75],"Shannon":[9],"probabilistic":[10],"entropy":[11,23],"for":[12,45,97],"MEMS":[13,82],"devices":[14],"exhibiting":[15],"some":[16,80,98],"uncertainty":[17,73,112],"in":[18,33,79],"their":[19],"structural":[20,53,64],"response.":[21],"a":[25,105],"universal":[26],"measure":[27],"statistical":[29],"or":[30,36],"stochastic":[31,88],"disorder":[32],"static":[34],"deformation":[35],"dynamic":[37],"vibrations":[38,78,90],"engineering":[40],"systems":[41],"and":[42,48,62,108],"available":[44],"both":[46],"continuous":[47],"discrete":[49],"distributions":[50],"functions":[51],"parameters.":[54],"An":[55],"interval":[56],"algorithm":[57],"using":[58],"Monte":[59],"Carlo":[60],"simulation":[61],"polynomial":[63],"response":[65],"recovery":[66],"has":[67],"been":[68],"implemented":[69],"to":[70],"demonstrate":[71],"an":[72],"propagation":[74],"forced":[77],"small":[81],"devices.":[83],"A":[84],"computational":[85],"example":[86],"includes":[87],"nonlinear":[89],"described":[91],"by":[92],"Duffing":[94],"equation":[95],"calibrated":[96],"micro-resonators,":[99],"whose":[100],"damping":[101],"adopted":[103],"as":[104],"Gaussian,":[106],"uniformly":[107],"triangularly":[109],"distributed":[110],"input":[111],"source.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-07-29T00:00:00"}