{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T17:07:42Z","timestamp":1769879262388,"version":"3.49.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T00:00:00Z","timestamp":1676505600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T00:00:00Z","timestamp":1676505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003945","name":"Link\u00f6ping University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003945","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Combining performance and numerical stability is a key issue in co-simulation. The Transmission Line Modeling method uses physically motivated communication delays to ensure numerical stability for stiff connections. However, using a fixed communication delay may limit performance for some models. This paper proposes Steady-State Identification for enabling variable communication delays. Three algorithms for online Steady-State Identification are evaluated in three different co-simulation models. All algorithms are able to identify steady state and can thereby determine when communication delays can be allowed to increase without compromising accuracy and stability. The results show a reduction in number of the solver derivative evaluations by roughly 40\u201360% depending on the model. The proposed method additionally supports connections with asymmetric communication delays, which allows each sub-model to independently control the delay of its input variables. Models supporting delay-size control can thereby be connected to those that do not, so that the step length of each individual sub-model is maximized. Controlling the delay-size in sub-models also makes the method independent of the master co-simulation algorithm.<\/jats:p>","DOI":"10.1007\/s00366-023-01791-1","type":"journal-article","created":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T11:03:11Z","timestamp":1676545391000},"page":"301-312","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Transmission line modeling co-simulation with distributed delay-size control using steady-state identification"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7480-1922","authenticated-orcid":false,"given":"Robert","family":"Braun","sequence":"first","affiliation":[]},{"given":"Robert","family":"H\u00e4llqvist","sequence":"additional","affiliation":[]},{"given":"Dag","family":"Fritzson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,16]]},"reference":[{"key":"1791_CR1","doi-asserted-by":"publisher","unstructured":"Benedikt M, Drenth E (2017) Relaxing stiff system integration by smoothing techniques for non-iterative co-simulation. In: IUTAM symposium on solver-coupling and co-simulation, Darmstadt, Germany. https:\/\/doi.org\/10.1007\/978-3-030-14883-6_1","DOI":"10.1007\/978-3-030-14883-6_1"},{"issue":"5","key":"1791_CR2","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1080\/13873954.2013.784340","volume":"19","author":"M Benedikt","year":"2013","unstructured":"Benedikt M, Watzenig D, Hofer A (2013) Modelling and analysis of the non-iterative coupling process for co-simulation. Math Comput Model Dyn Syst 19(5):451\u2013470. https:\/\/doi.org\/10.1080\/13873954.2013.784340","journal-title":"Math Comput Model Dyn Syst"},{"key":"1791_CR3","volume-title":"System identification: theory for the user","author":"L Ljung","year":"1999","unstructured":"Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice Hall, Upper Saddle River","edition":"2"},{"issue":"3","key":"1791_CR4","doi-asserted-by":"publisher","first-page":"179","DOI":"10.4173\/mic.2018.3.4","volume":"39","author":"D Fritzson","year":"2018","unstructured":"Fritzson D, Braun R, Hartford J (2018) Composite modelling in 3-D mechanics utilizing transmission line modelling (TLM) and functional mock-up interface (FMI). Model Identif Control 39(3):179\u2013190. https:\/\/doi.org\/10.4173\/mic.2018.3.4","journal-title":"Model Identif Control"},{"key":"1791_CR5","doi-asserted-by":"crossref","unstructured":"Braun R, Krus P (2014) An explicit method for decoupled distributed solvers in an equation-based modelling language. In: Proceedings of the 6th international workshop on equation-based object-oriented modeling languages and tools, pp 57\u201364","DOI":"10.1145\/2666202.2666212"},{"key":"1791_CR6","unstructured":"Braun R, H\u00e4llqvist R, Fritzson (2017) TLM-based asynchronous co-simulation with the functional mockup interface. In: IUTAM symposium on solver-coupling and co-simulation, Darmstadt, Germany"},{"key":"1791_CR7","volume-title":"Ljud Och Vibrationer","author":"H Boden","year":"1999","unstructured":"Boden H, Carlsson U, Glav R, Wallin H, \u00c5bom M (1999) Ljud Och Vibrationer. Kungliga Tekniska H\u00f6gskolan, Institutionen f\u00f6r farkostteknik, Stockholm, Sweden"},{"key":"1791_CR8","doi-asserted-by":"crossref","unstructured":"Schierz T, Arnold M, Clau\u00df C (2012) Co-simulation with communication step size control in an FMI compatible master algorithm. In: 9th International Modelica conference, Munich, Germany, pp 205\u2013214","DOI":"10.3384\/ecp12076205"},{"key":"1791_CR9","doi-asserted-by":"crossref","unstructured":"Kraft J, Meyer T, Schweizer B (2019) Reduction of the computation time of large multibody systems with co-simulation methods. In: Schweizer B (ed) IUTAM symposium on solver-coupling and co-simulation. Springer, Cham, pp 131\u2013152","DOI":"10.1007\/978-3-030-14883-6_8"},{"issue":"5","key":"1791_CR10","doi-asserted-by":"publisher","first-page":"4501","DOI":"10.1007\/s00366-022-01610-z","volume":"38","author":"Y Eguillon","year":"2022","unstructured":"Eguillon Y, Lacabanne B, Tromeur-Dervout D (2022) F3ornits: a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilities. Eng Comput 38(5):4501\u20134543. https:\/\/doi.org\/10.1007\/s00366-022-01610-z","journal-title":"Eng Comput"},{"key":"1791_CR11","doi-asserted-by":"publisher","unstructured":"Meyer T, Kraft J, Schweizer B (2021) Co-simulation: error estimation and macro-step size control. J Comput Nonlinear Dyn 16(4). https:\/\/doi.org\/10.1115\/1.4048944. 041002","DOI":"10.1115\/1.4048944"},{"issue":"3","key":"1791_CR12","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1177\/003754979807100304","volume":"71","author":"A Leva","year":"1998","unstructured":"Leva A, Bartolini A, Maffezzoni C (1998) A process simulation environment based on visual programming and dynamic decoupling. Simulation 71(3):183\u2013193","journal-title":"Simulation"},{"issue":"10","key":"1791_CR13","doi-asserted-by":"publisher","first-page":"1158","DOI":"10.1177\/0037549714547296","volume":"90","author":"AV Papadopoulos","year":"2014","unstructured":"Papadopoulos AV, Leva A (2014) Automating efficiency-targeted approximations in modelling and simulation tools: dynamic decoupling and mixed-mode integration. Simulation 90(10):1158\u20131176. https:\/\/doi.org\/10.1177\/0037549714547296","journal-title":"Simulation"},{"issue":"3","key":"1791_CR14","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1177\/0037549716684026","volume":"93","author":"ABK-E Feki","year":"2017","unstructured":"Feki ABK-E, Duval L, Faure C, Simon D, Gaid MB (2017) Choptrey: contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems. Simulation 93(3):185\u2013200. https:\/\/doi.org\/10.1177\/0037549716684026","journal-title":"Simulation"},{"key":"1791_CR15","doi-asserted-by":"publisher","unstructured":"Busch M (2019) Performance improvement of explicit co-simulation methods through continuous extrapolation. In: Schweizer B (ed) IUTAM symposium on solver-coupling and co-simulation. Springer, Cham, pp 57\u201380. https:\/\/doi.org\/10.1007\/978-3-030-14883-6_4","DOI":"10.1007\/978-3-030-14883-6_4"},{"key":"1791_CR16","doi-asserted-by":"publisher","unstructured":"M\u00fcller W, Breitenecker F (2016) An explicit approach for asynchronous step size control in co-simulation. In: ASIM 2016 23. Symposium Simulationstechnik, pp. 75\u201380. https:\/\/doi.org\/10.11128\/arep.52","DOI":"10.11128\/arep.52"},{"key":"1791_CR17","unstructured":"Jansson A, Krus P, Palmberg J.O (1992) Variable time step size applied to simulation of fluid power systems using transmission line elements. In: Fifth bath international fluid power workshop, Bath, England"},{"issue":"2","key":"1791_CR18","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1002\/jnm.1660030208","volume":"3","author":"SH Pulko","year":"1990","unstructured":"Pulko SH, Mallik A, Allen R, Johns PB (1990) Automatic timestepping in TLM routines for the modelling of thermal diffusion processes. Int J Numer Model Electron Netw Devices Fields 3(2):127\u2013136. https:\/\/doi.org\/10.1002\/jnm.1660030208","journal-title":"Int J Numer Model Electron Netw Devices Fields"},{"key":"1791_CR19","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1049\/ip-a-3.1993.0046","volume":"140","author":"SYR Hui","year":"1993","unstructured":"Hui SYR, Fung KK, Zhang MQ, Christopoulos C (1993) Variable time step technique for transmission line modelling. IEE Proc A (Sci Meas Technol) 140:299\u20133023. https:\/\/doi.org\/10.1049\/ip-a-3.1993.0046","journal-title":"IEE Proc A (Sci Meas Technol)"},{"key":"1791_CR20","doi-asserted-by":"publisher","unstructured":"H\u00e4llqvist R (2019) On standardized model integration: automated validation in aircraft system simulation. Licentiate thesis, Link\u00f6ping University. https:\/\/doi.org\/10.3384\/lic.diva-162810","DOI":"10.3384\/lic.diva-162810"},{"key":"1791_CR21","doi-asserted-by":"crossref","unstructured":"Krus P (2009) Whole mission simulation for aircraft system design and optimization. In: Proceedings of the CEAS 2009 European air and space conference","DOI":"10.2514\/6.2010-1320"},{"key":"1791_CR22","doi-asserted-by":"crossref","unstructured":"H\u00e4llqvist R, Eek M, Braun R, Krus P (2016) Methods for automating model validation: steady-state identification applied on gripen fighter environmental control system measurements. In: Proceedings of the 30th congress of the international council of the aeronautical sciences. international council of the aeronautical sciences, DCC, Daejon, Korea","DOI":"10.3384\/ecp15119199"},{"issue":"6","key":"1791_CR23","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0959-1524(95)00009-F","volume":"5","author":"S Cao","year":"1995","unstructured":"Cao S, Rhinehart RR (1995) An efficient method for on-line identification of steady state. J Process Control 5(6):363\u2013374. https:\/\/doi.org\/10.1016\/0959-1524(95)00009-F","journal-title":"J Process Control"},{"issue":"2","key":"1791_CR24","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1214\/aoms\/1177731746","volume":"12","author":"J von Neumann","year":"1941","unstructured":"von Neumann J, Kent RH, Bellinson HR, Hart BI (1941) The mean square successive difference. Ann Math Stat 12(2):153\u2013162. https:\/\/doi.org\/10.1214\/aoms\/1177731746","journal-title":"Ann Math Stat"},{"key":"1791_CR25","doi-asserted-by":"publisher","DOI":"10.1201\/9780203022184","volume-title":"Transmission line matrix (TLM) in computational mechanics","author":"D De Cogan","year":"2005","unstructured":"De Cogan D, O\u2019Connor WJ, Pulko S (2005) Transmission line matrix (TLM) in computational mechanics. CRC Press, Boca Raton, Florida"},{"key":"1791_CR26","unstructured":"Nakhimovski I (2006) Contributions to the modeling and simulation of mechanical systems with detailed contact analyses. PhD thesis, Link\u00f6ping University, PELAB\u2014Programming Environment Laboratory, The Institute of Technology"},{"key":"1791_CR27","doi-asserted-by":"crossref","unstructured":"Braun R, Fritzson D (2022) Numerically robust co-simulation using transmission line modelling and the functional mockup interface. Simulation","DOI":"10.1177\/00375497221097128"},{"key":"1791_CR28","doi-asserted-by":"crossref","unstructured":"Ochel L, Braun R, Thiele B, Asghar A, Buffoni L, Eek M, Fritzson P, Fritzson D, Horkeby S, H\u00e4llquist R, \u00c5ke Kinnander Palanisamy A, Pop A, Sj\u00f6lund M (2019) OMSimulator-integrated FMI and TLM-based co-simulation with composite model editing and SSP. In: 13th International Modelica conference","DOI":"10.3384\/ecp1915769"},{"key":"1791_CR29","doi-asserted-by":"publisher","unstructured":"Xu H, Wu J, Tseng T.L.B (2018) An efficient method for online identification of steady state for multivariate system. In: International manufacturing science and engineering conference, vol. 4: processes. https:\/\/doi.org\/10.1115\/MSEC2018-6565. V004T03A005","DOI":"10.1115\/MSEC2018-6565"},{"issue":"3","key":"1791_CR30","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1145\/1089014.1089020","volume":"31","author":"AC Hindmarsh","year":"2005","unstructured":"Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005) SUNDIALS: suite of nonlinear and differential\/algebraic equation solvers. ACM Trans Math Softw (TOMS) 31(3):363\u2013396","journal-title":"ACM Trans Math Softw (TOMS)"},{"key":"1791_CR31","unstructured":"Modelica and the Modelica Association. https:\/\/www.modelica.org\/. Accessed 25 Apr 2022"},{"key":"1791_CR32","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545669","volume-title":"Principles of object oriented modeling and simulation with Modelica 2.1","author":"P Fritzson","year":"2004","unstructured":"Fritzson P (2004) Principles of object oriented modeling and simulation with Modelica 2.1. Wiley-IEEE Press, Hoboken. https:\/\/doi.org\/10.1109\/9780470545669"},{"issue":"4","key":"1791_CR33","doi-asserted-by":"publisher","first-page":"241","DOI":"10.4173\/mic.2020.4.1","volume":"41","author":"P Fritzson","year":"2020","unstructured":"...Fritzson P, Pop A, Abdelhak K, Ashgar A, Bachmann B, Braun W, Bouskela D, Braun R, Buffoni L, Casella F, Castro R, Franke R, Fritzson D, Gebremedhin M, Heuermann A, Lie B, Mengist A, Mikelsons L, Moudgalya K, Ochel L, Palanisamy A, Ruge V, Schamai W, Sj\u00f6lund M, Thiele B, Tinnerholm J, \u00d6stlund P (2020) The OpenModelica integrated environment for modeling, simulation, and model-based development. Model Identif Control Nor Res Bull 41(4):241\u2013295. https:\/\/doi.org\/10.4173\/mic.2020.4.1","journal-title":"Model Identif Control Nor Res Bull"},{"key":"1791_CR34","unstructured":"Junghanns A, Gomes C, Schulze C, Schuch K, Pierre R, Blaesken M, Zacharias I, Pillekeit A, Wernersson K, Sommer T (2021) The functional mock-up interface 3.0-new features enabling new applications. In: Modelica conferences, pp 17\u201326"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01791-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01791-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01791-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T02:03:52Z","timestamp":1706753032000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01791-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,16]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["1791"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01791-1","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,16]]},"assertion":[{"value":"8 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}