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@PHDTHESIS{vanEnkhuizen:690010,
      author       = {van Enkhuizen, Marinus},
      othercontributors = {Reh, Stefan and Hirt, Gerhard Kurt Peter and Marissen, R.},
      title        = {{D}evelopment of a validation method for multivariate
                      arbitrarily distributed results},
      school       = {Rheinisch-Westfälische Technische Hochschule Aachen},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2017-04769},
      pages        = {1 Online-Ressource (xx, 160 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2017},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, Rheinisch-Westfälische Technische
                      Hochschule Aachen, 2017},
      abstract     = {During product development, engineers and scientist use a
                      variety of numerical models to determine how assemblies,
                      components or parts behave. To describe the behaviour of
                      these products, multiple performance relevant quantities are
                      used such as weight, stiffness, lifetime, efficiency and
                      energy consumption. These performance quantities can be
                      estimated using experiments or numerical models. However, it
                      is often not possible to obtain all performance quantities
                      using one approach. Therefore, it is necessary to combine
                      the experimental and the numerical approach to obtain the
                      performance quantities of interest. Consequently, it is
                      necessary to ensure that both approaches represent reality
                      accurately. To determine whether the numerical results
                      differ from reality, validation is performed. During
                      validation it is determined whether the distance between the
                      numerical results and reality is significant, where reality
                      is represented by the experimental results.In context of
                      validation, it is necessary to point out that experimental
                      results scatter due to variations in the production process
                      and the operation conditions to which the product is
                      subjected. Therefore, it would be appropriate to compare the
                      stochastic experimental results to stochastic numerical
                      results. Since these results are generally multivariate and
                      arbitrarily distributed, it is required to use a validation
                      method that is suitable for arbitrarily distributed
                      multivariate results. However, currently no validation
                      method exists to compare such results.In this work, a method
                      is developed to validate numerical models using arbitrarily
                      distributed multivariate results. To quantify the shape
                      difference between the samples without assuming a
                      distribution function, the underlying distributions of the
                      experimental and numerical results are estimated based on
                      the results. Furthermore, the measurement uncertainties and
                      the numerical uncertainties can be used explicitly in the
                      distance measure for additional information. To determine
                      whether the numerical model is valid, it is determined if
                      the numerical model is significantly different from the
                      experimental results using a hypothesis test. Furthermore,
                      it is determined whether the distance between the numerical
                      results and the experimental results is larger than the
                      uncertainties present in the numerical and experimental
                      results.To investigate if the developed validation method is
                      more effective than the typically used methods for
                      multivariate problems, benchmark tests are performed. Since
                      these distance measures were developed for multivariate
                      normally distributed data, the benchmarks are performed
                      using normally distributed data and a test data set that
                      represents non-normally distributed data. Using these
                      benchmark tests, it is shown that the developed method is
                      more effective to determine the distance between the
                      numerical and the experimental results than the typically
                      used distance measures. Furthermore, it is demonstrated that
                      it is meaningful to use the developed validation method for
                      engineering problems by an example of a spherical
                      indentation model.Using the developed method, it is now
                      possible to validate stochastic numerical models without
                      assuming distribution functions for the experimental and
                      numerical results. It is also possible to incorporate the
                      measurement uncertainties and the simulation uncertainties
                      in the distance measure of this method.},
      cin          = {525420 / 520000},
      ddc          = {620},
      cid          = {$I:(DE-82)525420_20140620$ / $I:(DE-82)520000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2017-04769},
      url          = {https://publications.rwth-aachen.de/record/690010},
}