Control of batch product quality by trajectory manipulation using latent variable models

A novel inferential strategy for controlling end-product quality properties by adjusting the complete trajectories of the manipulated variables is presented. Control through complete trajectory manipulation using empirical models is possible by controlling the process in the reduce space (scores) of a latent variable model rather than in the real space of the manipulated variables. Model inversion and trajectory reconstruction is achieved by exploiting the correlation structure in the manipulated variable trajectories captured by a partial least squares model. The approach is illustrated with a condensation polymerisation example for the production of nylon and with data gathered from an industrial emulsion polymerisation process. The data requirements for building the model are shown to be modest.     

基于伪谱法的翼伞系统归航轨迹容错设计

针对翼伞系统在归航过程中,控制电机工作异常致使控制性能发生变化,无法按原有规划轨迹到达目标点的问题,提出一种基于Gauss伪谱法的归航轨迹容错设计方法.首先根据翼伞系统控制特性的不同,分别建立了正常和单电机异常工作状态下的质点模型,并根据伞形参数确定了两种工作状态下的约束条件和目标函数;其次,利用Gauss伪谱法分别对两种工作状态下轨迹规划的最优控制问题求解,获得翼伞系统不同状态下的最优飞行轨迹.仿真结果表明,在约束情况下,翼伞系统无论在正常和单电机异常工作时都可以顺利到达目标点,获得高精度的飞行轨迹.     

Latent Variable Model Predictive Control (LV-MPC) for trajectory tracking in batch processes

Latent Variable Model Predictive Control (LV-MPC) algorithms are developed for trajectory tracking and disturbance rejection in batch processes. The algorithms are based on multi-phase PCA models developed using batch-wise unfolding of batch data arrays. Two LV-MPC formulations are presented, one based on optimization in the latent variable space and the other on direct optimization over a finite vector of future manipulated variables. In both cases prediction of the future trajectories is accomplished using statistical latent variable missing data imputation methods. The proposed LV-MPCs can handle constraints. Furthermore, due to the batch-wise unfolding approach selected in the modeling section, the nonlinear time-varying behavior of batch processes is captured by the linear LV models thereby yielding very simple and computationally fast nonlinear batch MPC. The methods are tested and compared on a simulated batch reactor case study.     

Latent variable MPC for trajectory tracking in batch processes

A novel multivariate empirical model predictive control strategy (LV-MPC) for trajectory tracking and disturbance rejection for batch processes is presented. The strategy is based on dynamic principal component analysis (PCA) models of the batch process. The solution to the control problem is computed in the low dimensional latent variable space of the PCA model. The trajectories of all variables over the future horizon are then computed from the latent variable solution of the controller. The excellent control performance and the modest closed-loop data requirements for identification are illustrated for the temperature tracking in simulations of an emulsion polymerization process, an exothermic chemical reaction system and for MIMO temperature and pressure tracking in a nylon polymerization autoclave.     

基于轨迹分析的行人异常行为识别

提出一种基于轨迹分段主题模型的异常行为检测方法。为了解决跟踪偏差引起的轨迹不连续问题,首先使用模糊聚类算法对所有的轨迹进行全局聚类,然后对每一类轨迹采用分段采样的方式对段内轨迹点使用主题模型LDA进行局部聚类;以最大概率的轨迹点作为视觉单词,每类轨迹表示成一系列视觉单词的集合,在此基础上建立局部隐马尔科夫模型HMM;最后通过轨迹匹配的方法进行异常轨迹识别。在CAVIAR数据库上的实验结果表明,该算法能识别多种异常行为,提高了异常行为检测的准确率。     

Semantic segmentation of trajectories with improved agent models for pedestrian behavior analysis

ABSTRACT

In this paper, we propose a method for semantic segmentation of pedestrian trajectories based on pedestrian behavior models, or agents. The agents model the dynamics of pedestrian movements in two-dimensional space using a linear dynamics model and common start and goal locations of trajectories. First, agent models are estimated from the trajectories obtained from image sequences. Our method is built on top of the Mixture model of Dynamic pedestrian Agents (MDA); however, the MDA's trajectory modeling and estimation are improved. Then, the trajectories are divided into semantically meaningful segments. The subsegments of a trajectory are modeled by applying a hidden Markov model using the estimated agent models. Experimental results with a real trajectory dataset show the effectiveness of the proposed method as compared to the well-known classical Ramer-Douglas-Peucker algorithm and also to the original MDA model.     

Maximizing a deep submodular function optimization with a weighted MAX-SAT problem for trajectory clustering and motion segmentation

Computer vision models are commonly defined for maximum constrained submodular functions lies at the core of low-level and high-level models. In such that, the pixels that are to be grouped or segmenting moving object remains a challenging task. This paper proposes a joint framework for maximizing submodular energy subject to a matroid constraint using Deep Submodular Function (DSF) optimization approximately to solve the weighted MAX-SAT (Maximum Satisfiability) problem and a new trajectory clustering method called Simple Slice Linear clustering (SSLIC) and motion cue method for trajectory clustering and motion segmentation. In this objective function, the illustrative trajectories of a small number are selected automatically by deep submodular maximization. Although, the exploitation of monotone and submodular properties are further maximized and the complexity is reduced by a continuous greedy algorithm. The bound guarantees a fully sliced curve of (1- S/e) to (1–1/e) with less running time. Lastly, the motion is segmented by the motion cue method to accurately differentiate the set of frames for different scenes. Experiments on the Hopkins 155, Berkley Motion Segmentation (BMS) and FBMS-59 datasets display the trajectory clustering and motion segmentation result over its superior performance with respect to 14 quality evaluation metrics. Hence the simulation result shows that the proposed joint framework attains better performance than existing methods on trajectory clustering and motion segmentation task.

     

Multi-target tracking by learning local-to-global trajectory models

The multi-target tracking problem is challenging when there exist occlusions, tracking failures of the detector and severe interferences between detections. In this paper, we propose a novel detection based tracking method that links detections into tracklets and further forms long trajectories. Unlike many previous hierarchical frameworks which split the data association into two separate optimization problems (linking detections locally and linking tracklets globally), we introduce a unified algorithm that can automatically relearn the trajectory models from the local and global information for finding the joint optimal assignment. In each temporal window, the trajectory models are initialized by the local information to link those easy-to-connect detections into a set of tracklets. Then the trajectory models are updated by the reliable tracklets and reused to link separated tracklets into long trajectories. We iteratively update the trajectory models by more information from more frames until the result converges. The iterative process gradually improves the accuracy of the trajectory models, which in turn improves the target ID inferences for all detections by the MRF model. Experiment results revealed that our proposed method achieved state-of-the-art multi-target tracking performance.     

A hybrid strategy for the time- and energy-efficient trajectory planning of parallel platform manipulators

In planning the trajectories of motor-driven parallel platform manipulators, the objective is to identify the trajectory which accomplishes the assigned motion with the minimal travel time and energy expenditure subject to the constraints imposed by the kinematics and dynamics of the manipulator structure. In this study, the possible trajectories of the manipulator are modeled using a parametric path representation, and the optimal trajectory is then obtained using a hybrid scheme comprising the particle swarm optimization method and the local conjugate gradient method. The numerical results confirm the feasibility of the optimized trajectories and show that the hybrid scheme is not only more computationally efficient than the standalone particle swarm optimization method, but also yields solutions of a higher quality.     

Learning motion patterns in unstructured scene based on latent structural information

ContextAs trajectory analysis is widely used in the fields of video surveillance, crowd monitoring, behavioral prediction, and anomaly detection, finding motion patterns is a fundamental task for pedestrian trajectory analysis.ObjectiveIn this paper, we focus on learning dominant motion patterns in unstructured scene.MethodsAs the invisible implicit indicator to scene structure, latent structural information is first defined and learned by clustering source/sink points using CURE algorithm. Considering the basic assumption that most pedestrians would find the similar paths to pass through an unstructured scene if their entry and exit areas are fixed, trajectories are then grouped based on the latent structural information. Finally, the motion patterns are learned for each group, which are characterized by a series of statistical temporal and spatial properties including length, duration and envelopes in polar coordinate space.ResultsExperimental results demonstrate the feasibility and effectiveness of our method, and the learned motion patterns can efficiently describe the statistical spatiotemporal models of the typical pedestrian behaviors in a real scene. Based on the learned motion patterns, abnormal or suspicious trajectories are detected.ConclusionThe performance of our approach shows high spatial accuracy and low computational cost.     

Lorenz系统的线性反馈控制

设计了状态变量的线性反馈控制器对Lorenz系统的平衡点和周期轨道进行控制.首先,利用Routh-Hurwitz准则对受控系统进行了稳定性分析,证明了达到控制目标反馈系数的选择原则.然后,通过数值计算证明了该方法能够有效地控制混沌系统达到稳定的平衡点同时也能使系统控制到1p周期轨道,并且得到了相应的稳定的1p周期轨道的控制参数和系统幅值的关系曲线.最后给出了控制到1p周期轨道的控制参数的选取范围.     

双连杆刚柔机械臂无残余振动位置控制

针对双连杆刚柔机械臂,提出一种基于轨迹规划的无残余振动位置控制方法,在将机械臂的末端执行器从任意初始位置移动到目标位置的同时,确保系统没有残余振动产生.首先,建立系统的动力学模型,并通过分析该模型得到系统的状态约束方程.其次,基于状态约束方程,运用双向轨迹规划方法规划一条系统前向轨迹和一条系统反向轨迹.然后,利用时间倒转方法及基于遗传算法的轨迹优化方法对两条轨迹进行拼合,得到一条从系统初始状态到目标状态的期望轨迹.最后,设计轨迹跟踪控制器使系统沿期望轨迹到达目标状态,实现系统的无残余振动位置控制目标.仿真结果验证了本文所提方法的有效性.     

Gradient dynamic optimization with Legendre chaos

The polynomial chaos approach for stochastic simulation is applied to trajectory optimization, by conceptually replacing random variables with free variables. Using the gradient method, we generate with low computational cost an accurate parametrization of optimal trajectories.     

基于学习的群体动画生成技术研究

为了降低群体动画中生成大量自然而又相似的人体运动的难度和复杂性,研究了一种基于学习的群体动画生成技术。该技术首先通过建立基于高斯过程隐变量模型和隐空间动态模型的运动姿势学习模型,将高维运动姿势映射到低维隐空间中,并在低维隐空间对相邻姿势的动态演化进行建模;然后通过对已有运动数据的学习来获得组成该运动的姿势的概率分布,再通过隐空间中的动态预测和Hybrid Monte Carlo采样来得到符合给定概率分布的隐轨迹;最后通过姿势重构来得到与原运动非常相似但又不同的一系列自然的运动,以产生群体动画,从而避开了传统的基于几何和物理约束的逆运动方法固有的困难和复杂性。     

Smooth and time‐optimal trajectory planning for industrial manipulators along specified paths

This article presents a method for determining smooth and time‐optimal path constrained trajectories for robotic manipulators and investigates the performance of these trajectories both through simulations and experiments. The desired smoothness of the trajectory is imposed through limits on the torque rates. The third derivative of the path parameter with respect to time, the pseudo‐jerk, is the controlled input. The limits on the actuator torques translate into state‐dependent limits on the pseudo‐acceleration. The time‐optimal control objective is cast as an optimization problem by using cubic splines to parametrize the state space trajectory. The optimization problem is solved using the flexible tolerance method. The experimental results presented show that the planned smooth trajectories provide superior feasible time‐optimal motion. © 2000 John Wiley & Sons, Inc.     

区别多种出行方式的城市活动轨迹预测

信息社会中,基于用户的历史活动轨迹发掘和预测人类位置轨迹及活动规律至关重要.已有研究大多采用基于时间和轨迹间相似度分类的马尔可夫模型,忽略了不同出行方式下的移动规律差异.对此,区别不同出行方式,基于轨迹的速度、加速度和航向变化速度等特征,用XGBoost算法识别轨迹所对应的出行方式,并采用基于优化的轨迹分割算法,将人类出行轨迹按出行方式分解成多个轨迹,采用由不同出行方式轨迹建立的马尔可夫模型实现出行轨迹的精准预测.实验表明,不同出行方式的轨迹的移动规律存在显著差异,且所提出方法的预测精度和距离偏差明显优于几个基准方法.     

Evolutionary multi-criteria trajectory modeling of industrial robots in the presence of obstacles

Optimal trajectory planning for robot manipulators is always a hot spot in research fields of robotics. This paper presents two new novel general methods for computing optimal motions of an industrial robot manipulator (STANFORD robot) in presence of obstacles. The problem has a multi-criterion character in which three objective functions, a maximum of 72 variables and 103 constraints are considered. The objective functions for optimal trajectory planning are minimum traveling time, minimum mechanical energy of the actuators and minimum penalty for obstacle avoidance. By far, there has been no planning algorithm designed to treat the objective functions simultaneously. When existing optimization algorithms of trajectory planning tackle the complex instances (obstacles environment), they have some notable drawbacks viz.: (1) they may fail to find the optimal path (or spend much time and memory storage to find one) and (2) they have limited capabilities when handling constraints. In order to overcome the above drawbacks, two evolutionary algorithms (Elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm) are used for the optimization. Two methods (normalized weighting objective functions method and average fitness factor method) are combinedly used to select best optimal solution from Pareto optimal front. Two multi-objective performance measures (solution spread measure and ratio of non-dominated individuals) are used to evaluate strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimizer overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analyzed.     

Indexing Spatio-Temporal Trajectories with Efficient Polynomial Approximations

Complex queries on trajectory data are increasingly common in applications involving moving objects. MBR or grid-cell approximations on trajectories perform suboptimally since they do not capture the smoothness and lack of internal area of trajectories. We describe a parametric space indexing method for historical trajectory data, approximating a sequence of movement functions with single continuous polynomial. Our approach works well, yielding much finer approximation quality than MBRs. We present the PA-tree, a parametric index that uses this method, and show through extensive experiments that PA-trees have excellent performance for offline and online spatio-temporal range queries. Compared to MVR-trees, PA-trees are an order of magnitude faster to construct and incur I/O cost for spatio-temporal range queries lower by a factor of 2-4. SETI is faster than our method for index construction and timestamp queries, but incurs twice the I/O cost for time interval queries, which are much more expensive and are the bottleneck in online processing. Therefore, the PA-tree is an excellent choice for both offline and online processing of historical trajectories     

Quality relevant nonlinear batch process performance monitoring using a kernel based multiway non-Gaussian latent subspace projection approach

Multiway kernel partial least squares method (MKPLS) has recently been developed for monitoring the operational performance of nonlinear batch or semi-batch processes. It has strong capability to handle batch trajectories and nonlinear process dynamics, which cannot be effectively dealt with by traditional multiway partial least squares (MPLS) technique. However, MKPLS method may not be effective in capturing significant non-Gaussian features of batch processes because only the second-order statistics instead of higher-order statistics are taken into account in the underlying model. On the other hand, multiway kernel independent component analysis (MKICA) has been proposed for nonlinear batch process monitoring and fault detection. Different from MKPLS, MKICA can extract not only nonlinear but also non-Gaussian features through maximizing the higher-order statistic of negentropy instead of second-order statistic of covariance within the high-dimensional kernel space. Nevertheless, MKICA based process monitoring approaches may not be well suited in many batch processes because only process measurement variables are utilized while quality variables are not considered in the multivariate models. In this paper, a novel multiway kernel based quality relevant non-Gaussian latent subspace projection (MKQNGLSP) approach is proposed in order to monitor the operational performance of batch processes with nonlinear and non-Gaussian dynamics by combining measurement and quality variables. First, both process measurement and quality variables are projected onto high-dimensional nonlinear kernel feature spaces, respectively. Then, the multidimensional latent directions within kernel feature subspaces corresponding to measurement and quality variables are concurrently searched for so that the maximized mutual information between the measurement and quality spaces is obtained. The I² and SPE monitoring indices within the extracted latent subspaces are further defined to capture batch process faults resulting in abnormal product quality. The proposed MKQNGLSP method is applied to a fed-batch penicillin fermentation process and the operational performance monitoring results demonstrate the superiority of the developed method as apposed to the MKPLS based process monitoring approach.