Abstract
This chapter is devoted to the application of various design of experiment strategies. First, some fundamental questions are addressed in simulation studies, such as “In what order should measurements be carried out?” and “Should corners of the input space be measured?” Then, HILOMOT-DoE, an active learning strategy based on the HILOMOT algorithm, is applied to a structural health monitoring application. In a second application example, HILOMOT-DoE is utilized for efficient combustion engine measurement at a test stand. With this approach, half of the measurement time could be saved compared to conventional DoE strategies, still achieving comparable model quality. Finally, the excitation signal generator proposed in Chap. 19 is very successfully applied to a common rail fuel injection system. The benefits of such a generator-based DoE approach are demonstrated.
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Notes
- 1.
- 2.
This is a special kind of optimal block design that is beyond the scope of this book. It was offered by the software and achieved good results in the past.
- 3.
Because the amount of data is much higher for the global DoE than for each local DoE, the degree of the polynomial is chosen higher as well.
- 4.
Many thanks to my research assistant Tim O. Heinz and my external Ph.D. student Mark Schillinger, Bosch Engineering, for providing me with the above application example.
References
Balageas, D., Fritzen, C.-P., Güemes, A.: Structural health monitoring, vol. 493. Wiley Online Library (2006)
Belz, J., Bamberger, K., Nelles, O.: Order of experimentation for metamodeling tasks. In: International Joint Conference on Neural Networks (IJCNN), pp. 4843–4849, Vancouver, Canada (2016)
Belz, J., Nelles, O.: Function generator application: shall corners be measured? In: Proceedings 25. Workshop Computational Intelligence, Dortmund. KIT Scientific Publishing (2015)
Belz, J., Nelles, O.: Proposal for a function generator and extrapolation analysis. In: 2015 International Symposium on Innovations in Intelligent Systems and Applications (INISTA), pp. 1–6, Madrid, Spain. IEEE (2015)
Bifet, A., Holmes, G., Kirkby, R., Pfahringer, B.: Moa: massive online analysis. J. Mach. Learn. Res. 11, 1601–1604 (2010)
Cai, X., Qiu, H., Gao, L., Shao, X.: Metamodeling for high dimensional design problems by multi-fidelity simulations. Struct. Multidiscip. Optim. 56(1), 151–166 (2017)
Chen, R.-B., Hsieh, D.-N., Hung, Y., Wang, W.: Optimizing Latin hypercube designs by particle swarm. Stat. Comput. 23(5), 663–676 (2013)
Chen, V.C.P., Tsui, K.-L., Barton, R.R., Meckesheimer, M.: A review on design, modeling and applications of computer experiments. IIE Trans. 38(4), 273–291 (2006)
Chiang, M.M.-T., Mirkin, B.: Intelligent choice of the number of clusters in k-means clustering: an experimental study with different cluster spreads. J. Classif. 27(1), 3–40 (2010)
Ciuffo, B., Casas, J., Montanino, M., Perarnau, J., Punzo, V.: Gaussian process metamodels for sensitivity analysis of traffic simulation models: case study of AIMSUN mesoscopic model. Transp. Res. Rec. J. Transp. Res. Board 2390, 87–98 (2013)
Correa, A.A., Grima, P., Tort-Martorell, X.: Experimentation order in factorial designs: new findings. J. Appl. Stat. 39(7), 1577–1591 (2012)
Ebert, T., Fischer, T., Belz, J., Heinz, T.O., Kampmann, G., Nelles, O.: Extended deterministic local search algorithm for maximin Latin hypercube designs. In: 2015 IEEE Symposium Series on Computational Intelligence: IEEE Symposium on Computational Intelligence in Control and Automation (2015 IEEE CICA), Cape Town, South Africa (2015)
Fang, K.-T., Li, R.: Uniform design for computer experiments and its optimal properties. Int. J. Mater. Prod. Technol. 25(1–3), 198–210 (2005)
Ford, I., Titterington, D.M., Kitsos, C.P.: Recent advances in nonlinear experimental design. Technometrics 31(1), 49–60x (1989)
Freeman, J.A.S.: Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189–1232 (2001)
Friedman, J.H.: Multivariate adaptive regression splines (with discussion). Ann. Stat. 19(1), 1–141 (1991)
Grosso, A., Jamali, A., Locatelli, M.: Finding maximin Latin hypercube designs by iterated local search heuristics. Eur. J. Oper. Res. 197(2), 541–547 (2009)
Gutjahr, T., Kleinegräber, H., Ulmer, H., Kruse, T., Eckstein, C.: New approaches for modeling dynamic engine behavior with gaussian processes. In: Röpke, K. (ed.) Design of Experiments (DoE) in Engine Development. Expert Verlag (2013)
Hartmann, B.: Lokale Modellnetze zur Identifikation und Versuchsplanung nichtlinearer Systeme. Ph.D. thesis, Universitätsbibliothek der Universität Siegen (2014)
Hartmann, B., Baumann, W., Nelles, O.: Axes-oblique partitioning of local model networks for engine calibration. In: Design of Experiments (DoE) in Engine Development, pp. 92–106, Berlin, Germany. Expert Verlag (2013)
Hartmann, B., Ebert, T., Nelles, O.: Model-based design of experiments based on local model networks for nonlinear processes with low noise levels. In: American Control Conference (ACC), pp. 5306–5311, 29 2011–July 1 2011 (2011)
Hartmann, B., Moll, J., Nelles, O., Fritzen, C.-P.: Modeling of nonlinear wave velocity characteristics in a structural health monitoring system. In: IEEE International Conference on Control Applications (CCA), Yokohama, Japan (2010)
Hartmann, B., Moll, J., Nelles, O., Fritzen, C.-P.: Hierarchical local model trees for design of experiments in the framework of ultrasonic structural health monitoring. In: IEEE International Conference on Control Applications (CCA), pp. 1163–1170. IEEE (2011)
Hartmann, B., Nelles, O.: Adaptive test planning for the calibration of combustion engines – methodology. In: Design of Experiments (DoE) in Engine Development, pp. 1–16, Berlin, Germany. Expert Verlag (2013)
Hastie, T., Tibshirani, R.: Generalized Additive Models. Wiley Online Library (1990)
Heinz, T.O., Nelles, O.: Vergleich von anregungssignalen für nichtlineare identifikationsaufgaben. In: Hoffman, F., Hüllermeier, E., Mikut, R. (eds.) Proceedings 26. Workshop Computational Intelligence, pp. 139–158. KIT Scientific Publishing (2016)
Heinz, T.O., Schillinger, M., Hartmann, B., Nelles, O.: Excitation signal design for nonlinear dynamic systems. In: Röpke, K., Gühmann, C. (eds.) International Calibration Conference – Automotive Data Analytics, Methods, DoE, pp. 191–208. expertVerlag (2017)
Hilow, H.: Comparison among run order algorithms for sequential factorial experiments. Comput. Stat. Data Anal. 58, 397–406 (2013)
Jin, R., Chen, W., Sudjianto, A.: On sequential sampling for global metamodeling in engineering design. In: ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 539–548. American Society of Mechanical Engineers (2002)
Jin, R., Chen, W., Sudjianto, A.: An efficient algorithm for constructing optimal design of computer experiments. J. Stat. Plan. Inference 134(1), 268–287 (2005)
Johnson, M.E., Moore, L.M., Ylvisaker, D.: Minimax and maximin distance designs. J. Stat. Plan. Inference 26(2), 131–148 (1990)
Johnson, R.T., Montgomery, D.C., Jones, B., Fowler, J.W.: Comparing designs for computer simulation experiments. In: Proceedings of the 40th Conference on Winter Simulation, pp. 463–470. Winter Simulation Conference (2008)
Kajero, O.T., Chen, T., Yao, Y., Chuang, Y.-C., Shan Hill Wong, D.: Meta-modelling in chemical process system engineering. J. Taiwan Inst. Chem. Eng. (2016)
Klein, P., Kirschbaum, F., Hartmann, B., Bogachik, J., Nelles, O.: Adaptive test planning for the calibration of combustion engines – application. In: Design of Experiments (DoE) in Engine Development, pp. 17–30, Berlin, Germany. Expert Verlag (2013)
McKay, D.M., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)
Mirkin, B.: Clustering for Data Mining: A Data Recovery Approach. Chapman & Hall/CRC, London (2005)
Moll, J., Hartmann, B., Chaaban, R., Fritzen, C.-P., Nelles, O.: A novel online learning approach for ultrasonic imaging applied to a non-convex structure. Technical report, Department of Mechanical Engineering (2011)
Moll, J.: Strukturdiagnose mit Ultraschallwellen durch Verwendung von piezoelektrischen Sensoren und Aktoren. Ph.D. thesis, Univ. of Siegen (2011)
Moll, J., Schulte, R.T., Hartmann, B., Fritzen, C.-P., Nelles, O.: Multi-site damage localization in anisotropic plate-like structures using an active guided wave structural health monitoring system. Smart Mater. Struct. 19(4), 045022 (2010)
Montgomery, D.C.: Design and Analysis of Experiments. John Wiley & Sons, Hoboken (2008)
Nelles, O.: Nonlinear System Identification. Springer, Berlin, Germany (2001)
Nelles, O.: Axes-oblique partitioning strategies for local model networks. In: IEEE International Symposium on Intelligent Control, pp. 2378–2383, Munich, Germany (2006)
Niederreiter, H.: Low-discrepancy and low-dispersion sequences. J. Number Theory 30(1), 51–70 (1988)
Pronzato, L., Müller, W.G.: Design of computer experiments: space filling and beyond. Stat. Comput. 22(3), 681–701 (2012)
Rasmussen, C.E., Williams, C.K.I.: Gaussian processes for machine learning. MIT Press, Cambridge, MA (2006)
Bosch GmbH, R. (ed.): Ottomotor-Management, 3rd edn. Friedr. Vieweg & Sohn Verlag (2005)
Schillinger, M., Hartmann, B., Skalecki, P., Meister, M., Nguyen-Tuong, D., Nelles, O.: Safe active learning and safe bayesian optimization for tuning a PI-controller. In: IFAC World Congress, pp. 5967–5972 (2017)
Schillinger, M., Mourat, K., Hartmann, B., Eckstein, C., Jacob, M., Kloppenburg, E., Nelles, O.: Modern online doe methods for calibration – constraint modeling, continuous boundary estimation, and active learning. In: Röpke, K., Gühmann, C. (eds.) Automotive Data Analytics, Methods, DoE. Expert Verlag (2017)
Schillinger, M., Ortelt, B., Hartmann, B., Schreiter, J., Meister, M., Nguyen-Tuong, D., Nelles, O.: Safe active learning of a high pressure fuel supply system. In: 9th EUROSIM Congress on Modelling and Simulation, pp. 286–292 (2016)
Singhee, A., Rutenbar, R.A.: Why Quasi-Monte Carlo is better than Monte Carlo or Latin hypercube sampling for statistical circuit analysis. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(11), 1763–1776 (2010)
Sobol’, I.M.: On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7(4), 86–112 (1967)
Tambouratzis, T.: Counter-clustering for training pattern selection. Comput. J. 43(3), 177–190 (2000)
Tietze, N.: Model-Based Calibration of Engine Control Units Using Gaussian Process Regression. Ph.D. thesis, Technische Universität (2015)
Tietze, N., Konigorski, U., Fleck, C., Nguyen-Tuong, D.: Model-based calibration of engine controller using automated transient design of experiment. In: 14th Stuttgart International Symposium, Wiesbaden. Springer Fachmedien (2014)
Wan, H.-P., Ren, W.-X.: Parameter selection in finite-element-model updating by global sensitivity analysis using gaussian process metamodel. J. Struct. Eng. 141(6), 04014164 (2014)
Wang, G.G.: Adaptive response surface method using inherited Latin hypercube design points. J. Mech. Des. 125(2), 210–220 (2003)
Wang, G.G., Dong, Z., Aitchison, P.: Adaptive response surface method – a global optimization scheme for approximation-based design problems. Eng. Optim. 33(6), 707–734 (2001)
Wang, G.G., Shan, S.: Review of metamodeling techniques in support of engineering design optimization. J. Mech. Des. 129(4), 370–380 (2007)
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Nelles, O. (2020). Design of Experiments. In: Nonlinear System Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-47439-3_26
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