Continuous method of thermodynamic optimisation using first-derivative matrices for large multicomponent systems

Real-life applications require thermodynamic databases consisting of many elements. Currently, Pyrosearch supports a 20-component thermodynamic FactSage™, ver 8.2 (by Thermfact and GTT technologies) database for Cu-, Pb- and Fe-production provided to a group of industrial sponsors. The database development follows an agile cycle of experiment planning, modelling/update of database subsystems, quality tests and release. A unique challenge is development and maintenance of a database self-consistent across all binary/ternary and multicomponent systems. Practice shows that binary and ternary system data do not provide the necessary accuracy for predictions within multicomponent systems. Commercial databases are often developed using only available literature data and it is hard to estimate the prediction quality for industry-relevant multicomponent compositions. Therefore, to sustain a high reliability there is a need of targeted experiments including multicomponent data. To support the continuous development process, a new optimisation methodology has been developed. After long years of optimisation experience, it is an authors’ belief that for optimisation, it is essential to pinpoint a few trusted target points instead of using a whole cloud of available experimental data. In case if the optimisation procedure is automated, using all data, even with trust weights, still leads to inferior optimisation quality. This is caused by the fact that available optimisation algorithms usually assume a normal error distribution of experimental data which can be false in cases when experimental results are affected by sample contamination, evaporation, incomplete reactions, etc. Typically, iterative optimisation involves multiple re-calculations of targets values which can take significant time and the whole procedure is not interactive. It is hard to find an exact combination of target weights to achieve desired outcomes. This problem has been solved by the authors by replacing slow FactSage™/ChemApp™ calculations by parameter value/target value relations using first-order derivative matrices. Precalculated derivative matrices allow fast analysis of parameter influence across multiple systems, selection of interaction combinations with superior performance, and analytical matrix solution to the optimisation problems using weighted linear least squares. The current optimisation system supports in-sheet ChemApp™ (by GTT-technologies, version 614) calculations for Microsoft® Excel® using custom Python® binding code, graphical and statistical representation of experimental data and target points, and real-time first-derivative matrix analysis of parameter sensitivity.