Calibration of discrete element method (DEM) models is crucial for the realistic simulation of granular materials. However, it remains a challenging task, especially for multi-component mixtures due to their higher complexity and larger number of parameters involved. This study presents a systematic and computationally efficient calibration framework designed to address these challenges, focusing on pellet-sinter mixtures, as a representative case of two-component mixtures commonly used in blast furnace steelmaking. The framework integrates sensitivity analysis, machine learning-based surrogate modelling with adaptive sampling, and genetic algorithm-driven optimisation techniques to minimise the number of required DEM simulations. Using this approach, we achieved a high-accuracy surrogate model (R² = 0.95) for seven DEM parameters with only 110 data points, highlighting the efficiency and robustness of the framework. These parameters were successfully calibrated with a relative error of less than 2 %. Moreover, the calibrated parameters for the base case (i.e., 50–50 pellet-sinter mass ratio) remained valid across different mass ratios and layering orders, eliminating the need for recalibration. Overall, the proposed framework offers a reliable, cost-effective, and adaptable solution for DEM calibration of two-component mixtures. Its flexibility and efficiency make it a promising tool for extending to more complex systems, facilitating the development of DEM models for a wide range of industrial applications involving granular mixtures.

The stiffness model plays a crucial role in improving the performance of robots. During the operation of an underground mining cable-driven parallel robot (UMCDPR), insufficient stiffness can lead to motion instability, posing safety hazards. Additionally, the complexity of the underground mining environment, which is often accompanied by external disturbances, leads to offline stiffness indices failing when used underground as an optimal criterion. To address these problems, this article proposes a robust optimal stiffness direction (ROSD) index grounded in Rayleigh's theorem, which is characterized by three primary features: (1) strong robustness, (2) suitable for multi-trajectory optimization engineering problems, and (3) global visualization. Firstly, considering the influence of pulleys on the end-effector, the stiffness model of UMCDPR is modified. Secondly, a trajectory optimization method utilizing ROSD is introduced, incorporating the Kepler Conjecture and stiffness model correction. Finally, the characteristics of ROSD are validated through numerical simulations. Based on two numerical simulations, the ROSD index can serve as an optimal criterion for guiding stiffness optimization of UMCDPR. Furthermore, an optimal stiffness trajectory is obtained to meet the task objectives of UMCDPR.

To address the limitations in time–frequency feature representation of shearer arm gear faults and the issues of parameter redundancy and low training efficiency in standard convolutional neural networks (CNNs), this study proposes a diagnostic method based on an improved S-transform and a Depthwise Separable Convolutional Neural Network (DSCNN). First, the improved S-transform is employed to perform time–frequency analysis on the vibration signals, converting the original one-dimensional signals into two-dimensional time–frequency images to fully preserve the fault characteristics of the gear. Then, a neural network model combining standard convolution and depthwise separable convolution is constructed for fault identification. The experimental dataset includes five gear conditions: tooth deficiency, tooth breakage, tooth wear, tooth crack, and normal. The performance of various frequency-domain and time-frequency methods—Wavelet Transform, Fourier Transform, S-transform, and Gramian Angular Field (GAF)—is compared using the same network model. Furthermore, Grad-CAM is applied to visualize the responses of key convolutional layers, highlighting the regions of interest related to gear fault features. Finally, four typical CNN architectures are analyzed and compared: Deep Convolutional Neural Network (DCNN), InceptionV3, Residual Network (ResNet), and Pyramid Convolutional Neural Network (PCNN). Experimental results demonstrate that frequency–domain representations consistently outperform raw time-domain signals in fault diagnosis tasks. Grad-CAM effectively verifies the model’s accurate focus on critical fault features. Moreover, the proposed method achieves high classification accuracy while reducing both training time and the number of model parameters.

The accuracy and stability of robotic systems are significantly influenced by joint clearances, especially in precision applications like optical mirror polishing. This study focuses on a 5-DOF (Degree of Freedom) parallel manipulator designed for optical mirror polishing. The study conducts dynamic modeling by incorporating prismatic joint clearance and examines the resulting dynamic response. Previous studies on dynamic modeling have primarily focused on planar mechanisms with rotational or ball joint clearances, whereas research on parallel manipulators with spatial prismatic joint clearances remains limited. This study introduces a comprehensive dynamic modeling framework for parallel manipulators with prismatic joint clearance, utilizing the Lagrange multiplier method (LMD). First, the prismatic joint models of the guideway and slider in the parallel manipulator are simplified, enabling the determination of different contact states and the calculation of friction and contact forces for various contact types. Second, the dynamic equations of the parallel manipulator are derived by establishing system constraint equations. Finally, the dynamic responses of various clearance-related factors are determined through a combination of theoretical calculations and ADAMS simulations. This study provides a framework for modeling the dynamics of parallel manipulators with prismatic joint gaps, offering valuable insights into the design and control of high-precision robotic systems.

Digital twins and visual monitoring of conveyor systems require accurate digital models of dynamic bulk material flows, but existing methods struggle to achieve both speed and precision. This study develops a rapid online method to reconstruct dynamic bulk material flows on conveyor belts. First, a standardized online reconstruction scheme using visual detection of material flow contour lines is presented. Then, a feature detection algorithm is proposed to extract more refined points from laser line skeleton to accelerate the reconstruction process. An iterative-filtering interpolation algorithm that generates smooth interframe point clouds is introduced to improve mesh quality. Experimental results demonstrate that our method outperforms traditional corner detection-based reconstruction techniques in feature point detection, accuracy, mesh quality, and runtime performance. This research provides a practical solution for material handling digitalization, promoting the advancement of conveyor system digital twins and potentially improving operational efficiency and predictive maintenance in bulk material handling industries.

Accurate prediction of mill load parameters is crucial to improving grinding efficiency and saving energy. Traditional prediction models have challenges such as poor interpretability, low prediction efficiency and differences in data distribution. This study innovatively proposed a multi-task prediction model that integrates physical information and domain adaptation. By constructing a physical-data-driven hybrid model, the physical relationship between mill load parameters is embedded into the model as prior knowledge to improve the prediction accuracy of the model. At the same time, multi-task learning is used to predict the material-to-ball volume ratio and the pulp density at the same time, which improves efficiency and reduces repetitive work. The domain adaptation method is introduced to ensure that the model maintains stable prediction performance when the data distribution changes. Laboratory ball mill data verification shows that the proposed model not only improves the prediction accuracy, but also adapts well to variable working conditions, showing significant superiority.

Multiagent reinforcement learning (RL) training is usually difficult and time-consuming due to mutual interference among agents. Safety concerns make an already difficult training process even harder. This study proposes a safe adaptive policy transfer RL approach for multiagent cooperative control. Specifically, a pioneer and follower off-policy policy transfer learning (PFOPT) method is presented to help follower agents acquire knowledge and experience from a single well-trained pioneer agent. Notably, the designed approach can transfer both the policy representation and sample experience provided by the pioneer policy in the off-policy learning. More importantly, the proposed method can adaptively adjust the learning weight of prior experience and exploration according to the Wasserstein distance between the policy probability distributions of the pioneer and the follower. Case studies show that the distributed agents trained by the proposed method can complete a collaborative task and acquire the maximum rewards while minimizing the violation of constraints. Moreover, the proposed method can also achieve satisfactory performance in terms of learning speed and success rate.

To address the challenges of extracting rolling bearing degradation information and the insufficient performance of conventional convolutional networks, this paper proposes a rolling bearing degradation state identification method based on the improved monopulse feature extraction and a one-dimensional dilated residual convolutional neural network (1D-DRCNN). First, the fault pulse envelope waveform features are extracted through phase scanning and synchronous averaging, and a two-stage grid search strategy is employed to achieve FCC calibration. Subsequently, a 1D-DRCNN model is constructed to identify rolling bearing degradation states under different working conditions. The experimental study collects the vibration signals of nine degradation states, including the different sizes of inner and outer ring local faults as well as normal conditions, to comparatively analyze the proposed method’s rapid calibration capability and feature extraction quality. Furthermore, t-SNE visualization is utilized to analyze the network response to bearing degradation features. Finally, the degradation state identification performance across different network architectures is compared in pattern recognition experiments. The results show that the proposed improved feature extraction method significantly reduces the iterative calibration computational burden while effectively extracting local fault degradation information and overcoming complex working condition influence. The established 1D-DRCNN model integrates the advantages of dilated convolution and residual connections and can deeply mine sensitive features and accurately identify different bearing degradation states. The overall recognition accuracy can reach 97.33%.

This article presents an innovative visual method for measuring material mass online by quantified conveyor belt deformation with deep learning, which offers a noncontact and safe alternative to traditional pressure- and radioactivity-based weighing techniques. The correlation between the belt deformation and the carried material mass is further investigated through finite element simulations. Then, a visual weighing method by belt deformation is proposed, comprising a calibration algorithm to construct a measurement model using a gated recurrent unit-based network, and an online measurement algorithm to calculate material mass with the trained network. Finally, a case study is presented to analyze the effect of different dimension configurations and networks. The results validate that the proposed method attains a notable accuracy and is suitable for high-velocity conveyor environments. The demonstrated benefits signify an advancement in visual perception of materials, enabling a new approach for intelligent operation and monitoring in material handling field.

The accuracy of high-precision optical processing robots is influenced by various factors, including static error factors and dynamic error factors. These factors pose significant challenges to the deterministic processing of precision optics. This article proposes a pose residual prediction model for optical processing hybrid robots based on deep spatio-temporal graph convolutional neural networks. In this study, we establish a geometric error model for hybrid robots and calibrate the geometric error parameters using an extended Kalman filter to obtain the pose residuals component. To address the complex spatio-temporal interactions between multiple sensor variables in joint space during robot motion, we introduce the non-Euclidean spatio-temporal graph convolutional neural network. This model effectively extracts advanced spatio-temporal interaction features based on a spatio-temporal attention mechanism. Finally, the performance of the proposed method in pose residual prediction was validated through real experiments, and the results demonstrated its advantages over other state-of-the-art methods.

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.

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.

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.

Deep-sea mining activities have lately attracted growing interest. Recent research has led to the development of a hydraulic–mechanical hybrid vertical lifting system for deep-sea mining. Predicting the resistance of vertical plug flow in this system is critical for its engineering design. In this paper, an analytical model was developed to determine the resistance of vertical plug flow in a hydraulic–mechanical hybrid vertical lifting system in the presence of coarse particles. A recent model of the stress transmission ratio for pneumatic plug flow was verified and applied to the proposed model of resistance. In addition, it is considered that the co-existence of turbulent and laminar flows in the fluid flowing through the particles provides the necessary pressure gradient. A test setup was built to measure the resistance of vertical plug flow with/without water, along with varying particle diameters, plug lengths, and lifting speeds. Comparisons between the predictions of the analytical model and experimental measurements showed that they deviated by less than 13.6% on average. This shows that the proposed analytical model can be used to predict the resistance of vertical plug flow involving coarse particles.

Bed permeability is a crucial factor in blast furnace performance which depends on the material distribution achieved through charging. Since a homogeneous bed of pellet and sinter is recommended, it is crucial to understand whether segregation of the pellet-sinter mixture occurs during charging. The Discrete Element Method is useful in this regard; however, simulations of pellet-sinter mixture charging currently lack credibility since pellet-sinter interaction parameters have not yet been calibrated and validated. Determining pellet-sinter interaction parameters will require significant efforts, so it is useful to know whether mixture segregation and the resulting bed permeability are sensitive to these parameters. In this work, we investigate to what extent the restitution coefficient, sliding friction coefficient and rolling friction coefficient between pellet and sinter affect segregation during bed formation and the resulting permeability in terms of porosity using a simplified charging setup. The investigation is done for different mixture compositions and flow velocities, and analysis settings including sample size and sampling directions. We conclude that all parameters affect segregation and porosity, regardless of the composition and velocity. Hence, all mixture parameters including the interaction parameters between the components must be carefully calibrated when developing a model for predicting permeability.

Aiming to address soft sensing model degradation under changing working conditions, and to accommodate dynamic, nonlinear, and multimodal data characteristics, this paper proposes a nonlinear dynamic transfer soft sensor algorithm. The approach leverages time-delay data augmentation to capture dynamics and projects the augmented data into a latent space for constructing a nonlinear regression model. Two regular terms, distribution alignment regularity and first-order difference regularity, are introduced during data projection to address data distribution disparities. Laplace regularity is incorporated into the nonlinear regression model to ensure geometric structure preservation. The final optimization objective is formulated within the framework of partial least squares, and hyperparameters are determined using Bayesian optimization. The effectiveness of the proposed algorithm is demonstrated through experiments on three public datasets.

The inland waterway transport sector is facing increasingly stringent legislation to reduce emissions and improve energy efficiency. Speed planning methods are an attractive option as they provide energy-efficient, timely and emission-reducing voyage planning for ships. However, current methods do not consider dynamic conditions of waterways and traffic. Due to these dynamic navigational conditions the static speed planning methods do not guarantee optimality, nor do they satisfy the constraints of the optimization problem throughout the journey. In this paper we propose an optimization structure that is based on the Model Predictive Control algorithm, which uses the most current information on water depth, water speed and expected delays to re-optimize the speed planning throughout the journey. Through a use case we show a 4.31% energy reduction compared to other speed planning strategies. Additionally, we show that the constraints regarding desired arrival times and safety are satisfied throughout the journey. Therefore, the method proves useful from a logistical, energy, emissions, and safety perspective. Modelling of uncertainties, lock interactions and predictions of waterway conditions will make our method an even more attractive option for speed planning.