In order to stay competitive the requirements on machinery in the producing industry have enormously increased. Within the automation industry these demands, like higher throughput or better energy efficiency, result in increasing complexity of the installed plants. Additionally, Industry 4.0 and the Internet of Things continuously increase the amount of software. Using model-based development methods is one approach to deal with this complexity. But model-based methods can also be utilized during the operational phase of a plant in order to generate additional value for the plant operator. Introducing smart services based on the usage of physical models enables new control and diagnosis features, e.g. the utilization of inverse plant models for feedforward control or comparing the output of a model with measurements of the plant in order to prove for correct behavior. For all these services the accuracy of the considered models is crucial. With an inexact model neither the future behavior can be foreseen nor the control quality can be improved. The used models don’t have to be built up from scratch, existing models already created for sizing can be reused. However, these models cannot be used directly. First a reparametrization is necessary, because effects like friction or manufacturing tolerances cannot be taken into account correctly during sizing. For this special kind of problem dedicated optimization algorithms are available for parameter estimation, which take randomly distributed measurement errors and the special structure of this problem class into account.
In this paper a work flow for parameter estimation based on open source tools is presented, in which the considered models are provided as Functional Mock-up Unit. Afterwards the performance of this work flow is demonstrated on a real industrial problem: A three arm Delta Robot.
Keywords: Parameter Estimation, Levenberg-Marquardt Algorithm, FMI, Least Squares Optimization, Log-likelihood Method
Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017
Sameer Agarwal, Keir Mierle, et al. Ceres solver. http://ceres-solver.org.
Åke Björck. Numerical methods for least squares problems. SIAM, 1996.
Torsten Blochwitz, Martin Otter, Martin Arnold, Constanze Bausch, H Elmqvist, A Junghanns, J Mauß, M Monteiro, T Neidhold, D Neumerkel, et al. The functional mockup interface for tool independent exchange of simulation models. In Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany, number 063, pages 105–114. Linköping University Electronic Press, 2011.
Torsten Blochwitz, Martin Otter, Johan Akesson, Martin Arnold, Christoph Clauss, Hilding Elmqvist, Markus Friedrich, Andreas Junghanns, Jakob Mauss, Dietmar Neumerkel, et al. Functional mockup interface 2.0: The standard for tool independent exchange of simulation models. In Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany, number 076, pages 173–184. Linköping University Electronic Press, 2012.
Reymond Clavel. A fast robot with parallel geometry. In Proc. Int. Symposium on Industrial Robots, pages 91–100, 1988.
Sofia Gedda, Christian Andersson, Johan Åkesson, and Stefan Diehl. Derivative-free parameter optimization of functional mock-up units. In Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany, number 076, pages 819–828. Linköping University Electronic Press, 2012.
Alan C Hindmarsh, Peter N Brown, Keith E Grant, Steven L Lee, Radu Serban, Dan E Shumaker, and Carol S Woodward. Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software (TOMS), 31(3):363–396, 2005.
Ulrich Krengel. Einführung in die Wahrscheinlichkeitstheorie und Statistik, volume 8. Springer, 1988.
DonaldWMarquardt. An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics, 11(2):431–441, 1963.
A. Raue, M. Schilling, J. Bachmann, A. Matteson, M. Schelke, D. Kaschek, S. Hug, C. Kreutz, B. D. Harms, F. J. Theis, U. Klingmüller, and J. Timmer. Lessons learned from quantitative dynamical modeling in systems biology. PLoS ONE, 8(9):e74335, Sept. 2013. doi: https://doi.org/10.1371/journal.pone.0074335.