Development of a validation method for multivariate arbitrarily distributed results

Kurzfassung

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, 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 whether 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 whether 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 evidenced 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 by means of an example, that it is meaningful to use the developed validation method for engineering problems. Using the developed method, it is now possible to validate stochastic numerical models without assuming distributions for the experimental and numerical results. In this method, it is also possible to incorporate the measurement uncertainties and the simulation uncertainties in its distance measure.