Scheduling Dual-Arm Multi-Cluster Tools With Regulation of Post-Processing Time

As wafer circuit width shrinks down to less than ten nanometers in recent years,stringent quality control in the wafer manufacturing process is increasingly important.Thanks to the coupling of neighboring cluster tools and coordination of multiple robots in a multi-cluster tool,wafer production scheduling becomes rather complicated.After a wafer is processed,due to high-temperature chemical reactions in a chamber,the robot should be controlled to take it out of the processing chamber at the right time.In order to ensure the uniformity of integrated circuits on wafers,it is highly desirable to make the differences in wafer post-processing time among the individual tools in a multicluster tool as small as possible.To achieve this goal,for the first time,this work aims to find an optimal schedule for a dual-arm multi-cluster tool to regulate the wafer post-processing time.To do so,we propose polynomial-time algorithms to find an optimal schedule,which can achieve the highest throughput,and minimize the total post-processing time of the processing steps.We propose a linear program model and another algorithm to balance the differences in the post-processing time between any pair of adjacent cluster tools.Two industrial examples are given to illustrate the application and effectiveness of the proposed method.

Scheduling method for single-arm cluster tools of wafer fabrications with residency and continuous reentrancy

In order to enhance the utilization of single-ann cluster tools and optimize the scheduling problems of dynamic reaching wafers with residency time and continuous reentrancy constraints, a structural heuristic scheduling algorithm is presented. A nonlinear programming scheduling model is built on the basis of bounding the scheduling problem domain. A feasible path search scheduling method of single-arm robotic operations is put forward with the objective of minimal makespan. Finally, simulation experiments are designed to analyze the scheduling algorithms. Results indicate that the proposed algorithm is feasible and valid to solve the scheduling problems of multiple wafer types and single-ann clusters with the conflicts and deadlocks generated by residency time and continuous reentrancy constraints.

Scheduling algorithm of dual-armed cluster tools with residency time and reentrant constraints

To solve the scheduling problem of dual-armed cluster tools for wafer fabrications with residency time and reentrant constraints,a heuristic scheduling algorithm was developed.Firstly,on the basis of formulating scheduling problems domain of dual-armed cluster tools,a non-integer programming model was set up with a minimizing objective function of the makespan.Combining characteristics of residency time and reentrant constraints,a scheduling algorithm of searching the optimal operation path of dual-armed transport module was presented under many kinds of robotic scheduling paths for dual-armed cluster tools.Finally,the experiments were designed to evaluate the proposed algorithm.The results show that the proposed algorithm is feasible and efficient for obtaining an optimal scheduling solution of dual-armed cluster tools with residency time and reentrant constraints.

晶圆制造中单臂Cluster tool的建模与仿真

对于单臂的Cluster tool,由于晶圆驻留时间的约束和作业时间的波动性,还没有解析的方法能够验证其调度的可行性和有效的调度方法。介绍了晶圆制造过程并基于Petri网模型,利用eM-Plant仿真平台建立了相应的晶圆制造的仿真模型。通过实例说明仿真模型能够虚拟单臂的Cluster tool、准确地仿真单臂的Cluster tool的晶圆制造模式;晶圆制造的仿真模型为研究其调度可行性分析和控制器设计提供了一种有效的手段。

Try and error-based scheduling algorithm for cluster tools of wafer fabrications with residency time constraints

To improve the productivity of cluster tools in semiconductor fabrications,on the basis of stating scheduling problems,a try and error-based scheduling algorithm was proposed with residency time constraints and an objective of minimizing Makespan for the wafer jobs in cluster tools.Firstly,mathematical formulations of scheduling problems were presented by using assumptions and definitions of a scheduling domain.Resource conflicts were analyzed in the built scheduling model,and policies to solve resource conflicts were built.A scheduling algorithm was developed.Finally,the performances of the proposed algorithm were evaluated and compared with those of other methods by simulations.Experiment results indicate that the proposed algorithm is effective and practical in solving the scheduling problem of the cluster tools.

Polynomial Approach to Optimal One-wafer Cyclic Scheduling of Treelike Hybrid Multi-Cluster Tools via Petri Nets

A treelike hybrid multi-cluster tool is composed of both single-arm and dual-arm cluster tools with a treelike topology. Scheduling such a tool is challenging. For a hybrid treelike multi-cluster tool whose bottleneck individual tool is process-bound, this work aims at finding its optimal one-wafer cyclic schedule. It is modeled with Petri nets such that a onewafer cyclic schedule is parameterized as its robots' waiting time.Based on the model, this work proves the existence of its onewafer cyclic schedule that features with the ease of industrial implementation. Then, computationally efficient algorithms are proposed to find the minimal cycle time and optimal onewafer cyclic schedule. Multi-cluster tool examples are given to illustrate the proposed approach. The use of the found schedules enables industrial multi-cluster tools to operate with their highest productivity.

Post-Processing Time-Aware Optimal Scheduling of Single Robotic Cluster Tools

Integrated circuit chips are produced on silicon wafers.Robotic cluster tools are widely used since they provide a reconfigurable and efficient environment for most wafer fabrication processes.Recent advances in new semiconductor materials bring about new functionality for integrated circuits.After a wafer is processed in a processing chamber,the wafer should be removed from there as fast as possible to guarantee its high-quality integrated circuits.Meanwhile,maximization of the throughput of robotic cluster tools is desired.This work aims to perform post-processing time-aware scheduling for such tools subject to wafer residencytime constraints.To do so,closed-form expression algorithms are derived to compute robot waiting time accurately upon the analysis of particular events of robot waiting for singlearm cluster tools.Examples are given to show the application and effectiveness of the proposed algorithms.

Cycle Time Analysis for Wafer Revisiting Process in Scheduling of Single-arm Cluster Tools

Some wafer fabrication processes performed by cluster tools require revisiting. With wafer revisiting, a cluster tool is very difficult to be scheduled due to a large number of possible schedules for the revisiting process. Atomic layer deposition （ALD） is a typical process with wafer revisiting that should be performed by cluster tools. This paper discusses the scheduling problem of single-arm cluster tools for the ALD process. In scheduling such a system, the most difficult part is to schedule the revisiting process such that the cycle time is minimized. Thus, this paper studies the revisiting process of ALD with revisiting times k = 3, 4, and 5, and analytical expressions are obtained to calculate the cycle time for the k possible schedules. Then, the schedule with the minimal cycle time is the optimal one. In this way, the scheduling problem of such a revisiting process becomes very simple and this is a significant improvement in scheduling cluster tools with wafer revisiting. Illustrative example is presented to show the application of the proposed method.

The Fuzzy Cluster Analysis in Identification of Key Temperatures in Machine Tool

The thermal-induced error is a very important sour ce of machining errors of machine tools. To compensate the thermal-induced machin ing errors, a relationship model between the thermal field and deformations was needed. The relationship can be deduced by virtual of FEM (Finite Element Method ), ANN (Artificial Neural Network) or MRA (Multiple Regression Analysis). MR A is on the basis of a total understanding of the temperature distribution of th e machine tool. Although the more the temperatures measured are, the more accura te the MRA is, too more temperatures will hinder the analysis calculation. So it is necessary to identify the key temperatures of the machine tool. The selectio n of key temperatures decides the efficiency and precision of MRA. Because of th e complexities and multi-input and multi-output structure of the relationships , the exact quantitative portions as well as the unclear portions must be taken into consideration together to improve the identification of key temperatures. I n this paper, a fuzzy cluster analysis was used to select the key temperatures. The substance of identifying the key temperatures is to group all temperatures b y their relativity, and then to select a temperature from each group as the repr esentation. A fuzzy cluster analysis can uncover the relationships between t he thermal field and deformations more truly and thoroughly. A fuzzy cluster ana lysis is the cluster analysis based on fuzzy sets. Given U={u i|i=0,...,N}, in which u i is the temperature measured, a fuzzy matrix R can be obta ined. The transfer close package t(R) can be deduced from R. A fuzzy clu ster of U then conducts on the basis of t(R). Based on the fuzzy cluster analysis discussed above, this paper identified the k ey temperatures of a horizontal machining center. The number of the temperatures measured was reduced to 4 from 32, and then the multiple regression relationshi p models between the 4 temperatures and the thermal deformations of the spindle were drawn. The remnant errors between the regression models and measured deform ations reached a satisfying low level. At the same time, the decreasing of tempe rature variable number improved the efficiency of measure and analysis greatly.

我国社会工作政策区域特征研究

采用因子分析法对2015年至2022年我国29个省份的社会工作政策进行研究,通过提取立体推进、基础构建、引领推广、多元协同、人才发展5个主成分,分析我国社会工作政策特点,并基于因子得分对其展开聚类分析。研究显示,我国社会工作政策工具结构失衡,注重供给型和环境型政策工具的运用,忽视需求型政策工具的使用;各地区社会工作政策重点存在显著差异,尤其是社会工作政策供给水平具有较大差距;社会工作政策区域聚类特征明显。考虑到我国社会工作政策工具均衡化发展和地区差异化问题,各地区应均衡使用政策工具,强化需求型政策工具的运用;因地制宜,制定差异化的社会工作政策;加强区域合作与交流,促进政策经验的共享与借鉴。在此基础上,进一步完善与优化我国社会工作政策体系。

基于聚类与Transformer算法的上软下硬地层盾构滚刀正常磨损预测

盾构法是隧道施工的主流方法,广泛应用于软土地层与复合地层。盾构机在上软下硬地层中掘进时,准确预测滚刀的磨损以便及时更换滚刀是确保施工安全与效率的关键。基于机器学习中的无监督kmeans聚类算法、有监督Transformer算法以及遗传算法,提出了一种根据刀盘前方地层条件、滚刀布设以及施工参数预测滚刀正常磨损的方法。kmeans聚类算法用于实时分析当前盾构施工参数间的关系,从而划分不同施工状态,并为不同施工状态分配不同的磨损修正系数作为Transformer模型的输入参数。根据地层条件及施工参数相关关系确定磨损修正系数初始值的大小,借助遗传算法对磨损修正系数进行优化。Transformer算法中,以地层条件、施工参数、滚刀安装半径和切削距离以及kmeans聚类得到的磨损修正系数作为输入参数,以滚刀磨损量作为输出参数,并由遗传算法对模型的超参数进行优化。所使用的数据采集自某大直径泥水平衡盾构隧道,所穿越地层条件包含全断面软土、上软下硬地层以及全断面硬岩,样本集包含217条数据。聚类结果所揭示的施工状态与滚刀的磨损速度具有明显的对应关系,预测模型的滚刀磨损平均预测误差为3.6mm,占滚刀换刀磨损量40.0mm的9%。

腔室清洗的单臂组合设备初始暂态调度

为了提升腔室洁净度,晶圆厂需对组合设备腔室进行清洗操作,从而提高晶圆的加工质量.考虑腔室清洗时间和晶圆驻留时间的约束条件下,本文研究了单臂组合设备的初始暂态调度问题.首先,提出了机械手的初始暂态活动规则,并对机械手活动序列进行描述,实现了系统的初始暂态可调度性;其次,对机械手在初始暂态和稳态的活动时间进行了建模;然后,根据系统的时间特性,建立了初始暂态调度的线性规划模型;最后,通过实例验证了该方法的有效性.与已有的虚拟晶圆方法相比,该调度方法能有效减少初始暂态的完工时间,提高了组合设备的晶圆生产效率.

考虑晶圆驻留时间约束的双臂组合设备群调度

组合设备群代表了当前晶圆制造装备发展的新趋势,其调度控制水平直接攸关半导体芯片制造企业的整体经济效益。针对半导体芯片制造中考虑晶圆驻留时间约束的双臂组合设备群,文章提出了一种基于特征转换的调度控制方法。首先,引入一种概念型晶圆制造系统,即特征双臂组合设备,并给出相应的稳态调度方法。其次,采用特征转换方法,将线性/树形结构的双臂组合设备群转换为特征双臂组合设备。随后,根据转换后的特征双臂组合设备重新调整双臂组合设备群的机械手作业序列,并求解可行的稳态调度方案。最后,通过实例验证了所提方法的有效性。

慢性阻塞性肺疾病患者症状群的研究进展

慢性阻塞性肺疾病(Chronic Obstructive Pulmonary Disease,COPD)患者同时存在的症状数量达7~18种,甚至存在症状集中趋势,患者会经历多种令人痛苦的身体和心理症状,严重影响患者的生活质量;全面了解COPD患者的症状群,可以进行更彻底的症状评估,并实施有针对性的症状管理策略,以改善患者的临床症状。文章针对COPD患者症状群种类、评估工具进行综述,通过以循证的方式帮助临床工作者评估COPD患者的症状类别,为临床工作的开展提供理论依据。

肝硬化病人症状群识别及评估工具的研究进展

综述肝硬化病人症状群研究现状、识别方法、评估工具及应用情况,以期为临床医务人员评估、管理多种症状提供依据,以帮助确定评估病人长期结局风险的最佳时间,及时进行临床干预。

基于GA-BP神经网络的微磨具磨损预测研究

为提高硬脆材料微结构的加工效率和精度,需要预测微磨具的不确定性磨损。基于微磨具在位视觉磨损检测和聚类分析,提出基于遗传算法的反向神经网络(genetic algorithm back propagation,GA-BP)模型。选取微磨具磨头截面面积损失量为指标,以表征微磨具不确定性磨损特征。利用K-均值聚类算法划分微磨具磨损状态阶段。最后构建以主轴转速、进给率、微槽深度、磨削长度和微磨具初始截面面积为输入层神经元,以磨头截面面积损失量预测值为输出层的GA-BP神经网络模型。设计不同工艺参数条件下的单晶硅微槽微细磨削实验,基于自搭建的机器视觉系统在位测量微磨具的磨头截面面积磨损量。将实验测得的微磨具磨损量作为训练数据,与传统高斯过程回归预测模型对比,验证GA-BP神经网络模型的有效性和准确性。结果表明,GA-BP神经网络模型能够实现不同工艺参数和不同磨削长度下的微磨具磨损预测,比传统高斯过程回归预测模型具有更高预测精度,平均误差精度达到5%,可以实现微磨具磨损阶段状态预测。

脑卒中患者症状群的研究进展

脑卒中患者易形成症状群,如肢体活动障碍、吞咽障碍、睡眠障碍、疼痛、疲劳、癫痫、抑郁等,这些症状聚集成群,造成患者自理能力下降,生活质量降低,给社会、家庭及患者本人带来沉重负担。尽早对脑卒中患者实施症状评估及干预对提高患者的生活质量具有重要作用,也是当前慢性病护理研究领域的重点。本文回顾分析了国内外脑卒中患者症状群研究的现状与不足;介绍了脑卒中症状群的评估工具,介绍了各评估量表的开发学者、适用范围、条目数、信效度以及优缺点;介绍了脑卒中症状群的研究方法,包括探索性研究、验证性研究和网络分析,以及每种研究方法的概念以及统计学分析方法;介绍了脑卒中患者症状群的护理干预措施,包括中医护理技术干预、运动干预、远程护理干预,以期为医务人员快速识别脑卒中患者症状群及症状管理提供参考。

基于u-shapelets聚类的刀具剩余寿命预测方法

针对不同刀具的性能衰退规律呈现出多种趋势,单一固定的全局模型难以对不同性能衰退规律的刀具进行准确剩余寿命预测的问题,提出一种基于u-shapelets聚类与长短时记忆网络(LSTM)模型相结合的刀具剩余寿命预测方法。首先,对刀具加工过程监控信号提取u-shapelets集合,并计算各u-shapelet与时间序列的距离得到距离矩阵;其次,通过基于密度聚类方法对距离矩阵进行聚类,得到聚类结果;最后,根据聚类结果基于各类别数据分别训练长短时记忆网络模型进行刀具剩余寿命的预测。以轮槽铣刀加工过程监控数据进行验证,并与Kmeans聚类、谱聚类、层次聚类、DBSCAN聚类方法进行比较,验证了所提方法的有效性。

基于Kubernetes的集群节能策略研究

在Kubernetes中,HPA具备自动扩展Pod的能力,它可以根据流量的波动情况,在高峰时增加Pod数量以应对需求,而在低谷时减少数量以节省资源。然而,由于HPA是根据当前Pod的性能指标来进行扩展的,当流量激增时,可能会对应用服务的可用性产生不利影响,并且当压力较小时,算力资源的空载会导致电子资源的浪费。针对上述问题,研究并验证一种基于时序预测的集群资源自动缩放与智能休眠唤醒策略,使用GC-TimesNet模型对集群资源的使用情况进行预测。当资源利用率较低时,计算出需要关闭的算力节点数量,将这些节点设置为不可调度状态,并驱逐节点现有的Pod,然后将这些机器置于睡眠状态。相反,当资源需求增加时,会唤醒足够数量的机器,并通过HPA控制器增加所需数量的Pod副本。实验结果表明,该策略能够较为准确地预测集群负载的变化趋势,结合实施智能的休眠与唤醒策略,提升优化集群的运维管理能力,最大程度地提高计算资源的利用率,为降低集群能源开销提供数据支撑,实现节能减排。

Temperature Variable Optimization for Precision Machine Tool Thermal Error Compensation on Optimal Threshold

Machine tool thermal error is an important reason for poor machining accuracy. Thermal error compensation is a primary technology in accuracy control. To build thermal error model, temperature variables are needed to be divided into several groups on an appropriate threshold. Currently, group threshold value is mainly determined by researchers experience. Few studies focus on group threshold in temperature variable grouping. Since the threshold is important in error compensation, this paper arms to find out an optimal threshold to realize temperature variable optimization in thermal error modeling. Firstly, correlation coefficient is used to express membership grade of temperature variables, and the theory of fuzzy transitive closure is applied to obtain relational matrix of temperature variables. Concepts as compact degree and separable degree are introduced. Then evaluation model of temperature variable clustering is built. The optimal threshold and the best temperature variable clustering can be obtained by setting the maximum value of evaluation model as the objective. Finally, correlation coefficients between temperature variables and thermal error are calculated in order to find out optimum temperature variables for thermal error modeling. An experiment is conducted on a precise horizontal machining center. In experiment, three displacement sensors are used to measure spindle thermal error and twenty-nine temperature sensors are utilized to detect the machining center temperature. Experimental result shows that the new method of temperature variable optimization on optimal threshold successfully worked out a best threshold value interval and chose seven temperature variables from twenty-nine temperature measuring points. The model residual of z direction is within 3 μm. Obviously, the proposed new variable optimization method has simple computing process and good modeling accuracy, which is quite fit for thermal error compensation.