Segregation of granular materials is a critical challenge in many industries, often aimed at being controlled or minimised. The discrete element method (DEM) offers valuable insights into this phenomenon. However, calibrating DEM models is a crucial, albeit time-consuming, step. Recently, using machine learning (ML)-based surrogate models (SMs) in the calibration process has emerged as a promising solution. Nevertheless, developing such SMs is challenging due to the high number of DEM simulations required for training. Additionally, choosing a suitable ML model is not trivial. This study aims to develop SMs that effectively link particle-particle and particle-wall DEM interaction parameters to segregation of a multi-component mixture. We evaluate several ML models, ranging from artificial neural networks to ensemble learning, that are trained on a very cost-effective dataset, employing Bayesian optimisation with cross-validation to tune their hyperparameters. Next, we introduce a novel transfer learning (TL)-based approach that leverages knowledge from a few scenarios to handle new “unseen” ones. This method enables the construction of adaptive SMs for unseen scenarios, such as a new initial configuration (IC) of granular mixtures, without the need for a full-sized dataset. Our findings indicate that Gaussian process regression (GPR) efficiently builds accurate SMs on a very small dataset. We also demonstrate that only a few samples are required to build an accurate SM for the unseen IC, which significantly reduces the data preparation burden. By incorporating one and five samples from unseen scenarios to update the TL-GPR-based surrogate model, the SM’s performance (based on ) on unseen scenarios improves by 17 and 47%, respectively. The insights and methodology presented in this study will facilitate and accelerate the development of accurate SMs for DEM calibration, assisting in developing reliable DEM models in a shorter timeframe.@en

Segregation of granular materials is a critical phenomenon in various industries, such as food processing, pharmaceuticals, and mining. The Discrete Element Method (DEM) is an effective tool for gaining insight into granular segregation by providing particle-level information and the freedom to model mixtures that are often difficult or impossible to achieve through experiments. To ensure realistic material behaviour and correct representation of segregation, it is essential to calibrate the model parameters systematically. However, in the context of multi-component segregation, it is extremely challenging and computationally expensive to consider all parameters in the calibration procedure since interaction parameters between components must also be considered. This work aims to identify the dominant DEM parameters for modelling multi-component segregation during hopper discharge, chute flow and heap formation in a mixture of pellet and sinter. Utilising a representative example of a multi-component mixture with different sizes, densities and shapes used in blast furnaces, the investigation is done for various initial configurations as well as various mass ratios of the mixture. Our findings revealed that, while only particle-geometry interaction parameters dominate the segregation after the hopper and chute flow, particle-particle parameters are also significant for segregation in the heap. We also demonstrated that the downstream segregation is significantly influenced by the segregation upstream. Moreover, we found that the effect of pellet-sinter interactions is negligible. This research provides insights into the dominant DEM parameters, facilitating more efficient and robust calibration of multi-component models in future research endeavours.

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Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-024-78455-7, published online 06 November 2024 The original version of this Article contained typographical errors in Equations. In Equation 8, where now reads: In Equation 17, where now reads: In Equation 18, where now reads: In Equation 24, where now reads: The original Article has been corrected.

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Segregation control is a challenging yet crucial aspect of bulk material handling processes. The discrete element method (DEM) can offer useful insights into segregation phenomena, provided that reliable models are developed. The main challenge in this regard is finding a good balance between including particle-level details and managing the computational load. This is especially true for industrial applications, where multi-component flows consisting of particles with various irregular shapes and wide size distributions are encountered in huge amounts. In this work, we review the state of the art in DEM modelling of segregation in industrial applications involving the gravity-driven flow of dry, cohesionless granular materials. We start by introducing a novel scientific notation to distinguish between different types of mixtures. Next, we review how parameters for mixture models are determined in the current literature, and how segregation is affected by material, geometric and operational parameters based on these models. Finally, we review existing segregation indices and their applicability to multi-component segregation. We conclude that systematic calibration procedures for segregation models are currently missing in the literature, and realistic models representing multi-component mixtures have not yet been developed. Filling these gaps will pave the way for optimising industrial processes dealing with segregation.@en

Segregation or de-mixing is the phenomenon occurring in moving granular materials in which particles with similar properties, e.g., size, density and shape, accumulate. This de-mixing reduces the homogeneity of the mixture which is generally considered undesirable and should be minimised. Despite many experimental and numerical attempts to investigate segregation in relation to different factors, the current literature has several shortcomings. Firstly, most of these studies have considered single-component mixtures, usually with a limited number of particle diameters, while most of the mixtures existing in industry and nature are complex multi-component mixtures. Secondly, a systematic calibration procedure for segregation is often missing while it is crucial for developing a reliable and predictive DEM model. This study proposes a combined global and local calibration strategy for DEM modelling of multi-component segregation. We demonstrate this for an iron ore mixture (i.e., the mixture of pellets and sinter), which is a good example of a multi-component mixture. The model was calibrated not only on the global level but also on the local level and hence it consists of two steps. First, pellets and sinter were individually calibrated on bulk level using the angle of repose measured in a shear box setup. Second, mixtures of pellets and sinter were discharged into a transparent quasi-3D hopper and the segregation index was used to calibrate the interaction parameters between pellets and sinter on a local level. Hereby, image analysis in conjunction with painting pellets have been utilised to measure segregation in a non-invasive manner. We conclude that the initial results of the proposed calibration procedure are promising. To improve it further, we suggest utilizing a more manageable experimental setup, improving the simulation model for the mixture, reducing the number of potential parameter sets, and testing other parameters resulting from single-component calibration.@en

To improve the understanding of the mixing performance of double shaft, batch-type paddle mixers, the discrete element method (DEM) in combination with a Plackett–Burman design of experiments simulation plan is used to identify factor significance on the system’s mixing performance. Effects of several factors, including three material properties (particle size, particle density and composition), three operational conditions (initial filling pattern, fill level and impeller rotational speed) and three geometric parameters (paddle size, paddle angle and paddle number), were quantitatively investigated using the relative standard deviation (RSD). Four key performance indicators (KPIs), namely the mixing quality, mixing time, average mixing power and energy required to reach a steady state, were defined to evaluate the performance of the double paddle mixer. The results show that the material property effects are not as significant as those of the operational conditions and geometric parameters. In particular, the geometric parameters were observed to significantly influence the energy consumption, while not affecting the mixing quality and mixing time, showing their potential towards designing more sustainable mixers. Furthermore, the analysis of granular temperature revealed that the centre area between the two paddles has a high diffusivity, which can be correlated to the mixing time.@en

This work aims to identify the most influential DEM parameters for modelling multi-component segregation during heap formation, hopper discharge, and chute flow.@en