随着煤炭洗选行业的智能化发展，柔索驱动拣矸机器人作为集识别、控制和驱动于一体的综合系统，已成为实现煤矸石自动识别和快速分拣的有效方案。机器人可靠性研究是机器人系统安全可靠工作的基本保障，是推动其工程应用的重要前提。本文对柔索驱动拣矸机器人的系统分拣可靠性和运动精度可靠性进行研究，旨在为柔索驱动拣矸机器人可靠性评估和轨迹规划提供理论依据和指导。本文主要研究工作如下：

(1)柔索驱动拣矸机器人系统分拣可靠性分析：针对柔索驱动拣矸机器人系统分拣可靠性评估问题，采用故障树分析方法进行研究。从系统结构组成及工作原理出发，分析系统分拣故障原因，构建分拣故障树模型。通过定性分析确定分拣故障树的最小割集和结构重要度。在定量分析中将故障树底事件发生概率视为为区间变量，计算出反映系统分拣可靠性程度的非概率可靠性指标，提出了一种区间重要度指标，并对底事件的区间重要度进行求解排序。计算结果表明，柔索驱动拣矸机器人分拣可靠性程度满足机器人分拣可靠性要求。煤矸石流瞬时含矸率增大和工业相机故障是影响其分拣可靠性的重要因素，并针对重要因素提出振荡混合煤矸石流、智能控制带速和增加备用工业相机3个改进措施。

(2)柔索驱动拣矸机器人运动精度可靠性分析：针对末端抓斗空间位置变化导致的多极限状态函数运动精度可靠性问题，提出一种柔索驱动拣矸机器人运动精度可靠性分析方法。采用矢量合成法和矩阵全微分法建立分别建立机器人运动学模型和运动误差模型。结合运动精度要求建立单点运动精度可靠性模型。运用均值一次二阶矩法对可靠性模型进行求解。将运动可靠工作空间定义为末端抓斗运动精度可靠性满足要求的所有位置点构成的集合，以单点运动精度可靠性模型为基础，运用空间离散重组思想对其进行求解。运动可靠工作空间为柔索驱动拣矸机器人运动精度可靠评估提供了理论依据，为轨迹规划提供了有益参考。

(3)柔索驱动拣矸机器人运动精度可靠性灵敏度分析：针对末端抓斗空间位置变化导致的多极限状态函数运动精度可靠性灵敏度问题，将运动精度可靠性灵敏度分为局部灵敏度和全局灵敏度。基于单点运动精度可靠性模型求解方法，推导相应的均值一次二阶矩公式，以求解单点局部灵敏度和轨迹局部灵敏度。以单点局部灵敏度为基础，运用空间离散思想对运动精度可靠性全局灵敏度进行求解。局部灵敏度和全局灵敏度为识别出运动精度可靠性敏感源提供理论依据，为轨迹规划提供有益参考。

With the advancement of intelligent technology in the coal washing industry, the cable-driven gangue sorting robot, which integrates identification, control, and driving, has emerged as an effective solution for automatic identification and rapid sorting of coal gangue. Research on robot reliability is fundamental for ensuring the safe and reliable operation of robot systems and is a crucial prerequisite for promoting their engineering applications. In this paper, the system sorting reliability and motion accuracy reliability of the cable-driven gangue sorting robot are studied, aiming to provide theoretical basis and guidance for the reliability evaluation and trajectory planning of the cable-driven gangue sorting robot. The main research work of this paper is as follows :

(1) Sorting reliability analysis of cable-driven gangue sorting robot system: To address the evaluation of sorting reliability in cable-driven gangue sorting robot systems, the fault tree analysis method is used to study. Starting from the system structure and working principle, the causes of system sorting failure are analyzed, and the sorting fault tree model is constructed.The minimum cut set and structural importance of the sorting fault tree are determined by qualitative analysis. In the quantitative analysis, the probability of the bottom event of the fault tree is regarded as an interval variable, and the non-probabilistic reliability index reflecting the reliability degree of the system sorting is calculated. An interval importance index is proposed, and the interval importance of the bottom event is solved and sorted. The calculation results demonstrate that the sorting reliability meets the requirements for robot sorting reliability. The increase of instantaneous gangue content of coal gangue flow and the failure of industrial camera are important factors affecting its sorting reliability. Three improvement measures are proposed for the important factors, including oscillating mixed coal gangue flow, intelligent control of belt speed and increasing standby industrial camera.

(2) Motion accuracy reliability analysis of cable-driven gangue sorting robot: To address the motion accuracy reliability issue in multi-limit state functions due to the change in spatial position of the end grab, a reliability analysis method for motion accuracy of cable-driven gangue sorting robots is proposed. The robot kinematics model and motion error model are established by vector synthesis method and matrix total differential method respectively. Combined with the motion accuracy requirements, a single point motion accuracy reliability model is established. The mean first-order second-moment method is used to solve the reliability model. The motion reliable workspace is defined as a set of all position points that meet the requirements of the motion accuracy reliability of the end grab. Based on the single point motion accuracy reliability model, the spatial discrete recombination idea is used to solve it. The reliable workspace provides a theoretical basis for the reliable evaluation of the motion accuracy of the cable-driven gangue sorting robot, and provides a useful reference for trajectory planning.

(3) Reliability sensitivity analysis of motion accuracy of cable-driven gangue sorting robot: To address the reliability sensitivity of motion accuracy in multi-limit state functions due to the change in spatial position of the end grab, the reliability sensitivity of motion accuracy is divided into local sensitivity and global sensitivity. Based on the single-point motion accuracy reliability model solution method, the corresponding mean first-order second-moment formula is derived to solve the single-point local sensitivity and trajectory local sensitivity. Based on the single point local sensitivity, the global sensitivity of motion accuracy reliability is solved by using the idea of spatial discretization. Local sensitivity and global sensitivity provide a theoretical basis for identifying the reliability sensitive source of motion accuracy and provide a useful reference for trajectory planning.

[1]谢和平, 吴立新, 郑德志. 2025年中国能源消费及煤炭需求预测[J]. 煤炭学报, 2019, 44(07): 1949-1960.

[2]李璐璐. 中国煤炭消耗的驱动因素及供应链路径分析[D]. 长沙: 长沙理工大学, 2020.

[3]杨钧晗. 燃煤电厂固体吸收剂捕集二氧化碳的研究进展[J]. 节能, 2023 ,42(02): 90-93.

[4]孙倩. 煤炭成本指数编制及应用研究[D]. 青岛: 山东科技大学, 2018.

[5]中矿(北京)煤炭产业景气指数研究课题组, 岳福斌.2020-2021年中国煤炭产业经济形势研究报告[J]. 中国煤炭, 2021, 47(03): 53-61.

[6]卢前明, 韩红强, 张瑞林,等. 三软煤层改造回风巷过断层技术研究[J]. 煤炭科学技术, 2017, 45(12): 64-69.

[7]缪协兴, 张吉雄. 井下煤矸分离与综合机械化固体充填采煤技术[J]. 煤炭学报, 2014, 39(08): 1424-1433.

[8]Hou W.Identification of coal and gangue by feed-forward neural network based on data analysis[J]. International Journal of Coal Preparation and Utilization,2019, 39(1):33-43.

[9]来文豪, 周孟然, 胡锋,等. 基于多光谱成像和改进YOLO v4的煤矸石检测[J]. 光学学报, 2020, 40(24): 72-80.

[10]夏晶, 张昊, 周世宁,等. 煤矸分拣机器人动态拣取避障路径规划[J].煤炭学报, 2021, 46(S1): 570-577.

[11]曹现刚, 吴旭东, 王鹏,等. 面向煤矸分拣机器人的多机械臂协同策略[J]. 煤炭学报, 2019, 44(S2): 763-774.

[12]王鹏, 曹现刚, 夏晶,等. 基于机器视觉的多机械臂煤矸石分拣机器人系统研究[J]. 工矿自动化, 2019, 45(9): 47-53.

[13]王晓波. 工程质量风险分析与质量事故损失预测研究[D]. 武汉: 华中科技大学, 2020.

[14]杨晓宇. DFFS自主乘用车发动机质量管理研究[D]. 武汉: 华中科技大学,2019.

[15]Fazlollahtabar H ,Niaki S. Integration of fault tree analysis , reliability block diagram and hazard decision tree for industrial robot reliability evaluation[J].Industrial Robot,2017,44(6):754-764.

[16]Balasundaram M , Muthuswamy S. Implementation of role assignment and fault tree analysis for multi robot interaction[J].International Journal of Robotics and Automation,2017,32(3):214-223.

[17]张蓉, 王春洁. 基于FMEA和FTA的三自由度直角坐标机器人系统可靠性仿真分析[J]. 机械科学与技术, 2006, 25(6): 651-654.

[18]刘瑞达. 基于微创手术机器人传动系统故障关联的可靠性研究[D]. 天津: 天津大学, 2019.

[19]周长聪, 常琦, 周春苹,等. 基于非概率模型的飞机襟翼故障树分析[J]. 清华大学学报(自然科学版), 2021, 61(06): 636-642.

[20]Jiang G J, Gao L.Reliability analysis of martial arts arena robot systems based on fuzzy set theory[J]. Journal of Mechanical Science and Technology, 2018, 32(11): 5069-5077.

[21]Fersguson T A, Lu L X. Fault tree analysis for an inspection robot in a nuclear power plant[C]// IOP Conference Series: Materials Science and Engineering,2nd International Conference on Automation, Control and Robotics Engineering (CACRE 2017), Prague, 2017:1-5.

[22]陈科百. 机器人智能柔性生产线远程维护系统研究[D]. 重庆: 重庆交通大学, 2020.

[23]方启程, 周俊, 戴文静,等. 基于Petri网的柔性制造系统中工业机器人故障诊断[J]. 上海工程技术大学学报, 2015, 29(03): 203-208.

[24]胡晓伟. 串联机器人运动误差及可靠性分析[D]. 青岛: 青岛科技大学, 2019.

[25]陈霞. 蠕动式缆索机器人模糊故障树分析与应用[J]. 机械设计, 2015, 32(8): 31-35.

[26]白斌, 张俊一, 周策,等. 基于T-S模糊故障树的工业机器人可靠性分析[J]. 机械强度, 2021, 43(06): 1348-1358.

[27]刘禹含. 空间细胞机器人运动误差及可靠性分析[D].哈尔滨: 哈尔滨工业大学,2020.

[28]张钰曼. 工业机器人健康状态诊断与评估方法研究[D]. 邯郸: 河北工程大学, 2022.

[29]宋文军. 焊接机器人故障树分析[D]. 沈阳: 东北大学, 2015.

[30]邓超, 陶志奎, 吴军. 脚踝康复机器人的可靠性评估[J]. 工业工程, 2018, 21(05): 50-56.

[31]杨鲲, 卢倪斌, 隋海琛,等. 基于D-H方法的波浪滑翔器动力学仿真分析[J]. 哈尔滨工程大学学报, 2020, 41(01): 145-152.

[32]Jiang L, Gao B, Zhu Z. Dynamic modeling and control of a cable-driven parallel mechanism with a spring spine[J]. ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 1989-1996 (vols 203-210), 2017, 231(21):095440621769817.

[33]Erika O, Andrea A, Vincenzo G. Geometrically exact three-dimensional modeling of cable-driven parallel manipulators for end-effector positioning[J]. Mechanism and Machine Theory, 2021, 155.

[34]Cheng L,Hou Z G,Tan M. Adaptive neural network tracking control for manipulators with uncertain kinematics,dynamics and actuator model[J]. Automatica,2009,45(10):2312-2318.

[35]Wan A,Xu J, Chen H P,et al. Optimal path planningand control of assembly robots for hard-measuring easy-deformation assemblies[J]. IEEE/ASMET ransactionson Mechatronics, 2017, 22(4): 1600-1609.

[36]张馨龙, 田光宇, 黄勇. 三轴正交机器人运动误差的建模与分析[J]. 计量学报, 2017, 38(04): 396-401.

[37]张志雄, 江志新, 杨拥民,等. 关节对中误差对机械臂末端定位精度影响[J]. 国防科技大学学报, 2014, 36(06): 185-190.

[38]陈钢, 贾庆轩, 李彤,等. 基于误差模型的机器人运动学参数标定方法与实验[J]. 机器人, 2012, 34(06): 680-688.

[39]刘恩, 曾凯, 何晓聪,等. TGK46100数控坐标镗床机构运动精度可靠性建模分析[J]. 组合机床与自动化加工技术, 2014, 486(08): 31-33+43.

[40]Pandey M D,Zhang X.System reliability analysis of the robotic manipulator with random joint clearances[J].Mechanism and Machine Theory, 2012, 58: 137-152.

[41]Wang L,Zhang X, Zhou Y. An effective approach for kinematic reliability analysis of steering mechanisms[J]. Reliability Engineering & System Safety, 2018, 180: 62-76.

[42]文瑞桥, 杨梦鸥, 刘涛,等. 机器人的运动时变可靠性分析[J]. 工程设计学报, 2018, 25(1): 50-55.

[43]吴海淼, 陈鹏, 崔国华,等. 基于改进四阶矩估计法的六轴机器人运动可靠性分析[J]. 机械设计与研究, 2019,35(05): 11-14+23.

[44]王伟, 王进, 陆国栋. 基于四阶矩估计的机器人运动可靠性分析[J]. 浙江大学学报(工学版), 2018, 52(01): 1-7+49.

[45]冯嘉珍, 贾庆轩, 孙汉旭. 空间柔性机械臂运动功能可靠性分析[J]. 制造业自动化, 2010, 32(11): 116-118.

[46]王汝贵, 陈辉庆.变胞机构多失效模式运动可靠性分析与优化[J]. 机械工程学报, 2021, 57(11): 184-194.

[47]胡鹏. 非线性齿轮系统动力学与稳态可靠性及灵敏度分析[D]. 沈阳: 东北大学, 2019.

[48]Bruls O, Eberhard P. Sensitivity analysis for dynamic mechanical systems with finite rotation[J].International Journal for Numerical Methods in Engineering, 2008, 74(13): 1897-1927.

[49]Vanvinckenroye H, Denoel .Second-ordermoment of the first passage time of a quasi-Hamiltonian oscillator with stochastic parametric and forcing excitations[J].Journal of Sound and Vibration, 2018, 427: 178-187.

[50]张永利, 吕震宙, 李生兰. 可靠性及可靠性灵敏度分析的改进点估计方法[J]. 南京航空航天大学学报, 2016, 48(5): 705-714.

[51]Hassan A, Mohsen R. Reliability and reliability-based sensitivity analysis of shell and tube heat exchangers using Monte Carlo Simulation[J]. Applied Thermal Engineering, 2019, 159: 113842.

[52]Sbol I. A primer for the Monte Carlo method[M]. CRC Press,1994.

[53]吕震宙, 宋述芳, 李洪双,等. 结构机构可靠性及可靠性灵敏度分析[M]. 北京: 科学出版社, 2009, 91-114.

[54]史妍妍, 孙志礼, 闫明. 基于响应面法的隐式极限状态函数可靠性灵敏度分析方法[J]. 机械科学与技术, 2009, 28(5): 648-651.

[55]Tannousa M, Carob S, Goldsztejn A. Sensitivity analysis of parallel manipulators using an interval linearization method[J]. Mechanism and Machine Theory, 2014, 71: 93-114.

[56]王海芳, 皇甫一樊, 张恒,等. 两种典型串、并联机器人速度精度可靠性分析[J]. 中国工程机械学报, 2019, 17(02): 166-171.

[57]李明昊, 乔捷, 赵丽娟,等. 仿生虎鲸负载特性数值模拟及可靠性灵敏度分析[J]. 机械强度, 2021, 43(03): 622-628.

[58]李国发, 韩良晟, 何佳龙,等. 考虑制造误差的工业机器人精度可靠性分析[J]. 制造技术与机床, 2022, 719(05): 5-11.

[59]金玲燕. 工业机器人运动精度可靠性分析及关节状态监测研究[D]. 杭州: 浙江理工大学, 2021.

[60]巴凯先, 康岩, 俞滨,等. 足式机器人轻量化液压驱动执行器质量建模及灵敏度分析[J]. 机械工程学报, 2021, 57(24): 39-48+82.

[61]毕富国, 何广平. 微型扑翼飞行器动力学模型参数的灵敏度分析[J]. 兵器装备工程学报, 2019, 40(08): 94-99.

[62]宰玉. 某重型商用车可靠性评价体系研究[D]. 合肥：合肥工业大学, 2018.

[63]朱文予. 机械概率设计与模糊设计[M]. 北京: 高等教育出版社, 2001: 199-201.

[64]Cheng S R, Liu B S, Hsu B M, et al. Fault-tree analysis for liquefied natural gas terminal emergency shutdown system[J]. Expert Systems with Applications, 2009, 36(9): 11918-11924.

[65]訾斌. 混合驱动柔索并联机器人力学分析与跟踪控制技术[M]. 北京: 科学出版社, 2018: 86-102.

[66]黄鹏. 混合不确定性下工业机器人运动精度可靠性分析与优化设计[D]. 成都: 电子科技大学, 2021.

[67]贡金鑫. 工程结构可靠度计算方法[M]. 大连: 大连理工大学出版社, 2003: 325-331.

[68]杨健. 四索牵引摄像机器人稳定性分析[D]. 西安: 西安电子科技大学, 2014.

[69]刘鹏, 马宏伟, 乔心州,等. 柔索驱动拣矸机器人最小索拉力等值曲面研究[J]. 西安科技大学学报, 2020, 40(05): 797-804.

[70]刘晓静. 基于蒙特卡洛方法的可靠性灵敏度分析[J].机械管理开发, 2021, 36(11): 53-55