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Nonlinear model predictive control with set terminal constraint for safe robot motion planning via speed and separation monitoring 非线性模型预测控制与设定终端约束,通过速度和分离监控实现安全的机器人运动规划
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-08 DOI: 10.1016/j.conengprac.2024.106155
Aigerim Nurbayeva, Matteo Rubagotti
This paper proposes a methodology for safely planning the motion of a robot manipulator sharing its workspace with a human operator. The motion of the robot is continuously re-planned via nonlinear model predictive control (NMPC), imposing the so-called speed and separation monitoring (SSM) condition to guarantee human safety. Contrary to previous works in the field, the NMPC algorithm is designed with an ellipsoidal terminal constraint, to enlarge the domain of attraction compared to the case in which a point terminal constraint was imposed. This is a very important aspect in real-world applications, allowing the robot to plan its motion from initial configurations that are relatively far from the goal point. Theoretical results are proved on recursive feasibility and closed-loop stability for both cases of NMPC with point and set terminal constraints, under the simplifying assumption of a static human. The effectiveness of the proposed approach is verified via numerical evaluation of the domain of attraction and with experiments on a UR5 manipulator.
本文提出了一种方法,用于安全规划与人类操作员共享工作空间的机器人机械手的运动。通过非线性模型预测控制(NMPC)不断重新规划机器人的运动,并施加所谓的速度和分离监控(SSM)条件,以确保人类安全。与该领域以前的工作不同,NMPC 算法设计了一个椭圆形终端约束,与施加点终端约束的情况相比,扩大了吸引域。这在实际应用中是非常重要的,它允许机器人从离目标点相对较远的初始配置开始规划运动。在人类静态的简化假设下,证明了带有点和集合终端约束的 NMPC 两种情况下的递归可行性和闭环稳定性的理论结果。通过对吸引域进行数值评估以及在 UR5 机械手上进行实验,验证了所提方法的有效性。
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引用次数: 0
Randomized iterative feedback tuning for fast MIMO feedback design of a mechatronic system 随机迭代反馈调整用于机电一体化系统的快速 MIMO 反馈设计
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-06 DOI: 10.1016/j.conengprac.2024.106152
Leontine Aarnoudse , Peter den Toom , Tom Oomen
Iterative feedback tuning (IFT) enables the tuning of feedback controllers using only measured data to obtain the gradient of a cost criterion. The aim of this paper is to reduce the required number of experiments for MIMO IFT. It is shown that, through a randomization technique, an unbiased gradient estimate can be obtained from a single dedicated experiment, regardless of the size of the MIMO system. The gradient estimate is used in a stochastic gradient descent algorithm. The approach is experimentally validated on a mechatronic system, showing a significantly reduced number of experiments compared to standard IFT.
迭代反馈调谐(IFT)可以仅使用测量数据来获得成本准则的梯度,从而对反馈控制器进行调谐。本文旨在减少 MIMO IFT 所需的实验次数。研究表明,通过随机化技术,无论多输入多输出系统的规模如何,都能从一次专门实验中获得无偏梯度估计值。梯度估计值用于随机梯度下降算法。该方法在机电一体化系统上进行了实验验证,结果表明,与标准 IFT 相比,实验次数大大减少。
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引用次数: 0
Control design and analysis for autonomous underwater vehicles using integral quadratic constraints 使用积分二次约束的自主式水下航行器控制设计与分析
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-05 DOI: 10.1016/j.conengprac.2024.106142
Sourav Sinha , Mazen Farhood , Daniel J. Stilwell
This paper addresses the design and analysis of path-following controllers for an autonomous underwater vehicle (AUV) using a robustness analysis framework based on integral quadratic constraints (IQCs). The AUV is modeled as a linear fractional transformation (LFT) on uncertainties and is affected by exogenous inputs such as measurement noise and ocean currents. The proposed approach leverages a learning-based method to approximate the nonlinear hydrodynamic model with a linear parameter-varying one. Additionally, modeling uncertainties are incorporated into the other subsystem models of the AUV to capture the discrepancies between the outputs of the postulated mathematical abstractions and the experimental data. The resulting uncertain LFT system adequately captures the AUV behavior within a desired envelope. Ocean current disturbances are treated as uncertainties within the LFT system and properly characterized to reduce conservatism. The robust performance level, obtained from IQC analysis, serves as a qualitative measure of a controller’s performance, and is utilized in guiding the controller design process. The proposed approach is employed to design H and H2 controllers for the AUV. A comprehensive IQC-based analysis is subsequently conducted to demonstrate the robustness of the designed controllers to modeling uncertainties and disturbances. To validate the analysis results, extensive nonlinear simulations and underwater experiments are performed. The outcomes showcase the efficacy and reliability of the proposed approach in achieving robust control for the AUV.
本文采用基于积分二次约束(IQC)的鲁棒性分析框架,对自主潜水器(AUV)的路径跟踪控制器进行了设计和分析。AUV 被建模为不确定性线性分数变换 (LFT),并受到测量噪声和洋流等外生输入的影响。所提出的方法利用基于学习的方法,用线性参数变化模型来近似非线性流体动力学模型。此外,在 AUV 的其他子系统模型中加入了建模不确定性,以捕捉假设的数学抽象输出与实验数据之间的差异。由此产生的不确定 LFT 系统可在所需范围内充分捕捉 AUV 的行为。洋流干扰被视为 LFT 系统中的不确定因素,并被适当描述以减少保守性。通过 IQC 分析获得的鲁棒性能水平可作为控制器性能的定性衡量标准,并用于指导控制器的设计过程。所提出的方法被用于为 AUV 设计 H∞ 和 H2 控制器。随后进行了基于 IQC 的综合分析,以证明所设计的控制器对模型不确定性和干扰的鲁棒性。为了验证分析结果,进行了大量的非线性模拟和水下实验。结果表明了所提出的方法在实现 AUV 鲁棒控制方面的有效性和可靠性。
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引用次数: 0
Time-optimal multi-point trajectory generation for robotic manipulators with continuous jerk and constant average acceleration 为具有连续颠簸和恒定平均加速度的机器人机械手生成时间最优多点轨迹
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-05 DOI: 10.1016/j.conengprac.2024.106154
Weiguang Yu , Daokui Qu , Fang Xu , Lei Zhang , Fengshan Zou , Zhenjun Du
To meet the demands of high-speed and high-accuracy applications of robotic manipulators, this paper proposes a time-optimal multi-point trajectory planning method with continuous jerk and constant average acceleration. A piecewise sine jerk model is developed for jerk continuity throughout the entire motion profile. An equivalent transformation of this complex model into the simple trapezoidal velocity model is proposed, effectively reducing the computational complexity and ensuring the reliability of real-time planning. The introduction of a parameter, named the trajectory smoothness coefficient, allows for a convenient trade-off between the priorities of speed and smoothness. The adaptive computation algorithm for peak jerk results in a constant average acceleration along paths of any length, ensuring a consistent level of work efficiency regardless of the density of path control points. Through a comprehensive evaluation of the critical constraints for each potential profile type, the single joint’s time-optimal and multiple joints’ time-synchronized planning problems are solved with closed-form solutions. Furthermore, by designing a multi-joint multi-point velocity look-ahead strategy, time-optimal multi-point trajectory planning for robotic manipulators is realized. Simulation and experimental results on a manipulator demonstrate the effectiveness of the proposed approach in improving time efficiency.
为满足机器人机械手高速、高精度的应用需求,本文提出了一种具有连续颠簸和恒定平均加速度的时间最优多点轨迹规划方法。为了实现整个运动曲线的颠簸连续性,本文开发了一种片状正弦颠簸模型。将这一复杂模型等效转换为简单的梯形速度模型,有效降低了计算复杂度,确保了实时规划的可靠性。通过引入一个名为轨迹平滑系数的参数,可以方便地权衡速度和平滑的优先级。峰值颠簸的自适应计算算法使得任何长度的路径都能获得恒定的平均加速度,从而确保了无论路径控制点的密度如何,都能达到一致的工作效率水平。通过对每种潜在轮廓类型的关键约束条件进行综合评估,单关节时间最优规划问题和多关节时间同步规划问题均以闭合形式求解。此外,通过设计多关节多点速度前瞻策略,实现了机器人机械手的时间最优多点轨迹规划。在机械手上进行的仿真和实验结果证明了所提出的方法在提高时间效率方面的有效性。
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引用次数: 0
Lane-free signal-free intersection crossing via model predictive control 通过模型预测控制实现无车道无信号交叉口穿越
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-05 DOI: 10.1016/j.conengprac.2024.106115
Mehdi Naderi , Panagiotis Typaldos , Markos Papageorgiou
The operation of signal-free intersections, where Connected Automated Vehicles (CAVs) cross simultaneously for all Origin-Destination (OD) movements, has the potential to greatly increase throughput and reduce fuel consumption. Since the intersection crossing areas naturally include no lanes, an extended crossing area, appropriately delineated, can be considered as a lane-free infrastructure so as to enable further efficiency benefits. This paper presents two Model Predictive Control (MPC) schemes to manage CAVs in signal-free and lane-free intersections. In fact, the control inputs of all vehicles are optimized over a time-horizon by online solving of a joint Optimal Control Problem (OCP) that minimizes a cost function including proper terms to ensure smooth and collision-free vehicle motion, while also considering fuel consumption and desired-speed tracking, when possible. Additionally, appropriate constraints are designed to respect the intersection boundaries and ensure smooth vehicle movements towards their respective destinations. A fast Feasible Direction Algorithm (FDA) is employed for the numerical solution of the introduced OCP. Multiple simulations are carried out to assess the efficiency and practicality of the proposed methods. A comparison with signalized intersection operation is provided.
在无信号灯交叉路口,互联自动驾驶车辆(CAV)可同时穿越所有起点-终点(OD)运动,这有可能大大提高吞吐量并降低油耗。由于交叉路口的交叉区域自然不包括车道,因此可将适当划定的扩展交叉区域视为无车道基础设施,从而进一步提高效率。本文提出了两种模型预测控制(MPC)方案,用于在无信号灯和无车道交叉路口管理 CAV。事实上,所有车辆的控制输入都是通过在线求解联合最优控制问题(OCP)在时间范围内进行优化的,该问题可使成本函数最小化,其中包括适当的条款,以确保车辆运动平稳、无碰撞,同时在可能的情况下还考虑到油耗和理想速度跟踪。此外,还设计了适当的约束条件,以尊重交叉路口的边界,确保车辆平稳地驶向各自的目的地。采用快速可行方向算法(FDA)对引入的 OCP 进行数值求解。为了评估所建议方法的效率和实用性,我们进行了多次模拟。此外,还提供了与信号灯路口运行的比较。
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引用次数: 0
Active disturbance rejection path tracking control of vehicles with adaptive observer bandwidth based on Q-learning 基于 Q-learning 的自适应观测器带宽的车辆主动干扰抑制路径跟踪控制
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-04 DOI: 10.1016/j.conengprac.2024.106137
Longqing Li , Kang Song , Guojie Tang , Wenchao Xue , Hui Xie , Jingping Ma
In this paper, a novel algorithm for vehicle path tracking control is introduced, focusing on maintaining tracking accuracy and minimizing steering wheel oscillation to enhance mechanism lifespan and passenger comfort. Vehicle kinematics model is utilized to formulate a second-order dynamic equation for lateral error, integrating yaw error into the standard first-order dynamic equation. A Proportional-Derivative (PD) controller is designed, incorporating an ‘extended state’ to compensate for the discrepancy between the model and actual vehicle dynamics, termed as the ‘total disturbance’. This ‘total disturbance’ is observed by an Extended State Observer (ESO), and a disturbance rejection law, combined with the PD controller, is employed to achieve the desired yaw rate. For improved vehicle safety and comfort, a dynamic constraint on the yaw rate, based on the vehicle’s motion and dynamic principles, is proposed. The vehicle’s nonlinear dynamics are addressed through feedback linearization, converting the target yaw rate into the required steering angle, which is then executed by the steer-by-wire system. An adaptive online algorithm for adjusting the ESO bandwidth, using Q-learning, is implemented. This optimization aims to balance tracking accuracy and steering wheel oscillation. A mathematical analysis confirms the stability of the time-varying bandwidth ESO and the overall system, ensuring limited estimation and control errors. Experimental comparison with the classical Stanley and Model Predictive Control (MPC) method demonstrates the algorithm’s effectiveness, maintaining lateral error within ±0.1 m.
本文介绍了一种新的车辆路径跟踪控制算法,重点是保持跟踪精度和尽量减少方向盘摆动,以提高机构寿命和乘客舒适度。利用车辆运动学模型制定了横向误差的二阶动态方程,并将偏航误差整合到标准的一阶动态方程中。设计了一个比例-派生(PD)控制器,其中包含一个 "扩展状态",用于补偿模型与实际车辆动态之间的差异,即 "总干扰"。这种 "总扰动 "由扩展状态观测器(ESO)进行观测,并采用扰动抑制法则与 PD 控制器相结合,以实现所需的偏航率。为了提高车辆的安全性和舒适性,根据车辆的运动和动态原理,提出了偏航率动态约束。通过反馈线性化处理车辆的非线性动态,将目标偏航率转换为所需的转向角,然后由线控转向系统执行。利用 Q-learning 实现了调整 ESO 带宽的自适应在线算法。这种优化旨在平衡跟踪精度和方向盘振荡。数学分析证实了时变带宽 ESO 和整个系统的稳定性,确保了有限的估计和控制误差。与经典斯坦利和模型预测控制(MPC)方法的实验对比证明了该算法的有效性,可将横向误差保持在 ±0.1 米以内。
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引用次数: 0
Study of control strategy for cylinder-to-cylinder combustion homogeneity of marine medium-speed diesel engines 船用中速柴油机汽缸间燃烧均匀性控制策略研究
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-04 DOI: 10.1016/j.conengprac.2024.106156
Shunhua Ou , Yonghua Yu , Nao Hu , Lei Hu , Jianguo Yang
Closed-loop combustion control (CLCC) is an efficient method for minimizing cylinder-to-cylinder combustion variation by adjusting individual cylinder fuel injection parameters. It is complementary to the closed-loop speed control, which precisely controls the engine speed by manipulating the global fuel injection parameters. However, the application of CLCC changed the conventional closed-loop speed control to a complex control structure. In addition, the selection of combustion control parameters will not only influence the combustion heat release control precisely, but also lead to increased calibration effort for the combustion controller. In this research, a triple closed-loop control strategy, in conjunction with a set-point online generation method, was proposed to improve the cylinder-to-cylinder combustion homogeneity, maintain the desired engine speed, and reduce the calibration effort simultaneously. A coefficient of variation in crank angle domain was utilized to analyze the cylinder-to-cylinder combustion homogeneity. The triple closed-loop control strategy was implemented on a marine medium-speed diesel engine. The experimental results indicated that the proposed control strategy, compared with the speed & IMEP (indicated mean effective pressure) cooperative control and speed & MFB50 (crank angle when 50 % fuel is consumed) cooperative control, has a better potential to alleviate cylinder-to-cylinder pressure variations at the same crankshaft angle. The cylinder-to-cylinder variation of IMEP and MFB50 decreased by 61 % and 38 % compared to the closed-loop speed control, respectively. The cylinder-to-cylinder combustion inhomogeneity, resulting from engine long-time operation and ambient conditions change, was significantly reduced as well. Therefore, the proposed strategy provides a multi-objective precise control method that allows the extension to low-carbon and zero-carbon marine engines.
闭环燃烧控制(CLCC)是一种通过调整单个气缸的燃油喷射参数来最大限度减少气缸间燃烧变化的有效方法。它是闭环转速控制的补充,后者通过操纵全局喷油参数来精确控制发动机转速。然而,CLCC 的应用改变了传统的闭环转速控制,使其成为一种复杂的控制结构。此外,燃烧控制参数的选择不仅会影响燃烧放热的精确控制,还会导致燃烧控制器的标定工作量增加。本研究提出了一种三重闭环控制策略,并结合设定点在线生成方法,以改善缸与缸之间的燃烧均匀性,保持理想的发动机转速,并同时减少标定工作量。利用曲柄角域的变化系数分析了气缸到气缸的燃烧均匀性。在船用中速柴油机上实施了三重闭环控制策略。实验结果表明,与转速& IMEP(指示平均有效压力)协同控制和转速& MFB50(消耗 50% 燃料时的曲柄角)协同控制相比,所提出的控制策略在相同曲轴角度下具有更好的缓解气缸到气缸压力变化的潜力。与闭环转速控制相比,IMEP 和 MFB50 的气缸间变化分别减少了 61% 和 38%。发动机长时间运行和环境条件变化导致的气缸间燃烧不均匀性也显著降低。因此,所提出的策略提供了一种多目标精确控制方法,可扩展到低碳和零碳船用发动机。
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引用次数: 0
Synchronous DTC for torque sub-harmonic reduction in low switching frequency induction motor drives 用于降低低开关频率感应电机驱动器转矩次谐波的同步 DTC
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.conengprac.2024.106133
A. Benevieri, M. Marchesoni, M. Passalacqua, P. Pozzobon, L. Vaccaro
A direct torque control (DTC) algorithm with synchronous modulation for high-power induction motors is presented in this paper. While maintaining the dynamic response and robustness of a PI-based DTC operating in the stationary reference frame, the proposed scheme is able to keep an integer PWM modulation ratio, adjusting the stator flux angle and the switching period at each control step so that the synchronicity condition is always satisfied. In this way, it is possible to achieve an improvement of the very low-frequency harmonic spectrum of the torque, in particular by reducing torque sub-harmonics. These represent one of the main problems associated with low-frequency modulation typical of high-power drives and their reduction allows to avoid drawbacks such as resonance and mechanical stresses. The performance of the proposed algorithm is evaluated with experimental tests on a small-scale test bench.
本文提出了一种针对大功率感应电机的同步调制直接转矩控制(DTC)算法。在保持基于 PI 的 DTC 在静态参考帧中运行的动态响应和鲁棒性的同时,所提出的方案能够保持整数 PWM 调制比,在每个控制步骤中调整定子磁通角和开关周期,从而始终满足同步性条件。通过这种方式,可以改善转矩的极低频谐波频谱,特别是通过减少转矩次谐波。次谐波是与大功率驱动器典型的低频调制相关的主要问题之一,减少次谐波可以避免共振和机械应力等缺点。通过在小型试验台上进行实验测试,对所提出算法的性能进行了评估。
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引用次数: 0
Bayesian optimization with embedded stochastic functionality for enhanced robotic obstacle avoidance 具有嵌入式随机功能的贝叶斯优化技术,用于增强机器人的避障能力
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-30 DOI: 10.1016/j.conengprac.2024.106141
Catalin Stefan Teodorescu, Andrew West, Barry Lennox
Designing an obstacle avoidance algorithm that incorporates the stochastic nature of human–robot-environment interactions is challenging. In high risk activities, such as those found in nuclear environments, a comprehensive approach towards handling uncertainty is essential. In this article, in the context of safe teleoperation of robots, an automated iterative sampling procedure based on Bayesian optimization is proposed, where the robot is trained to predict the behaviour of a human operator. Specifically, a Gaussian process regression model is used to learn an effective representation of a safe stop manoeuvre, required for implementing an obstacle avoidance shared control algorithm. This model is then used to predict the future time duration to execute a safe stop manoeuvre, given the current real-world circumstances. The control algorithm expects this value to be reasonably high; if not, it will gradually reduce the human operator’s authority. A distinctive attribute of the proposed method is the use of statistical confidence metrics as tuning parameters, intended to provide a statistical indication of whether or not an obstacle will be avoided. The proof-of-concept experiments were carried out using three robotic platforms suited for use in nuclear robotics, an amphibious SuperDroid HD2 robot equipped with a Velodyne VLP16 (a 3D lidar), an AgileX Scout Mini R&D Pro land robot fitted with a Realsense D435 depth camera, and a Husarion ROSBot 2.0 Pro supplied with an RPLIDAR A3 (a 2D lidar). The test results show that the proposed Bayesian optimization method uses 8 times less data compared to an exhaustive grid approach, and that it provides a robot-agnostic, robust obstacle avoidance.
设计一种能将人-机器人-环境互动的随机性纳入其中的避障算法具有挑战性。在核环境等高风险活动中,必须采用综合方法来处理不确定性。本文以机器人的安全远程操作为背景,提出了一种基于贝叶斯优化的自动迭代采样程序,训练机器人预测人类操作员的行为。具体来说,使用高斯过程回归模型来学习安全停止动作的有效表示,这是实施避障共享控制算法所必需的。然后,根据当前的实际情况,利用该模型预测未来执行安全停车动作所需的时间。控制算法希望这个值是合理的高值;如果不是,它将逐渐降低人类操作员的权限。拟议方法的一个显著特点是使用统计置信度指标作为调整参数,旨在提供是否能避开障碍物的统计指示。概念验证实验使用了三个适合核机器人技术使用的机器人平台:配备 Velodyne VLP16(三维激光雷达)的 SuperDroid HD2 水陆两用机器人、配备 Realsense D435 深度相机的 AgileX Scout Mini R&D Pro 陆地机器人,以及配备 RPLIDAR A3(二维激光雷达)的 Husarion ROSBot 2.0 Pro。测试结果表明,与穷举式网格方法相比,所提出的贝叶斯优化方法所使用的数据量减少了 8 倍,而且还能提供与机器人无关的稳健避障功能。
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引用次数: 0
Causal similarity learning with multi-level predictive relation aggregation for grouped root cause diagnosis of industrial faults 采用多级预测关系聚合的因果相似性学习,用于工业故障的分组根源诊断
IF 5.4 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-29 DOI: 10.1016/j.conengprac.2024.106140
Liujiayi Zhao, Pengyu Song, Chunhui Zhao
Existing root cause diagnosis (RCD) methods infer causal relationships among abnormal variables by decomposing causal graphs into intra-group and inter-group levels, reducing redundancy according to direct causality. However, the indirect causality trigged by wide-range fault propagation may be ignored when inferring within groups, leading to the mismatch between causality distribution and grouping results. To overcome the challenge, we propose a causal similarity learning method with multi-level predictive relation aggregation, which contains a complementary similarity measurement framework covering both single-level and high-level causal relationships. First, an attention mechanism with temporal misalignment is designed, which can convert the undirected correlations of features into directed high-level causal similarity by extracting lagged predictive relations. Further, a graph-cutting penalty term is proposed to promote causality distribution to exhibit intra-group denseness and inter-group sparsity, so that single-level causal similarity can be considered during grouping. Finally, a dual RCD method is proposed to search root causes from the causal graph with intra-group and inter-group causality. In this way, numerous redundant causations caused by complex fault propagation can be succinctly described by inter-group causation, and the search for root cause variables can be limited to subgroups to improve diagnosis efficiency. The validity of the proposed method is illustrated through both the Tennessee Eastman benchmark example and a real industrial process.
现有的根源诊断(RCD)方法通过将因果图分解为组内和组间两个层次来推断异常变量之间的因果关系,从而根据直接因果关系减少冗余。然而,在组内推断时,可能会忽略大范围故障传播引发的间接因果关系,导致因果关系分布与分组结果不匹配。为了克服这一难题,我们提出了一种多层次预测关系聚合的因果相似性学习方法,该方法包含一个互补的相似性测量框架,涵盖单层次和高层次的因果关系。首先,我们设计了一种具有时间错位的关注机制,通过提取滞后的预测关系,将特征的无向相关性转化为有向的高层次因果相似性。此外,还提出了一个图切割惩罚项,以促进因果关系分布呈现出组内密集、组间稀疏的特点,从而在分组时可以考虑单层次的因果相似性。最后,提出了一种双重 RCD 方法,从具有组内和组间因果关系的因果图中搜索根本原因。这样,复杂故障传播引起的大量冗余因果关系就可以通过组间因果关系得到简洁描述,而根源变量的搜索也可以局限于子组,从而提高诊断效率。通过田纳西伊士曼基准实例和实际工业流程,说明了所提方法的有效性。
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引用次数: 0
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Control Engineering Practice
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