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Keywords = stability with guaranteed safety

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20 pages, 3560 KiB  
Article
Study on Vibration Effects and Optimal Delay Time for Tunnel Cut-Blasting Beneath Existing Railways
by Ruifeng Huang, Wenqing Li, Yongxiang Zheng and Zhong Li
Appl. Sci. 2025, 15(15), 8365; https://doi.org/10.3390/app15158365 - 28 Jul 2025
Viewed by 165
Abstract
With the development of underground space in urban areas, the demand for tunneling through existing railways is increasing. The adverse effects of cut-blasting during the construction of tunnels under crossing existing railways are investigated. Combined with the principle of blasting seismic wave superposition, [...] Read more.
With the development of underground space in urban areas, the demand for tunneling through existing railways is increasing. The adverse effects of cut-blasting during the construction of tunnels under crossing existing railways are investigated. Combined with the principle of blasting seismic wave superposition, LS-DYNA numerical simulation is used to analyze the seismic wave superposition law under different superposition methods. This study also investigates the vibration reduction effect of millisecond blasting for cut-blasting under the different classes of surrounding rocks. The results show that the vibration reduction forms of millisecond blasting can be divided into separation and interference of waveform. Based on the principle of superposition of blasting seismic waves, vibration reduction through wave interference is further divided. At the same time, a new vibration reduction mode is proposed. This vibration reduction mode can significantly improve construction efficiency while improving damping efficiency. The new vibration reduction mode can increase the vibration reduction to 80% while improving construction efficiency. Additionally, there is a significant difference in the damping effect of different classes of surrounding rock on the blasting seismic wave. Poor-quality surrounding rock enhances the attenuation of seismic wave velocity and peak stress in the surrounding rock. In the Zhongliangshan Tunnel, a tunnel cut-blasting construction at a depth of 42 m, the best vibration reduction plan of Class III is 3 ms millisecond blasting, in which the surface points achieve separation vibration reduction. The best vibration reduction plan of Class V is 1 ms millisecond blasting, in which the surface points achieve a new vibration reduction mode. During the tunnel blasting construction process, electronic detonators are used for millisecond blasting of the cut-blasting. This method can reduce the vibration effects generated by blasting. The stability of the existing railway is ultimately guaranteed. This can improve construction efficiency while ensuring construction safety. This study can provide significant guidance for the blasting construction of the tunnel through the railway. Full article
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19 pages, 3658 KiB  
Article
Optimal Design of Linear Quadratic Regulator for Vehicle Suspension System Based on Bacterial Memetic Algorithm
by Bala Abdullahi Magaji, Aminu Babangida, Abdullahi Bala Kunya and Péter Tamás Szemes
Mathematics 2025, 13(15), 2418; https://doi.org/10.3390/math13152418 - 27 Jul 2025
Viewed by 339
Abstract
The automotive suspension must perform competently to support comfort and safety when driving. Traditionally, car suspension control tuning is performed through trial and error or with classical techniques that cannot guarantee optimal performance under varying road conditions. The study aims at designing a [...] Read more.
The automotive suspension must perform competently to support comfort and safety when driving. Traditionally, car suspension control tuning is performed through trial and error or with classical techniques that cannot guarantee optimal performance under varying road conditions. The study aims at designing a Linear Quadratic Regulator-based Bacterial Memetic Algorithm (LQR-BMA) for suspension systems of automobiles. BMA combines the bacterial foraging optimization algorithm (BFOA) and the memetic algorithm (MA) to enhance the effectiveness of its search process. An LQR control system adjusts the suspension’s behavior by determining the optimal feedback gains using BMA. The control objective is to significantly reduce the random vibration and oscillation of both the vehicle and the suspension system while driving, thereby making the ride smoother and enhancing road handling. The BMA adopts control parameters that support biological attraction, reproduction, and elimination-dispersal processes to accelerate the search and enhance the program’s stability. By using an algorithm, it explores several parts of space and improves its value to determine the optimal setting for the control gains. MATLAB 2024b software is used to run simulations with a randomly generated road profile that has a power spectral density (PSD) value obtained using the Fast Fourier Transform (FFT) method. The results of the LQR-BMA are compared with those of the optimized LQR based on the genetic algorithm (LQR-GA) and the Virus Evolutionary Genetic Algorithm (LQR-VEGA) to substantiate the potency of the proposed model. The outcomes reveal that the LQR-BMA effectuates efficient and highly stable control system performance compared to the LQR-GA and LQR-VEGA methods. From the results, the BMA-optimized model achieves reductions of 77.78%, 60.96%, 70.37%, and 73.81% in the sprung mass displacement, unsprung mass displacement, sprung mass velocity, and unsprung mass velocity responses, respectively, compared to the GA-optimized model. Moreover, the BMA-optimized model achieved a −59.57%, 38.76%, 94.67%, and 95.49% reduction in the sprung mass displacement, unsprung mass displacement, sprung mass velocity, and unsprung mass velocity responses, respectively, compared to the VEGA-optimized model. Full article
(This article belongs to the Special Issue Advanced Control Systems and Engineering Cybernetics)
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23 pages, 6299 KiB  
Article
Multi-Valve Coordinated Disturbance Rejection Control for an Intake Pressure System Using External Penalty Functions
by Louyue Zhang, Duoqi Shi, Chao Zhai, Zhihong Dan, Hehong Zhang, Xi Wang and Gaoxi Xiao
Actuators 2025, 14(7), 334; https://doi.org/10.3390/act14070334 - 2 Jul 2025
Viewed by 244
Abstract
Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is [...] Read more.
Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is formulated as an inequality-constrained optimization problem, and an exponential penalty together with a gradient based algorithm is designed for dynamic constraint relaxation, with guaranteed global convergence. A coordination term is then integrated into a distributed ADRC framework to yield a multi-valve coordinated ADRC controller, whose asymptotic stability is established via Lyapunov theory. Hardware-in-the-loop simulations using MATLAB/Simulink and a PLC demonstrate that, under ±3 kPa pressure constraints, the maximum engine inlet pressure error is 1.782 kPa (77.1% lower than PID control), and under an 80 kg/s2 flow-rate disturbance, valve oscillations decrease from ±27% to ±5%. These results confirm the superior disturbance rejection and decoupling performance of the proposed method. Full article
(This article belongs to the Special Issue Actuation and Robust Control Technologies for Aerospace Applications)
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22 pages, 4907 KiB  
Article
Predefined Time Control of State-Constrained Multi-Agent Systems Based on Command Filtering
by Jianhua Zhang, Xuan Yu, Quanmin Zhu and Zhanyang Yu
Mathematics 2025, 13(13), 2151; https://doi.org/10.3390/math13132151 - 30 Jun 2025
Viewed by 282
Abstract
This paper resolves the predefined-time control problem for multi-agent systems under predefined performance metrics and state constraints, addressing critical limitations of traditional methods—notably their inability to enforce strict user-specified deadlines for mission-critical operations, coupled with difficulties in simultaneously guaranteeing transient performance bounds and [...] Read more.
This paper resolves the predefined-time control problem for multi-agent systems under predefined performance metrics and state constraints, addressing critical limitations of traditional methods—notably their inability to enforce strict user-specified deadlines for mission-critical operations, coupled with difficulties in simultaneously guaranteeing transient performance bounds and state constraints while suffering prohibitive stability proof complexity. To overcome these challenges, we propose a predefined performance control methodology that integrates Barrier Lyapunov Functions command-filtered backstepping. The framework rigorously ensures exact convergence within user-defined time independent of initial conditions while enforcing strict state constraints through time-varying BLF boundaries and further delivers quantifiable performance such as overshoot below 5% and convergence within 10 s. By eliminating high-order derivative continuity proofs via command-filter design, stability analysis complexity is reduced by 40% versus conventional backstepping. Stability proofs and dual-case simulations (UAV formation/smart grid) demonstrate over 95% tracking accuracy under disturbances and constraints, validating broad applicability in safety-critical multi-agent systems. Full article
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15 pages, 13217 KiB  
Article
Production Reliability Technology Based on Vacuum Infusion Process Convergence to Design Strengthen Boat Safety
by Jong-Hwa Yoon, Hoon-Min Park and Dal-Hwan Yoon
Processes 2025, 13(7), 2025; https://doi.org/10.3390/pr13072025 - 26 Jun 2025
Viewed by 317
Abstract
In this paper, we develop technology to improve the stability and quality of boat equipment manufacturing through vacuum injection process fusion to increase the safety of boats. Safe mold design and fabrication are carried out to determine the resin flow rate and water [...] Read more.
In this paper, we develop technology to improve the stability and quality of boat equipment manufacturing through vacuum injection process fusion to increase the safety of boats. Safe mold design and fabrication are carried out to determine the resin flow rate and water flow rate of a boat, and the performance of vacuum maintenance work is guaranteed through the tensile and compressive strength of the manufactured hull and deck. When manufacturing the boat air mechanism (Aerostat), the adhesion between equipment materials and the deformation of the joints are very important factors for safety. Due to the nature of equipment manufacturing, process fusion to minimize manual process minimizes deformation after manufacturing through accurate manufacturing ratio. Accordingly, it is possible to accurately control the mixing ratio of resin and hardener as optimal conditions for boat drying and securing safety, and to convert optimal information into a database by analyzing working conditions over time such as resin flow rate and flow rate, thereby improving durability and quality. Through this, it is expected that production efficiency and safety design will be improved by enabling efficient production process management with a small number of personnel. Full article
(This article belongs to the Section AI-Enabled Process Engineering)
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18 pages, 1451 KiB  
Article
Sustainable Trajectory Tracking Control for Underactuated Ships Using Non-Singular Fast Terminal Sliding Mode Control
by Minjie Zheng, Qianqiang Chen, Yulai Su and Guoquan Chen
Sustainability 2025, 17(13), 5866; https://doi.org/10.3390/su17135866 - 26 Jun 2025
Viewed by 278
Abstract
Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To [...] Read more.
Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To address these challenges, this paper proposes a novel non-singular fast terminal sliding mode control (NFTSMC) strategy for sustainable trajectory tracking of underactuated ships. The proposed approach first designs a virtual control law based on surge and sway position errors, and then develops a non-singular fast terminal sliding mode control law using an exponential reaching strategy, guaranteeing finite-time convergence and eliminating singularities. The Lyapunov-based stability analysis proves the boundedness and convergence of tracking errors under external disturbances. The simulation results demonstrate that the proposed non-singular fast terminal sliding mode control outperforms traditional sliding mode control in terms of convergence speed, tracking accuracy, and control smoothness, especially under wind, wave, and current disturbances. Full article
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21 pages, 10392 KiB  
Article
Experimental Study of the Effect by Double-Stage Throttling on the Pressure Relief Characteristics of a Large-Scale CO2 Transportation Pipeline
by Huifang Song, Tingyi Wang, Jingjing Qi, Kai Jin, Jia Liu, Feng Li, Fanfan Qiao, Kun Zhao, Baoying Yin and Jianliang Yu
Energies 2025, 18(13), 3244; https://doi.org/10.3390/en18133244 - 20 Jun 2025
Viewed by 386
Abstract
The safety of pipeline transportation technology is the key to guaranteeing the development and application of CCUS. In the process of CO2 pipeline transportation, manual pressure relief may be required due to equipment failure, overpressure, or other reasons. However, the sharp temperature [...] Read more.
The safety of pipeline transportation technology is the key to guaranteeing the development and application of CCUS. In the process of CO2 pipeline transportation, manual pressure relief may be required due to equipment failure, overpressure, or other reasons. However, the sharp temperature drop in the evacuation process may lead to the formation of dry ice, which may cause a pipeline blockage and equipment damage. Although the multi-stage throttling method of pressure relief can effectively control the stability of the equipment, the effect on the low temperature of the pipeline needs to be further investigated. Therefore, in order to evaluate the safety of multi-stage throttling pressure relief, a comparative experiment of dense-phase venting with double-stage throttling was carried out based on an industrial-scale pipeline experimental device. The results show that the double-stage throttling pressure relief scheme can significantly reduce the pressure drop rate and improve the stability of the pressure relief structure. Moreover, the temperature drop limit upstream of the main pipeline is controlled under the double-stage throttling scheme, but it exacerbates the low temperature level downstream, which is not conducive to mitigating the risk of freeze-plugging of the pressure relief valve. Therefore, it is recommended that the double-stage throttling relief scheme be used to close the valve in time to return to the temperature and to adopt an intermittent means of pressure relief. Full article
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20 pages, 4965 KiB  
Article
Tools for Managing the Integrity of Tourist Volcanic Caves in the Canary Islands Due to Instability Problems
by Luis E. Hernández-Gutiérrez, Juan C. Santamarta, Leticia Pacheco, Esther Martín-González, Helena Hernández-Martín, Ramón Xifré and Carlos Calderón-Guerrero
Geosciences 2025, 15(7), 236; https://doi.org/10.3390/geosciences15070236 - 20 Jun 2025
Viewed by 756
Abstract
Natural caves have a great heritage and natural value, which has made them a tourist attraction that contributes positively to the diversification of tourist offerings in Spain. Volcanic caves are a particular type of natural cave, exclusive to the Canary Islands. The tourist [...] Read more.
Natural caves have a great heritage and natural value, which has made them a tourist attraction that contributes positively to the diversification of tourist offerings in Spain. Volcanic caves are a particular type of natural cave, exclusive to the Canary Islands. The tourist management of these caves entails certain peculiarities that do not occur in other types of tourist establishments. The caves are exposed to certain natural hazards that are important to recognize, evaluate, and where appropriate, plan and adopt the necessary measures to guarantee the safety of visitors and workers. The main natural hazard is the structural stability of the cavity, which can affect workers and visitors. Volcanic caves present structural, lithological, and geomechanical singularities that require a specific methodology to study their stability. This study proposes a specific protocol for the early detection and management of instabilities in tourist volcanic caves, in order to help with the proper management of this ecotourism resource. To this end, tools are provided for the recognition, characterization, and geological and geomechanical analysis, classification of the types of instability in volcanic tubes, and geospatial techniques to control the structural stability. Full article
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20 pages, 2636 KiB  
Article
Event-Triggered Secure Control Design Against False Data Injection Attacks via Lyapunov-Based Neural Networks
by Neslihan Karas Kutlucan, Levent Ucun and Janset Dasdemir
Sensors 2025, 25(12), 3634; https://doi.org/10.3390/s25123634 - 10 Jun 2025
Viewed by 462
Abstract
This paper presents a secure control framework enhanced with an event-triggered mechanism to ensure resilient and resource-efficient operation under false data injection (FDI) attacks on sensor measurements. The proposed method integrates a Kalman filter and a neural network (NN) to construct a hybrid [...] Read more.
This paper presents a secure control framework enhanced with an event-triggered mechanism to ensure resilient and resource-efficient operation under false data injection (FDI) attacks on sensor measurements. The proposed method integrates a Kalman filter and a neural network (NN) to construct a hybrid observer capable of detecting and compensating for malicious anomalies in sensor measurements in real time. Lyapunov-based update laws are developed for the neural network weights to ensure closed-loop system stability. To efficiently manage system resources and minimize unnecessary control actions, an event-triggered control (ETC) strategy is incorporated, updating the control input only when a predefined triggering condition is violated. A Lyapunov-based stability analysis is conducted, and linear matrix inequality (LMI) conditions are formulated to guarantee the boundedness of estimation and system errors, as well as to determine the triggering threshold used in the event-triggered mechanism. Simulation studies on a two-degree-of-freedom (2-DOF) robot manipulator validate the effectiveness of the proposed scheme in mitigating various FDI attack scenarios while reducing control redundancy and computational overhead. The results demonstrate the framework’s suitability for secure and resource-aware control in safety-critical applications. Full article
(This article belongs to the Special Issue Anomaly Detection and Fault Diagnosis in Sensor Networks)
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24 pages, 9811 KiB  
Article
A Robust Strategy for Sensor Fault Reconstruction of Lower Limb Rehabilitation Exoskeleton Robots
by Zhe Sun, Zhuguang Li, Jinchuan Zheng and Zhihong Man
Actuators 2025, 14(6), 277; https://doi.org/10.3390/act14060277 - 6 Jun 2025
Viewed by 1190
Abstract
Ensuring the reliability and stability of lower limb rehabilitation exoskeleton robots during rehabilitation training is of paramount importance. Sensor faults in such systems can degrade overall performance and may even pose significant safety hazards. Consequently, the effective reconstruction of sensor faults has become [...] Read more.
Ensuring the reliability and stability of lower limb rehabilitation exoskeleton robots during rehabilitation training is of paramount importance. Sensor faults in such systems can degrade overall performance and may even pose significant safety hazards. Consequently, the effective reconstruction of sensor faults has become a critical challenge in ensuring the safe and dependable operation of lower limb rehabilitation exoskeleton robots. This paper presents a novel sensor fault reconstruction method for systems subject to unknown external disturbances. Initially, an equivalent input disturbance (EID) approach based on an improved sliding mode observer is developed to mitigate the adverse effects of disturbances on the fault reconstruction process. Subsequently, a novel high-order sliding mode observer (NHSMO) is proposed to accurately reconstruct sensor faults. In contrast to conventional sliding mode observers, the proposed NHSMO guarantees finite-time convergence of the observation error, thereby enhancing both estimation accuracy and robustness. The effectiveness of this method is validated through both simulation and experimental results, demonstrating its superior fault reconstruction capabilities and strong resilience to external disturbances. Full article
(This article belongs to the Special Issue Advanced Perception and Control of Intelligent Equipment)
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35 pages, 9764 KiB  
Review
Development of Gas Sensors and Their Applications in Health Safety, Medical Detection, and Diagnosis
by Jiayu Wang and Rui Wang
Chemosensors 2025, 13(5), 190; https://doi.org/10.3390/chemosensors13050190 - 20 May 2025
Viewed by 2225
Abstract
Gas sensors assume a crucial role in the medical domain, offering substantial support for disease diagnosis, treatment, medical environment management, and the operation of medical equipment by virtue of their distinctive gas detection capabilities. This paper presents an overview of the key research [...] Read more.
Gas sensors assume a crucial role in the medical domain, offering substantial support for disease diagnosis, treatment, medical environment management, and the operation of medical equipment by virtue of their distinctive gas detection capabilities. This paper presents an overview of the key research and development orientations for gas sensors, encompassing the exploration and optimization of novel sensitive materials, such as nanomaterials and metal oxides, to augment sensor sensitivity, selectivity, and stability. The innovation in sensor structural design, particularly the integration of micro-electromechanical systems (MEMS) technology to attain miniaturization and integration, is also addressed. The applications of gas sensors in health safety are expounded, covering the real-time monitoring of indoor air quality for harmful gases such as formaldehyde, as well as the detection of toxic gases in industrial environments to guarantee the safety of living and working spaces and prevent occupational health hazards. In the sphere of medical detection and diagnosis, this paper focuses on the detection of biomarkers in human exhaled breath by gas sensors, which facilitates the early diagnosis of diseases such as lung cancer. Additionally, the existing challenges and future development trends in this field are analyzed, with the aim of providing a comprehensive reference for the in-depth research and extensive application of gas sensors in the health, safety, and medical fields. Full article
(This article belongs to the Special Issue Electrochemical Sensing in Medical Diagnosis)
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44 pages, 3653 KiB  
Review
Certified Neural Network Control Architectures: Methodological Advances in Stability, Robustness, and Cross-Domain Applications
by Rui Liu, Jianhua Huang, Biao Lu and Weili Ding
Mathematics 2025, 13(10), 1677; https://doi.org/10.3390/math13101677 - 20 May 2025
Viewed by 1129
Abstract
Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of [...] Read more.
Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of Lyapunov stability theory, NN controller frameworks, and robustness analysis. The review establishes that recurrent neural architectures inherently address time-delayed state compensation and disturbance rejection, achieving superior trajectory tracking performance compared to classical control strategies. By integrating imitation learning with barrier certificate constraints, the proposed methodology ensures provable closed-loop stability while maintaining safety-critical operation bounds. Experimental evaluations using chaotic system benchmarks confirm the exceptional modeling capacity of NN controllers in capturing complex dynamical behaviors, complemented by formal verification advances through reachability analysis techniques. Practical demonstrations in aerial robotics and intelligent transportation systems highlight the efficacy of controllers in real-world scenarios involving environmental uncertainties and multi-agent interactions. The theoretical framework synergizes data-driven learning with nonlinear control principles, introducing hybrid automata formulations for transient response analysis and adjoint sensitivity methods for network optimization. These innovations position NN controllers as a transformative technology in control engineering, offering fundamental advances in stability-guaranteed learning and topology optimization. Future research directions will emphasize the integration of physics-informed neural operators for distributed control systems and event-triggered implementations for resource-constrained applications, paving the way for next-generation intelligent control architectures. Full article
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25 pages, 20932 KiB  
Article
Study on the Failure Mechanism of Deep Foundation Pit of High-Rise Building: Comprehensive Test and Microstructure Coupling
by Zhiwu Zhou, Lorena Yepes-Bellver, Julián Alcalá and Víctor Yepes
Buildings 2025, 15(8), 1270; https://doi.org/10.3390/buildings15081270 - 12 Apr 2025
Viewed by 929
Abstract
Under the adverse geological conditions of silty soft soil in coastal, lakeside, and river areas of countries worldwide, safety and quality during deep foundation pit construction are research challenges that researchers must overcome. Through 3D simulation, micro-finite element coupling modeling and construction site [...] Read more.
Under the adverse geological conditions of silty soft soil in coastal, lakeside, and river areas of countries worldwide, safety and quality during deep foundation pit construction are research challenges that researchers must overcome. Through 3D simulation, micro-finite element coupling modeling and construction site monitoring tests, this paper comprehensively analyzes the formation mechanism and causes of deep foundation pit foundation quality defects and diseases under the most unfavorable environment and multi-factor interference and puts forward scientific treatment suggestions. The research process accurately applies multidisciplinary coupling model research such as computer science, instrument science and technology, and material mechanics to solve the impact of multi-factor and uncertain environments on construction. The final research results provide sufficient theoretical and physical cases for improving the safety and stability of deep foundation pits under soft foundation conditions and provide rich practical specifications for the testing, monitoring and construction of similar projects; it provides a strong guarantee for the global deep foundation pit monitoring and early warning system under soft foundation conditions. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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36 pages, 28924 KiB  
Article
Mechanical Research and Optimization of the Design of an Umbrella-Shaped Enlarged-Head Hollow Grouting Bolt with an Expansion Pipe
by Jiang Xiao, Tongxiaoyu Wang, Youyun Li, Yulin Wang, Yujiang Liu, Boyuan Zhang, Yihui Wang and Yufeng Guo
Appl. Sci. 2025, 15(8), 4182; https://doi.org/10.3390/app15084182 - 10 Apr 2025
Viewed by 569
Abstract
In geotechnical engineering, traditional anchor bolts often have problems such as an insufficient bearing capacity, their ease of loosening, and an unsatisfactory support effect under complex geological conditions (such as soft soil or broken surrounding rock), resulting in it being difficult to guarantee [...] Read more.
In geotechnical engineering, traditional anchor bolts often have problems such as an insufficient bearing capacity, their ease of loosening, and an unsatisfactory support effect under complex geological conditions (such as soft soil or broken surrounding rock), resulting in it being difficult to guarantee engineering stability. In order to solve these problems, this paper studies the supporting performance of a hollow grouting anchor with an umbrella-shaped expansion head with an expansion pipe. Through theoretical analysis, mechanical performance analysis, and experimental analysis, the supporting mechanisms and mechanical characteristics of a hollow grouting anchor with an umbrella-shaped expansion head are systematically discussed. The calculation formula for the maximum pull-out force of the umbrella-shaped expansion head is clarified, and the fixed range of the expansion body section in relation to the loose ring is quantified. Based on the analysis results, the structural parameters and material properties of the bolt were optimized, and the optimization effect was verified by numerical simulation. The results show that the optimized bolt has significantly improved the pull-out bearing capacity, shear resistance, and reinforcement effect on the soil. The maximum pull-out force of the umbrella-shaped expansion head can be increased by up to 35%, and the fixed range of the expansion body section can be expanded by 45%. The research provides an efficient and reliable support solution for geotechnical engineering fields, such as roadway engineering and tunnel engineering, which significantly improves the stability and safety of engineering under complex geological conditions. At the same time, it provides an important theoretical basis and practical reference for the design and construction of similar projects. Full article
(This article belongs to the Special Issue Progress and Challenges of Rock Engineering)
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13 pages, 284 KiB  
Article
Caputo Barrier Functions and Their Applications to the Safety, Safety-and-Stability, and Input-to-State Safety of a Class of Fractional-Order Systems
by Zheren Zhu, Bingbing Shen, Le Yao, Yi Chai and Zhihuan Song
Mathematics 2025, 13(8), 1215; https://doi.org/10.3390/math13081215 - 8 Apr 2025
Viewed by 367
Abstract
Safety control based on barrier functions has gradually become one of the emerging and more important directions in the field of safety. Scholars are attempting to apply barrier functions to integer-order dynamical systems, such as general nonlinear systems, hybrid systems, linear systems, etc. [...] Read more.
Safety control based on barrier functions has gradually become one of the emerging and more important directions in the field of safety. Scholars are attempting to apply barrier functions to integer-order dynamical systems, such as general nonlinear systems, hybrid systems, linear systems, etc. Moreover, the introduction of barrier functions has even expanded the research approaches on safe reinforcement learning. However, there is very little research on the safety control problem of fractional-order dynamical systems. Based on our previous work, this article further explores, in depth, the problem of the transfer and adaptability of barrier functions for integer-order systems in fractional-order systems, and it also proposes the Caputo reciprocal barrier function and Caputo zeroing barrier function. And we established two theorems, which proved that we can also achieve uniform asymptotic stability or exponential stability with guaranteed safety. In the end, we created a new description for the definition of input-to-state safety under Caputo’s fractional-order systems, and we used this description and the above two Caputo barrier functions to construct two criteria of the Caputo input-to-state safety. Thus, we, finally, established the embryonic form of the theoretical framework of safety control based on barrier functions for fractional-order systems. Full article
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