Control Engineering Practice最新文献_第8页

Quality prediction of a fermentation process using multi-scale GRU with hybrid modeling strategy 基于混合建模策略的多尺度GRU发酵过程质量预测

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-05 DOI: 10.1016/j.conengprac.2025.106408

Jiakai Zheng, Zheng Zhou, Shunyi Zhao, Xiaoli Luan, Fei Liu

{"title":"Quality prediction of a fermentation process using multi-scale GRU with hybrid modeling strategy","authors":"Jiakai Zheng, Zheng Zhou, Shunyi Zhao, Xiaoli Luan, Fei Liu","doi":"10.1016/j.conengprac.2025.106408","DOIUrl":"10.1016/j.conengprac.2025.106408","url":null,"abstract":"<div><div>Fermentation is a crucial process in the production of food, pharmaceuticals, and other products, but its inherent complexity often makes it challenging to consistently meet quality standards. This paper proposes a multi-scale gated recurrent unit-based quality prediction method using a hybrid modeling strategy to enhance product quality consistency. This hybrid approach integrates the advantages of regression models in extracting precise and effective features with the superior performance of classification models in handling complex decision boundaries. Specifically, the regression network maps process variables to quality-related features, while the classification network then assigns these features to the corresponding product quality categories. Additionally, changes in the metabolic demands of microorganisms and the continuous consumption of substrates give rise to multi-stage dynamics, thereby further complicating the modeling process. To address this issue, a multi-stage segmentation approach is implemented within the classification network to more effectively capture the distinct phases of fermentation. Moreover, stages with minimal impact on training performance are excluded, streamlining and accelerating the model training process. Experimental results demonstrate that the proposed approach significantly improves the accuracy of quality predictions, thereby achieving more consistent quality control in fermentation processes.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"164 ","pages":"Article 106408"},"PeriodicalIF":5.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimizing industrial oven temperature uniformity: A model predictive control framework with rapid control prototyping 优化工业烘箱温度均匀性：一个具有快速控制原型的模型预测控制框架

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-05 DOI: 10.1016/j.conengprac.2025.106409

Leandro Pitturelli, Davide Previtali, Fabio Previdi, Antonio Ferramosca

{"title":"Optimizing industrial oven temperature uniformity: A model predictive control framework with rapid control prototyping","authors":"Leandro Pitturelli, Davide Previtali, Fabio Previdi, Antonio Ferramosca","doi":"10.1016/j.conengprac.2025.106409","DOIUrl":"10.1016/j.conengprac.2025.106409","url":null,"abstract":"<div><div>Industrial ovens are pivotal in manufacturing, particularly food processing, electronics, and materials fabrication. In this context, temperature control algorithms must satisfy demanding control specifications, among which: setpoint tracking, disturbance rejection, energy saving, and actuator limitations. Specifically, one of the critical challenges in industrial ovens is achieving a uniform temperature distribution within the oven cavity, especially in the presence of disturbances. This paper focuses on a particular kind of industrial ovens installed in shrink tunnels, which are employed in manufacturing applications for polymeric packaging. In these applications, temperature uniformity is a key factor in determining the quality of the packages resulting from the heat shrinking process, making it a major concern. Consequently, we propose three Model Predictive Control (MPC) strategies for shrink tunnels aimed for temperature uniformity: an MPC for tracking (as a baseline), and two zone-based MPCs that steer the oven temperatures towards either a fixed or an adaptive range rather than a single target point. All control strategies are thoroughly and experimentally validated on a shrink tunnel workbench installed in a manufacturing facility. Specifically, we adopt the Rapid Control Prototyping (RCP) paradigm to speed up controller implementation and performance assessment. Experimental results demonstrate that the zone-based MPC strategies significantly improve the temperature uniformity within the oven cavity compared to the MPC for tracking formulation.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"164 ","pages":"Article 106409"},"PeriodicalIF":5.4,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An experiment study for unmanned aerial manipulator systems with L1 adaptive augmentation of geometric control 基于L1自适应增强几何控制的无人机机械臂系统实验研究

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-04 DOI: 10.1016/j.conengprac.2025.106418

Kexin Cai, Hai Yu, Zhaopeng Zhang, Xiao Liang, Yongchun Fang, Jianda Han

{"title":"An experiment study for unmanned aerial manipulator systems with L1 adaptive augmentation of geometric control","authors":"Kexin Cai, Hai Yu, Zhaopeng Zhang, Xiao Liang, Yongchun Fang, Jianda Han","doi":"10.1016/j.conengprac.2025.106418","DOIUrl":"10.1016/j.conengprac.2025.106418","url":null,"abstract":"<div><div>Unmanned aerial manipulators, integrating multi-rotor unmanned aerial vehicles (UAVs) and multi-link manipulators, are extending the capabilities of UAVs to interact with the environment and demonstrating vast potential for diverse applications. However, the dynamic coupling between the UAV and the manipulator, along with the unmodeled nonlinear disturbances exerting on the aerial platform, pose challenges for high-performance control of the aerial manipulator. To this end, this paper proposes an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> adaptive augmentation control method for the aerial manipulator to compensate the disturbances brought by manipulator motion and unmodeled uncertainties. Specifically, a baseline geometric controller is constructed to directly compensate the measurable wrench disturbances exerted on the UAV by the manipulator motion, while an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> adaptive controller is designed to compensate the residual unknown wrench disturbances. By Lyapunov techniques, it is proven that the error signals of the closed-loop system are uniformly ultimately bounded, which demonstrates the theoretical effectiveness of the proposed method. Finally, the feasibility and robustness of the proposed control method are validated through three groups of hardware experiments.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"164 ","pages":"Article 106418"},"PeriodicalIF":5.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Design of an adaptive MPC control system for unmanned ground vehicle based on FP-ADMM and RBFNN 基于FP-ADMM和RBFNN的无人地面车辆自适应MPC控制系统设计

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-04 DOI: 10.1016/j.conengprac.2025.106399

Yulong You , Zhong Yang , Hao-ze Zhuo , Nuo Xu , Luwei Liao , Wenbin Jiang

{"title":"Design of an adaptive MPC control system for unmanned ground vehicle based on FP-ADMM and RBFNN","authors":"Yulong You , Zhong Yang , Hao-ze Zhuo , Nuo Xu , Luwei Liao , Wenbin Jiang","doi":"10.1016/j.conengprac.2025.106399","DOIUrl":"10.1016/j.conengprac.2025.106399","url":null,"abstract":"<div><div>To address the challenges of nonlinearity, real-time performance, and parameter uncertainty in distributed six-wheel unmanned ground vehicles (UGV) operating in complex high-speed dynamic environments, this paper proposes a method for achieving precise control in such conditions. First, a dynamic predictive model is established, considering road inclination and time-varying curvature. Next, the grey wolf optimizer (GWO) is employed to adaptively optimize the weight coefficients of the model predictive control (MPC) objective function, creating an adaptive MPC (AMPC) system that enhances overall performance, allowing it to handle various complex terrains. Additionally, the Fast Proximal Alternating Direction Method of Multipliers (FP-ADMM) is utilized to solve the quadratic programming (QP) problem, improving computational efficiency and ensuring real-time performance for UGV at high speeds. To further reduce trajectory tracking errors caused by model uncertainties and external disturbances, a compensation controller based on the radial basis function neural network (RBFNN) is introduced. This controller learns from the system’s control errors and generates real-time compensation signals, combining its output with the AMPC output to perform trajectory tracking tasks for the UGV. The stability of the proposed method is proven based on Lyapunov stability theory. Experimental results from real-world testing show that the proposed method achieved trajectory tracking accuracies of 0.08 m on off-road and 0.06 m on inclined road. Compared to traditional MPC methods, this strategy demonstrates superior tracking performance on complex high-speed terrains, with significant improvements in both real-time performance and tracking accuracy.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"164 ","pages":"Article 106399"},"PeriodicalIF":5.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

TimeGPT-based multi-step-ahead key quality indicator forecasting for industrial processes 基于时间gpt的工业过程多步关键质量指标预测

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-04 DOI: 10.1016/j.conengprac.2025.106410

Xinmin Zhang , Yuwei Chen , Bocun He , Zhihuan Song , Manabu Kano

引用次数: 0

Resonance suppression of a piezo-actuated nanopositioning stage based on recursive positive velocity feedback control 基于递归正速度反馈控制的压电驱动纳米定位平台的共振抑制

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-04 DOI: 10.1016/j.conengprac.2025.106422

Suan Xu , Tengfei Chen , Kaixing Hong , Lushuai Qian , Yaping Xu , Luc Chassagne

{"title":"Resonance suppression of a piezo-actuated nanopositioning stage based on recursive positive velocity feedback control","authors":"Suan Xu , Tengfei Chen , Kaixing Hong , Lushuai Qian , Yaping Xu , Luc Chassagne","doi":"10.1016/j.conengprac.2025.106422","DOIUrl":"10.1016/j.conengprac.2025.106422","url":null,"abstract":"<div><div>The piezo-actuated nanopositioning stage is widely used in the applications requiring precise motion and control at the nanometer level, which determines whether the system is capable of high precision and fast response. In order to suppress the low-damping resonance of the one-dimensional nanopositioning stage, this paper proposes a novel dual-loop control method that combines recursive positive velocity feedback (RPVF) control and displacement tracking control. The RPVF-based inner control loop is proposed to mitigate the resonance mode of the nanopositioning stage, and the softplus function and simulated annealing are used to improve the flamingo search algorithm for parameter configuration. The proportional–integral (PI) controller is introduced in the outer loop to overcome the problems remain in the system after vibration compensation, such as hysteresis and creep. The experimental results show that the proposed controller combining RPVF and PI effectively suppresses the low-damping resonance modes of the nanopositioning stage and achieves outstanding performance in control bandwidth, step response and trajectory tracking.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"164 ","pages":"Article 106422"},"PeriodicalIF":5.4,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Adjust to reality: LLM-driven test-time semantic adjustment for zero-shot fault diagnosis 适应现实：llm驱动的测试时间语义调整，用于零射击故障诊断

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-03 DOI: 10.1016/j.conengprac.2025.106406

Jiancheng Zhao , Jiaqi Yue , Chunhui Zhao , Chen Chen

{"title":"Adjust to reality: LLM-driven test-time semantic adjustment for zero-shot fault diagnosis","authors":"Jiancheng Zhao , Jiaqi Yue , Chunhui Zhao , Chen Chen","doi":"10.1016/j.conengprac.2025.106406","DOIUrl":"10.1016/j.conengprac.2025.106406","url":null,"abstract":"<div><div>Zero-shot fault diagnosis methods identify unseen faults by predicting semantic knowledge from samples. However, existing studies require labor-intensive tasks of training domain experts and annotating semantic knowledge in a specified format. Moreover, due to the domain shift problem (DSP), models trained solely on seen faults experience a decrease in performance when transferred to unseen faults. To reduce the annotation burden and address the DSP, we propose a test-time semantic adjustment method driven by the large language models (LLMs), which focuses on annotating and optimizing semantic knowledge. Firstly, with carefully designed prompts, semantic knowledge is automatically annotated by the LLM based on unstructured professional corpora. Secondly, to overcome the DSP caused by the lack of unseen faults, this study introduces the concept of test-time adjustment for zero-shot diagnosis. Specifically, we design a dual-view semantic knowledge adjustment strategy that employs information on unseen faults from unlabeled test data to adjust the semantic knowledge. This simple yet effective strategy can also be applied to other zero-shot diagnosis methods. Last but not least, we propose the class-agnostic feature extraction to enhance the cross-category transferability of extracted features for preventing overfitting to seen faults. We conduct experiments on the Tennessee-Eastman process (TEP) and a real thermal power plant (TPP), and the proposed method achieves an average improvement of 11.34% in terms of the accuracy of unseen faults on the TEP dataset, and 6.87% on the TPP dataset.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"164 ","pages":"Article 106406"},"PeriodicalIF":5.4,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust prediction-based control for unknown time-varying delays and disturbances in spherical motion platform 球面运动平台未知时变时滞和扰动的鲁棒预测控制

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-06-01 DOI: 10.1016/j.conengprac.2025.106400

Seong-Min Lee , Sangheon Lee , Hungsun Son

{"title":"Robust prediction-based control for unknown time-varying delays and disturbances in spherical motion platform","authors":"Seong-Min Lee , Sangheon Lee , Hungsun Son","doi":"10.1016/j.conengprac.2025.106400","DOIUrl":"10.1016/j.conengprac.2025.106400","url":null,"abstract":"<div><div>This paper presents a new prediction-based controller utilizing enhanced preview and state prediction methods to deal with unknown time-varying delays and disturbances. In practice, uncertain and variable time delays in virtual reality applications can lead to control instability and a significant reduction in the overall sense of realism. In this paper, a robust prediction-based control (RPC) is proposed for the spherical motion platform (SMP) to compensate for the effects of the time-varying delays and disturbances. The RPC comprises a preview strategy and state/disturbance prediction methods with an estimator to handle unknown time-varying delays. In addition, a newly proposed preview method improves the system’s ability to follow a time-varying reference trajectory. The stability analysis for the time-delayed system incorporating the RPC is conducted using the Lyapunov–Krasovskii approach. Numerical simulations and various experiments demonstrate that the RPC effectively leads the state to converge to the desired trajectory within an error bound under various conditions of time-varying delays in the presence of disturbances, whereas the existing controllers have limitations in reducing the desired control errors. Consequently, the results validate the feasibility and effectiveness of the RPC in real-world applications, demonstrating its robustness in handling time-varying delays through practical implementation on the SMP.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"163 ","pages":"Article 106400"},"PeriodicalIF":5.4,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exponential decay adaptive robust control for electron spin magnetization in atomic spin gyroscopes 原子自旋陀螺仪中电子自旋磁化的指数衰减自适应鲁棒控制

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-05-31 DOI: 10.1016/j.conengprac.2025.106405

Feng Li , Zhuo Wang , Ruigang Wang , Haoying Pang , Wenfeng Fan , Xinxiu Zhou , Xusheng Lei , Wei Quan

{"title":"Exponential decay adaptive robust control for electron spin magnetization in atomic spin gyroscopes","authors":"Feng Li , Zhuo Wang , Ruigang Wang , Haoying Pang , Wenfeng Fan , Xinxiu Zhou , Xusheng Lei , Wei Quan","doi":"10.1016/j.conengprac.2025.106405","DOIUrl":"10.1016/j.conengprac.2025.106405","url":null,"abstract":"<div><div>As the demand for high-precision navigation and stability in engineering grows, traditional mechanical and optical gyroscopes face performance and size limitations. Atomic Spin Gyroscopes (ASGs) offer exceptional precision and stability, with potential for miniaturization. However, electron spin magnetization (ESM) is sensitive to interference from various physical fields, and its stability is crucial for ASGs performance. Current research lacks effective closed-loop control solutions to stabilize ESM under parameter fluctuation and external disturbance. In this study, we develop an affine nonlinear system model with non-autonomous characteristics for ESM and propose an exponential decay adaptive robust control (EDARC) strategy to address this challenge. In addition, an innovative hardware architecture for direct measurement and control of ESM is implemented. Comparative simulations reveal that the EDARC outperforms existing approaches, while experimental results show substantial improvements in system stability. The proposed method demonstrates a significant enhancement in ESM stabilization by reducing the Integral of Absolute Error (IAE) by over 95%, effectively mitigating the impact of magnetic and thermal disturbances. Allan deviation analysis further confirms the improvement in long-term stability, with reductions exceeding 90%, highlighting the robustness of the proposed strategy in maintaining precise ESM control over extended periods.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"163 ","pages":"Article 106405"},"PeriodicalIF":5.4,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hierarchical optimal planning and real-time tracking of parking trajectories based on risk field 基于风险场的停车轨迹分层优化规划与实时跟踪

IF 5.4 2区计算机科学

Control Engineering Practice Pub Date : 2025-05-31 DOI: 10.1016/j.conengprac.2025.106423

Dongxu Su, Zhiguo Zhao, Kun Zhao, Kaichong Liang, Qin Yu

{"title":"Hierarchical optimal planning and real-time tracking of parking trajectories based on risk field","authors":"Dongxu Su, Zhiguo Zhao, Kun Zhao, Kaichong Liang, Qin Yu","doi":"10.1016/j.conengprac.2025.106423","DOIUrl":"10.1016/j.conengprac.2025.106423","url":null,"abstract":"<div><div>In order to improve the safety, smoothness and robustness of the automatic parking trajectory for light commercial vehicles in dynamic environments, this paper designs a novel real-time parking trajectory planning and tracking control architecture. A parking risk field (PRF) is established to reflect the guiding role and constraints of the parking environment on the vehicle. Nonlinear Model Predictive Control (NMPC) incorporating the PRF is proposed to realize the trajectory smooth optimization and real-time dynamic obstacle avoidance while tracking the global trajectory. Firstly, in the global parking trajectory planning layer, the initial trajectory is generated based on hybrid A*, path quadratic smoothing and speed planning algorithms. The parking problem is then formulated as an optimization problem, with the global trajectory planned based on the initial one. Secondly, in the real-time tracking control layer, considering the influence of trajectory guidance, drivable area modeling and dynamic obstacle avoidance, the PRF is constructed, comprising the trajectory attraction field, parking boundary field and vehicle repulsion field. Based on the PRF, the NMPC cost function is formulated. Additionally, vehicle ellipse constraints are designed and work with the boundary field to confine the vehicle within the parking space. Finally, the proposed optimal planning and dynamic tracking method based on the PRF is verified through simulation and real vehicle experiments. Both simulation and experiment results demonstrate that the designed trajectory planning and control architecture can enable the vehicle to park safely, smoothly and accurately in the parking space, while avoiding dynamic obstacles in real time through NMPC.</div></div>","PeriodicalId":50615,"journal":{"name":"Control Engineering Practice","volume":"163 ","pages":"Article 106423"},"PeriodicalIF":5.4,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0