{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:44:49Z","timestamp":1777902289999,"version":"3.51.4"},"reference-count":22,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2013,12,29]],"date-time":"2013-12-29T00:00:00Z","timestamp":1388275200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>The amount of food transported long distances in reefer containers is constantly increasing and so is the cost per mile because of rising fuel prices. One way to reduce the cost is to minimize the energy consumed by reefer containers through a better controller but in order to achieve this a fast and flexible simulation model is needed for controller development. The simulation model may also be used for developing fault diagnosis methods for the reefer container and thereby further lowering costs by reducing the amount of functioning spare parts that is replaced and by providing early warning for faults enabling preventive maintenance. In this paper the feasibility of using different simulation methods is assessed with the goal of identifying a fast but accurate method that works well in a multi-rate environment. A modular multi-rate simulation environment for a dynamical system consisting of components with different dynamical speeds is presented with an improvement of previous results. The simulation speed is improved by 350% with no reduction in the accuracy of the solution, by substituting the Matlabode15s solver with an explicit first-order solver with a step-size calculation algorithm that ensures numerical stability and that the error is bounded using a minimum of calculations. The reefer container model is simulated using both ode15s and the proposed method both in multi-rate and monolithic configurations. The results are analyzed and compared with respect to speed and accuracy.<\/jats:p>","DOI":"10.1177\/0037549713515542","type":"journal-article","created":{"date-parts":[[2013,12,29]],"date-time":"2013-12-29T20:07:58Z","timestamp":1388347678000},"page":"249-264","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Modular simulation of reefer container dynamics"],"prefix":"10.1177","volume":"90","author":[{"given":"Kresten K","family":"S\u00f8rensen","sequence":"first","affiliation":[{"name":"Section for Automation and Control, Department of Electronic Systems, Aalborg University, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jens D","family":"Nielsen","sequence":"additional","affiliation":[{"name":"Section for Automation and Control, Department of Electronic Systems, Aalborg University, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakob","family":"Stoustrup","sequence":"additional","affiliation":[{"name":"Section for Automation and Control, Department of Electronic Systems, Aalborg University, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2013,12,29]]},"reference":[{"key":"bibr1-0037549713515542","unstructured":"Drewry Shipping Consultants Limited. Reefer shipping market annual report. Report, 2009. London: Drewry Publishing. Available at: http:\/\/www.drewry.co.uk\/get_file.php?id=1161. Accessed December 7, 2013."},{"key":"bibr2-0037549713515542","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05344-7"},{"key":"bibr3-0037549713515542","unstructured":"General Association of German Insurers. Container handbook: Cargo loss prevention information from German marine insurers, http:\/\/www.containerhandbuch.de\/chb_e\/wild\/index.html?\/chb_e\/wild\/wild_08_01_02.html. Accessed December 7, 2013."},{"key":"bibr4-0037549713515542","unstructured":"Maersk Container Industry. Homepage at: http:\/\/www.maerskbox.com\/. Accessed December 7, 2013."},{"key":"bibr5-0037549713515542","volume-title":"Proceedings of Danske K\u00f8ledage","author":"Larsen LSF"},{"key":"bibr6-0037549713515542","volume-title":"Proceedings of the 17th IFAC world congress","author":"Cai J"},{"key":"bibr7-0037549713515542","unstructured":"TRNSYS. Homepage at: http:\/\/sel.me.wisc.edu\/trnsys\/. Accessed December 7, 2013."},{"key":"bibr8-0037549713515542","unstructured":"Dymola\n                      . Homepage at: http:\/\/www.dynasim.se\/index.htm. Accessed December 7, 2013."},{"key":"bibr9-0037549713515542","unstructured":"Modelica\n                      . A unified object-oriented language for physical systems modeling. Available at: http:\/\/www.modelica.org\/documents\/ModelicaSpec30.pdf. Accessed December 7, 2013."},{"key":"bibr10-0037549713515542","first-page":"157","volume-title":"Proceedings of SIMS conference","author":"Skovrup M"},{"key":"bibr11-0037549713515542","unstructured":"Matlab Simulink\n                      . Homepage at: http:\/\/www.mathworks.com\/products\/simulink\/. Accessed December 7, 2013."},{"key":"bibr12-0037549713515542","first-page":"4238","volume-title":"Proceedings of the 18th IFAC world congress","author":"Yang Z"},{"key":"bibr13-0037549713515542","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009810318420"},{"key":"bibr14-0037549713515542","doi-asserted-by":"publisher","DOI":"10.2166\/wst.2006.521"},{"key":"bibr15-0037549713515542","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijrefrig.2007.02.001"},{"key":"bibr16-0037549713515542","first-page":"113","author":"Howe RM","year":"2001","journal-title":"Proceedings of the international society for optical engineering"},{"key":"bibr17-0037549713515542","first-page":"129","volume-title":"11th international conference on computer modelling and simulation","author":"Pearce JG"},{"key":"bibr18-0037549713515542","first-page":"983","volume-title":"Proceedings of the IEEE conference on control applications","author":"S\u00f8rensen KK"},{"key":"bibr19-0037549713515542","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594276424"},{"key":"bibr20-0037549713515542","doi-asserted-by":"publisher","DOI":"10.1002\/0470868279"},{"key":"bibr21-0037549713515542","volume-title":"Advanced engineering mathematics","author":"Kreyzig E","year":"2006","edition":"8"},{"key":"bibr22-0037549713515542","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2004.839572"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549713515542","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0037549713515542","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549713515542","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:25:10Z","timestamp":1777634710000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549713515542"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,29]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,3]]}},"alternative-id":["10.1177\/0037549713515542"],"URL":"https:\/\/doi.org\/10.1177\/0037549713515542","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,29]]}}}