MultOpt++: a fast regression-based model for the development of compositions with high robustness against scatter of element concentrations

Abstract

Alloys-by-design is a term used to describe new alloy development techniques based on numerical simulation. These approaches are extensively used for nickel-base superalloys to increase the chance of success in alloy development. During alloy production of numerically optimized compositions, unavoidable scattering of the element concentrations occurs. In the present paper, we investigate the effect of this scatter on the alloy properties. In particular, we describe routes to identify alloy compositions by numerical simulations that are more robust than other compositions. In our previously developed alloy development program package MultOpt, we introduced a sensitivity parameter that represents the influence of alloying variations on the final alloy properties in the post-optimization process, because the established sensitivity calculations require high computational effort. In this work, we derive a regression-based model for calculating the sensitivity that only requires one-time calculation of the regression coefficients. The model can be applied to any function with nearly linear behavior within the uncertainty range. The model is then successfully applied to the computational alloys-by-design work flow to facilitate alloy selection using the sensitivity of a composition owing to the inaccuracies in the manufacturing process as an additional minimization goal.

MultOpt++: a fast regression-based model for the constraint violation fraction due to composition uncertainties

“…) due to variation of design variables with standard deviation of c 0.5 D  • , which is satisfied for approximately 90% [14] of all CALPHAD-based functions used in the current work, we define according to [13] the approximation for the violation fraction V with the same uncertainty c 0.2wt% D = and the nearly the same γ′-fractions for both alloys c T ,…”

“…For the calculation of the sensitivity of alloy properties to fluctuations of the concentrations of alloying elements (e.g. due to fluctuations in manufacturing) the authors already proposed a fast regression-based model [14]. The straightforward calculation of sensitivity values allows direct integration as an optimization objective into the numerical alloy development.…”

“…In the current work, the existing regression-based model for sensitivity calculations [14] will be extended to enable the prediction of constraint violation fractions. This will allow setting up a robust optimization of alloy properties taking into account the violation of constraints as well as the sensitivity of the properties as a minimization goal.…”

An overview of laser-based multiple metallic material additive manufacturing: from macro- to micro-scales

“…Reichardt [135] proposed to use the CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) thermodynamic modeling method to predict the optimal W-CuCrZr composition, which can strategically avoid regions of insolubility and intermetallic formation. Müller et al [136] described a way to identify new alloy composition through numerical simulation to increase the chance of successful new alloy development.…”

Numerical Design of CoNi-Base Superalloys With Improved Casting Structure

“…[16,17] In this study, we employ the latter approach by coupling CALPHAD calculations to genetic multi-criteria optimization algorithms. We employ the numerical alloy design tool MultOpt++ [18][19][20] and its Python port PyMultOpt for the design process. In this framework, the alloy design task is defined as an optimization problem consisting of optimization goals that should be minimized or maximized and constraints that may not be violated.…”