Image-based prediction of granular flow behaviors in a wedge-shaped hopper by combing DEM and deep learning methods
Graphical abstract
Introduction
Due to the solid-, liquid-, or even gas-like properties of the granular materials [1,2], the granular flow presents unexpected behaviors, such as segregation [[3], [4], [5], [6], [7]], blockage [[8], [9], [10]] and eccentric flow [[11], [12], [13]] and so on. In order to overcome the difficulties in experimental characterization on aforementioned granular behaviors, Janssen et al. [14], as early as 1895, developed a continuum medium model to analyze the particles' static stress of the silo effect, while Adler et al. [15] established a molecular dynamics model to track particles' motions. Furthermore, Ogawa [16] introduced the square deviation of velocity fluctuations to characterize the average granular temperature, which was later used to modify the standard dynamic theory of inelastic collisions. Until the 1970s, Cundall and Strack [17] developed the Discrete Element Method (DEM) to analyze rock mechanic problems. Since then, this numerical solution has become one of the most powerful and effective methods of handling various engineering granular problems [[18], [19], [20], [21], [22]] by continuously updating itself for more complex systems [[23], [24], [25], [26], [27], [28]]. Nevertheless, the DEM simulation is computationally intensive, which limits the scale of a simulation [29,30]. Alternatively, machine learning methods have been introduced in recent years to improve the DEM computing efficiency. First of all, the machine learning methods were used to identify and calibrate a set of DEM input parameters by fitting the nonlinear relationship between the dynamic macroscopic particle properties and the DEM parameters [[31], [32], [33], [34]]. Specifically, Benvenuti et al. [31] and Ye et al. [32] identified the DEM parameters of any given non-cohesive granular materials by training the artificial neural network (ANN) and backpropagation (BP) neural network, respectively. Cheng et al. [33] proposed a Bayesian calibration procedure for the DEM modeling of dense granular materials, while Ma et al. [34] calibrated the micro-parameters of the rockfill based on a memetic algorithm with support vector machine (SVM). Second, the machine learning methods were combined to predict different granular flow behaviors [35]. For instance, in order to predict the granular velocity distribution and its influencing factors, Kumar et al. [36] selected seven parameters from the DEM simulation, such as the bulk density, the mean diameter, the particle-particle coefficient of friction and so on, as the inputs to train an ANN model. He et al. [37] used the relative neighbor particle positions as the inputs to train another ANN network, which improved the accuracy in drag force prediction. Third, the machine learning methods played a bridge-like role in the gap between different simulation scales [38], and the machine learning methods were proved to significantly reduce the computational burden while retain the prediction accuracy [[39], [40], [41]].
Although the granular flow has been studied through the combined DEM and machine learning methods, most predications of granular behaviors are data-driven rather than image-driven. However, the continuous real-time images, in comparison to the fetched data, are easier to provide intuitive results without further information extraction. Meanwhile, the deep learning algorithms are found to be very good at image recognition [42]. Therefore, this work focuses on using deep learning methods to predict the granular flow in a wedge-shaped hopper based on the image-based datasets extracted from the DEM simulation. The different initial granular packed patterns are first defined while the corresponding discharge processes are simulated by the DEM. After the relationships between instantaneous granular flow images and the discharge time and the number ratio of remaining particles (NRRP) in the hopper are established, the Alexnet-fully connection (FC) model is proposed to make point-to-point predictions about the discharge time, while the convolutional neural network (CNN)-long short-term memory (LSTM) network is proposed to make process predictions about the NRRP vs. the discharge time.
Section snippets
DEM Simulation
Briefly, the principles of DEM are using the Newton equations of motion to describe the translational and rotational motions of each particle, and its details can be found anywhere [21,22,43]. The geometrical dimensions of the wedge-shaped hopper are demonstrated in Fig. 1(a), while the DEM parameters are validated against the experimental measurements reported in our previous works [20,44].
One uniformly mixed bed (denoted by A) and four layer-by-layer mixed beds (denoted by B1 to B4) are
Image pre-processing and parameter sensitivity analysis
52,353 snapshots of the granular flow in the wedge-shaped hopper are randomly extracted from the front view in the aforementioned twenty-five cases of DEM simulations. Given that the original images' size is (420, 230, 3) in Fig. 3(a), the images are first cropped from the center to a rectangular size (224, 224, 3). The deep learning algorithm then greys these re-shaped images and converts them into a one-dimensional matrix in Fig. 3(b), which is immediately used for the subsequent calculation
Description of the process prediction
Although the Alexnet-FC model in the previous section achieves the point-to-point prediction of the discharge time, the process prediction of the granular flow in the timing sequence is of greater interest for practical applications. Therefore, the datasets of the NRRP, as defined in the Section 2.2, are also extracted from the DEM simulated images, and then they are sorted in a timing sequence rather than a random or arbitrary sequence used in the previous section. In the first step, only the
Conclusions
The deep learning-assisted prediction has advantages over the DEM alone in the computing efficiency, the large-scale simulation solution, and so on. Based on the extracted labels from the instantaneous DEM simulated images, this work introduces the Alexnet-FC model and CNN-LSTM model respectively to make the point-to-point and process predictions about granular flow behaviors in a wedge-shaped hopper. The main findings under present conditions are highlighted as follows:
- (1)
Although the spherical
Declaration of Competing Interest
None.
Acknowledgments
The authors gratefully acknowledge funding through projects from the Fundamental Research Funds for the Central Universities (2020CDJQY-A005), the Natural Science Foundation of Chongqing, China (cstc2019jcyj-msxmX0089) and the Young Top-notch Talent Program of Chongqing, China (CQYC2020057673), Z.L. acknowledges the Graduate Scientific Research and Innovation Foundation of Chongqing, China (CYS19035).
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