Advanced features of Robustimizer
Top three main advanced features of Robustimizer are listed below:
Advantages of analytical propagation of the uncertainty via metamodels [1]
Taking into account higher order moments [2]
Using principal component analysis and sensitivity analysis for dimension reduction [3]
References
[1] O. Nejadseyfi, H.J.M. Geijselaers & A.H. van den Boogaard (2019) Robust optimization based on analytical evaluation of uncertainty propagation, Engineering Optimization, 51:9, 1581-1603, DOI: 10.1080/0305215X.2018.1536752
Abstract:
Optimization under uncertainty requires proper handling of those input parameters that contain scatter. Scatter in input parameters propagates through the process and causes scatter in the output. Stochastic methods (e.g. Monte Carlo) are very popular for assessing uncertainty propagation using black-box function metamodels. However, they are expensive. Therefore, in this article a direct method of calculating uncertainty propagation has been employed based on the analytical integration of a metamodel of a process. Analytical handling of noise variables not only improves the accuracy of the results but also provides the gradients of the output with respect to input variables. This is advantageous in the case of gradient-based optimization. Additionally, it is shown that the analytical approach can be applied during sequential improvement of the metamodel to obtain a more accurate representative model of the black-box function and to enhance the search for the robust optimum.
[2] O. Nejadseyfi, H.J.M. Geijselaers & A.H. van den Boogaard (2019) Evaluation and assessment of non-normal output during robust optimization. Structural and multidisciplinary optimization, 59(6), 2063-2076. https://doi.org/10.1007/s00158-018-2173-2
Abstract:
In this work we present a robustness criterion that employs skewness of output for a metamodel-based robust optimization. The propagation of a normally distributed noise variable via nonlinear functions leads to a non-normal output distribution. To consider the non-normality of the output, we use a skew-normal distribution. Then, we calculate mean, standard deviation, and skewness of the output by applying an analytical approach. To show the applicability of the proposed method, a metal forming process is optimized. Furthermore, we define the optimization by an objective and a constraint, which are both nonlinear. Moreover we use Kriging metamodel as nonlinear model of that forming process. finally we show that the new robustness criterion is effective at reducing the output variability. Additionally, the results demonstrate that taking into account the skewness of the output helps to satisfy the constraints at the desired level accurately.
[3] O. Nejadseyfi, H.J.M. Geijselaers, E.H. Atzema, M.Abspoel & A.H. van den Boogaard (2021). Accounting for non-normal distribution of input variables and their correlations in robust optimization. Optimization and engineering https://doi.org/10.1007/s11081-021-09660-w
Abstract:
In this work, we use a metamodel-based robust optimization using measured scatter of noise variables. Then , we employ principal component analysis to describe the input noise using linearly uncorrelated principal components. Some of these principal components follow a normal probability distribution, others however deviate from a normal probability distribution. In that case, for more accurate description of material scatter, we use a multimodal distribution. In this work we implement an analytical method to propagate the noise distribution via metamodel and to calculate the statistics of the response accurately and efficiently. Then we adjust the robust optimization criterion as well as the constraints evaluation to properly deal with multimodal response. Finally we present two problems to show the effectiveness of the proposed approach and to validate the method.