Stochastic modeling of multidimensional particle properties with parametric copulas for the investigation of microstructure effects on the fractionation of fine particle system

使用参数联结函数对多维颗粒特性进行随机建模，用于研究微观结构对细颗粒系统分级的影响

• 批准号: 381447825
• 负责人: Professor Dr. Volker Schmidt
• 金额: --
• 依托单位: Institut für Stochastik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/381447825?language=en
• 关键词: Stochastic; modeling; multidimensional; particle; properties

In this project, the mathematical analysis and modeling techniques developed in the first funding period of the SPP 2045 will be applied on image data and measurements of particle systems which are investigated by the partners within SPP 2045. In addition, the methods are further developed, which quantify the separation success and the relationship between multidimensional particle characteristics and separation-relevant physical parameters. Furthermore, a stereological prediction model is developed to characterize 3D particles from 2D sections through the particle systems. In particular, the following tasks will be addressed. The methods developed in the first funding period for extracting particles from CT image data, for parametric modeling of multivariate distributions of particle characteristics, for characterizing the materials within composite-particles from CT data, and for quantifying the separation success, are applied to further particle systems and modified if necessary. For this purpose, the workflow, consisting of the automated extraction of particles from CT data and the subsequent modeling of multivariate feature distributions of the particles, is applied to particle systems before and after the application of separation processes. This reduces the (difficult) direct comparison of CT image data to the comparison of distributions of particle characteristics of the feed material and the product. Subsequently, measures for the separation success, such as purity and yield, are determined to analyze and compare the quality of the separation methods. Another project goal is to quantify the relationship between particle properties and separation success using stochastic 3D particle models, i.e., by generating "digital twins" which describe the shape and internal structure of the particles. Furthermore, these models allow the generation of a wide range of virtual but realistic particles with different feature distributions. These virtual particles will be made available to the partner groups of SPP 2045 via a particle database, such that the partners can use them as input for numerical simulations of sedimentation and flow processes. By correlating the simulation results with multivariate distributions of characteristics of the feed particles, relationships between particle properties and separation success will be determined. In addition, a stereological prediction model is developed, which determines multivariate distributions of characteristics of 3D particles from 2D slices (gained e.g. by SEM measurements) through the particle system. For this purpose, the above-mentioned stochastic (single) particle models are extended to a model for spatially dispersed particle systems. By generating a large number of virtual 3D particle systems neural networks are trained, which can characterize the 3D particles from 2D sections of the considered particle system.

在该项目中，SPP 2045第一个资助期开发的数学分析和建模技术将应用于SPP 2045合作伙伴研究的粒子系统的图像数据和测量。此外，进一步发展的方法，量化分离的成功和多维颗粒特性和分离相关的物理参数之间的关系。此外，体视学预测模型的开发，通过颗粒系统的二维截面来表征三维颗粒。具体而言，将处理以下任务。在第一个资助期内开发的用于从CT图像数据中提取颗粒、用于颗粒特征的多变量分布的参数化建模、用于从CT数据中表征复合颗粒内的材料以及用于量化分离成功的方法被应用于进一步的颗粒系统，并且在必要时进行修改。为此，工作流程，包括自动提取的颗粒从CT数据和随后的建模的多变量特征分布的颗粒，被应用到粒子系统之前和之后的应用程序的分离过程。这减少了CT图像数据的（困难的）直接比较，以比较进料和产品的颗粒特性的分布。随后，确定分离成功的措施，如纯度和收率，以分析和比较分离方法的质量。另一个项目目标是使用随机3D颗粒模型量化颗粒特性和分离成功之间的关系，即，通过产生“数字孪生”来描述粒子的形状和内部结构。此外，这些模型允许生成具有不同特征分布的各种虚拟但真实的粒子。这些虚拟粒子将通过粒子数据库提供给SPP 2045的合作伙伴，以便合作伙伴可以将它们用作沉降和流动过程的数值模拟的输入。通过将模拟结果与进料颗粒特性的多元分布相关联，将确定颗粒特性与分离成功率之间的关系。此外，开发了体视学预测模型，其通过颗粒系统从2D切片（例如通过SEM测量获得）确定3D颗粒的特征的多变量分布。为此，上述随机（单）颗粒模型扩展到空间分散的颗粒系统的模型。通过生成大量的虚拟3D粒子系统来训练神经网络，该神经网络可以从所考虑的粒子系统的2D截面中表征3D粒子。