Prediction and surrogate modelling of thermodynamics properties of mixtures with application to the inverse design under uncertainty

选择合适的工作流体是热力学循环设计中最重要的因素之一。由于流体必须满足多种标准，因此为了获得最合适的溶液（即纯化合物无法获得的所需性能组合），混合物变得越来越重要。在流体设计的文献中，采用了两种不同的策略：1。一种计算机辅助模型（混合）设计方法，结合混合非线性规划（MINLP）问题的公式-尽管通常使用精度有限的属性模型或不包括广泛使用的制冷剂的模型。2. 一种筛选方法，即通过高精度多参数亥姆霍兹状态方程（HEOS）对大量流体进行定义循环的系统模拟，这种方法被认为是计算热物理性质的最新技术。然而，HEOS的计算要求太高，不允许在MINLP中使用。此外，缺少HEOS混合参数或模型的潜在工作流体混合物需要排除在筛选之外。在使用HEOS时，建议项目的目的是克服这两个主要限制，即工作流体的选择。这将通过为（二元）制冷剂混合物的HEOS开发基于高斯过程（GP）的专用代理模型来实现，以便在基于MINLP的设计方法中有效地计算其热力学性质。此外，对尚未被优化的HEOS描述的混合物进行分子模拟将允许推导其混合参数，以便它们也可以包含在优化过程中。为了解释HEOS与分子模拟之间的不匹配，我们将引入随机HEOS模型，并为此生成随机GP代理。这些随机替代模型将在MINLP中使用，以确定适合特定应用的混合物。本建议所采用的随机方法还将考虑到潜在属性模型的不确定性进行优化。

The selection of a suitable working fluid represents one of the most important factors in the design of a thermodynamic cycle. As the fluid has to meet manifold criteria, mixtures are gaining increasingly importance in order to obtain the most appropriate solution, i.e. the required combination of properties unattainable by pure compounds. Two different strategies are followed in the literature for the fluid design: 1. A computer-aided model (mixture) design approach in combination with the formulation of a mixed-inter-nonlinear-programming (MINLP) problem - which though usually employs property models with limited accuracy or models, which do not include widely used refrigerants. 2. A screening approach, i.e. performing system simulations of the defined cycle for a large number of fluids described by highly accurate multiparameter Helmholtz equations of state (HEOS) that are considered state of the art for the calculation of thermophysical properties. HEOS though are too computationally demanding to allow for their use in the MINLP. Furthermore, potential working fluid mixtures whose mixing parameters or models for the HEOS are missing need to be excluded from screenings. The aim of the proposed project is to overcome these two main restrictions when using HEOS is the working fluid selection. This will be achieved by the development of dedicated surrogate models based on Gaussian processes (GP) for HEOS of (binary) refrigerant mixtures to enable the efficient calculation of their thermodynamic properties in a MINLP based design approach. Additionally, molecular simulations on mixtures not yet described by optimized HEOS will allow to derive their mixing parameters so that they can also be included in the optimization process. To account for the mismatch between the HEOS and molecular simulations, we will introduce stochastic HEOS models, for which stochastic GP surrogates will be generated. These stochastic surrogate models will be employed in a MINLP to identify a suitable mixture for a specific application. The stochastic approach followed in this proposal will additionally allow for optimization considering uncertainties of the underlying property models.