Technical paper  技术文件

Discrete manufacturing workshop (DMW)
离散制造车间（DMW）
Digital twin (DT) model
数字孪生（DT）模型
Migration modeling  迁移建模
Consistency verification
一致性验证
Synchronous evolution  同步进化

Facing with fierce market competition and diverse customer needs, the core task of the manufacturing industry has evolved from traditional mass production to matching the trend of mass user customization, which increase the pressure for modern enterprises to improve production efficiency, save costs, and quickly adapt to market changes [1]. In this context, the discrete manufacturing industry also needs to transform and upgrade from “manufacturing” to “smart manufacturing”.
面对激烈的市场竞争和多样化的客户需求，制造业的核心任务已从传统的大规模生产演变为与用户大规模定制趋势相匹配，这为现代企业提高生产效率、节约成本、快速适应市场变化增加了压力[1]。在此背景下，离散制造业也需要从 "制造 "向 "智造 "转型升级。

Discrete manufacturing workshop (DMW) is a large, dynamic and complex system. The accurate analysis, predication and evaluation of the manufacturing performance and manufacturing behavior of DMW under uncertain environment are needed to achieve high quality and mass efficiency [2]. Intelligent technologies, such as the Internet of Things, Big Data Analysis, and artificial intelligence technology have collectively made this requirement possible. Digital twin (DT) is an emerging and vital technology for digital transformation and intelligent upgrade, driven by data and model; it enables high-fidelity monitoring, simulation, prediction, optimization and real-time control of physical manufacturing processes via developing the virtual counterpart of the physical entities and processes in cyberspace [1,3]. Under this background, DT workshop, as a new mode of workshop operation, has been
离散制造车间（DMW）是一个庞大、动态和复杂的系统。要实现高质量、高效率的生产，就需要对不确定环境下 DMW 的制造性能和制造行为进行准确的分析、预测和评估[2]。物联网、大数据分析和人工智能技术等智能技术共同使这一要求成为可能。数字孪生（DT）是以数据和模型为驱动，实现数字化转型和智能化升级的重要新兴技术；它通过在网络空间开发物理实体和过程的虚拟对应物，实现对物理制造过程的高保真监控、模拟、预测、优化和实时控制[1,3]。在此背景下，DT 车间作为一种新的车间运作模式，已被
gradually explored and applied in the manufacturing industry $[4,5]$$[4,5]$[4,5][4,5]. There has been research on construction and verification of DT model issues for DT workshop, such as standard and framework for DT modeling [4], production process DT modeling [6], data-driven featur-e-based verification [7] and mechanism-based verification [8], etc. Besides, some adaptive evolutionary frameworks of DT [9] and the method of online training DT model [10], etc. are also studied. The above-mentioned studies have made great efforts to tackle the construction and verification of DT model issues. However, there still exist such problems as low modeling efficiency, high verification difficulty and status synchronism between physical workshop and virtual workshop, which limits the development of genuine DT applications for smart manufacturing in DMW. 

The DT has progressed from theoretical research to pragmatic implementation, whereas the DT model is a paramount constituent of DT and a prerequisite for successful DT applications [5]. The real-time data and status of physical workshop could be updated to its virtual model, and the simulation and analysis results could act on physical workshop in turn to form closed-loop control, making DT workshop hold the potential for simulation, monitoring and scheduling applications. DT workshop enables the optimizations and decision-making in virtual workshop, which depends on the real-time data updated from physical
DT已从理论研究发展到实际应用，而DT模型是DT的重要组成部分，也是DT成功应用的前提[5]。物理车间的实时数据和状态可以更新到其虚拟模型中，仿真和分析结果可以反过来作用于物理车间，形成闭环控制，这使得 DT 车间在仿真、监控和调度应用方面大有可为。DT 车间使虚拟车间的优化和决策成为可能，而虚拟车间的优化和决策取决于物理车间的实时数据更新。

workshop, through synchronization enabled by sensors and controls. All these are based on a very important prerequisite that the DT model is accurate [11]. So, how to efficiently construct the DT model and how to maintain the accuracy of DT model in application is a key issue. In this study, we discussed three aspects: the modeling, verification, evolution of DT model, and proposed a migration modeling method of DT model, GCN-TCN based verification of DT model and synchronous evolution of DT model respectively. The main contribution of this article can be concluded as follows.
通过传感器和控制装置实现同步。所有这些都基于一个非常重要的前提条件，即 DT 模型的准确性[11]。因此，如何有效地构建 DT 模型以及如何在应用中保持 DT 模型的准确性是一个关键问题。在本研究中，我们从 DT 模型的建模、验证和演进三个方面进行了讨论，并分别提出了 DT 模型的迁移建模方法、基于 GCN-TCN 的 DT 模型验证方法和 DT 模型的同步演进方法。本文的主要贡献可总结如下。

The rest of this article is organized as follows. Section 2 presents an overview of related works on modeling, model verification and evolution of DT workshop. This is followed by an in-depth discussion on the connotation and characteristics of DT in DMW in Section 3. The key technologies of DT modeling of DMW are discussed in Section 4, highlighting how to solve the issue of efficiently constructing DT model and maintaining the accuracy of DT model in application. Section 5 demonstrates the results on performance evaluation for the proposed method through a case study. Section 6 concludes this study.
本文接下来的内容安排如下。第 2 节概述了有关建模、模型验证和 DT 工作坊演变的相关工作。随后，第 3 节深入讨论了 DMW 中 DT 的内涵和特点。第 4 节讨论了 DMW DT 建模的关键技术，重点介绍了如何解决高效构建 DT 模型和在应用中保持 DT 模型准确性的问题。第 5 节通过案例研究展示了所提方法的性能评估结果。第 6 节为本研究的结论。

In this section, several issues relating to this article in complex industrial manufacturing systems, including modeling, verification and evolution techniques for DT model, and the research gaps in industrial applications, are discussed respectively.
本节将分别讨论本文在复杂工业制造系统中的几个相关问题，包括 DT 模型的建模、验证和演化技术，以及在工业应用中的研究空白。

The DT model modeling of DMW is grounded on modeling theory. In current years, researchers have spared no effort to tackle the construction and verification of DT model issues for DT workshop, which is an important prerequisite for the promotion of the implementation of industrial DT technology and the realiziation of smart manufacturing. Grieves [12] proposed a general and standard DT modeling reference framework, known as three-dimensional DT model, including three dimensions namely physical entities, virtual models, and their connections. But it is still abstract and lack of pertinence in the implementation process, for example, the establishment of DT model in industrial environment. To explore vulnerabilities in industrial DT, Tao et al. [4] put forward the concept of DT workshop, defined the DT model from five dimensions namely physical entity, virtual entity, service, digital twin data and connection, and presented the theoretical support and key technologies of information fusion from four aspects of physical integration, data integration, model integration and service integration. In terms of modeling framework, Zhang et al. [13] proposed a framework of digital workshop, including physical model, ontology-based digital model and virtual model. Zhuang et al. [14] introduced a framework of DT model modeling in workshop, including four dimensions such as modeling object, modeling dimension, real-time condition monitoring and state prediction. However, the proposed dimensional modeling approach for describing the physical shop-floor lacks the consideration for model reuse and efficient modeling, and it may be limited by enforceability in practical applications. To explore virtual-real mapping,
DMW的DT模型建模以建模理论为基础。近年来，研究人员不遗余力地解决 DT 车间 DT 模型的构建和验证问题，这是推动工业 DT 技术实施和实现智能制造的重要前提。Grieves [12]提出了一个通用的标准 DT 建模参考框架，即三维 DT 模型，包括物理实体、虚拟模型及其连接三个维度。但在实施过程中，例如在工业环境中建立 DT 模型时，它仍然比较抽象，缺乏针对性。为了探索工业 DT 中的漏洞，Tao 等人[4]提出了 DT 工作坊的概念，从物理实体、虚拟实体、服务、数字孪生数据和连接五个维度定义了 DT 模型，并从物理集成、数据集成、模型集成和服务集成四个方面提出了信息融合的理论支撑和关键技术。在建模框架方面，张文等[13]提出了数字车间框架，包括物理模型、基于本体的数字模型和虚拟模型。Zhuang 等[14]提出了车间 DT 建模框架，包括建模对象、建模维度、实时状态监测和状态预测等四个维度。然而，所提出的描述物理车间的维度建模方法缺乏对模型重用和高效建模的考虑，在实际应用中可能会受到可执行性的限制。探索虚实映射、

Ding et al. [15] established the virtual-real mapping approach of DT model in smart manufacturing space and the data modeling method in multidimensional spatio-temporal. Uhlemann et al. [16] presented a method of establishing DT production system by real-time data acquisition and processing technology. In terms of production process modeling, Bao et al. [6] introduced a method of modeling DT model from the perspectives of product, technological process and operation. However, this method just focused on generating process models in virtual space, which are hardly to reuse models when new modeling requirements arise in the manufacturing systems. Schleich et al. [17] established an interaction between virtual model design and manufacturing method of skin model shapes. Yi et al. [18] set up a DT model for intelligent assembly process design and built a three-layer application framework based on DT for complex product process design. Wang et al. [19] presented a unified modeling approach to a knowledge-based DT system design, which enables designers to create and document a system model, but it costs too much time in learning such a graphical modeling language and finding suitable models to reuse and lacks DT model reusable cases and patterns. Leng et al. [20] proposed a remote semi-physical commissioning method of flow-type smart manufacturing systems based on DT. Besides, Luo et al. [21] put forward a hybrid predictive maintenance approach driven by DT to promote the development from modeling to application.
Ding等人[15]建立了智能制造空间中DT模型的虚实映射方法和多维时空的数据建模方法。Uhlemann 等[16]提出了一种通过实时数据采集和处理技术建立 DT 生产系统的方法。在生产过程建模方面，Bao 等人[6]介绍了一种从产品、工艺流程和操作角度对 DT 模型进行建模的方法。然而，这种方法只是侧重于在虚拟空间中生成过程模型，当制造系统出现新的建模需求时，很难重复使用模型。Schleich 等人[17]建立了虚拟模型设计与皮肤模型形状制造方法之间的交互。Yi 等[18]建立了智能装配工艺设计的 DT 模型，并构建了基于 DT 的复杂产品工艺设计三层应用框架。Wang 等[19]提出了一种基于知识的 DT 系统设计的统一建模方法，使设计人员能够创建和记录系统模型，但在学习这种图形建模语言和寻找合适的模型重用方面花费了太多的时间，缺乏 DT 模型可重用的案例和模式。Leng 等人[20]提出了一种基于 DT 的流程型智能制造系统远程半实物调试方法。此外，Luo 等人[21]提出了一种以 DT 为驱动的混合预测性维护方法，以促进从建模到应用的发展。

Obviously, previous studies have shown the success in DT framework and manufacturing elements modeling of workshop. However, there is a lack of effective DT migration modeling theory and methods for DMW, which may lead to low efficiency of DT modeling.
显然，以往的研究已经在车间 DT 框架和制造要素建模方面取得了成功。然而，目前还缺乏针对 DMW 的有效 DT 迁移建模理论和方法，这可能会导致 DT 建模效率低下。

The DT model verification of DMW tests the consistency between physical and virtual workshop. Two DT model validity verification methods, data-driven feature-based verification and mechanism-based verification, are widely studied. The former is suitable for complex systems with mechanism unknown and difficult to characterize, but requires massive data and neural network model, while the latter is suitable for equipment or products with relatively clear mechanism. Saratha et al. [7] presented a DT model verification approach for industrial applications, including data modeling, data connection, attribute definition, semantic modeling, information connection and parameter verification. The sensor data from the real-time operation is used to compare with the corresponding data in DT model, which may be easily affected by noisy data. Semenkov et al. [8] put forward a hybrid digital model including virtual machine, simulator and actual hardware to verify large scale control systems. Besides, Qian et al. [22] proposed a model verification approach for DMW based on data characteristics to verify the modeling accuracy of DT model. However, the proposed layout similarity and model similarity index use expert scoring method, which has the characteristics of simple use and strong intuition, but its theoretical and systematic nature is ignored and it is sometimes difficult to ensure the objectivity and accuracy of the evaluation results. Jiang et al. [23] exploited blockchain to propose a new digital twin edge networks framework for enabling flexible and secure digital twin construction, and presented a DT model update and verification method based on blockchain and cooperative federated learning, which is efficient in the case of small data volumes, but may be inappropriate in the case of big data environment due to its properties (e.g., tracing historical data, the delay of the transactions, etc.) of the blockchain. Zhang et al. [24] proposed a consistency evaluation framework towards DT shop-floor models, which mainly contains two phases: before and after model assembly and model fusion. Specifically, the geometry models, physics models, behavior models and rule models are mainly considered before model assembly and model fusion. After model assembly and fusion, the overall performance of assembled models and fusion models is paid more attention. But the analytic hierarchy process is used to form a comprehensive consistency evaluation result for DT shop-floor models,
DMW 的 DT 模型验证测试物理车间与虚拟车间之间的一致性。基于数据驱动的特征验证和基于机理的验证这两种 DT 模型有效性验证方法被广泛研究。前者适用于机理未知、难以表征的复杂系统，但需要海量数据和神经网络模型；后者适用于机理相对清晰的设备或产品。Saratha 等人[7]提出了一种面向工业应用的 DT 模型验证方法，包括数据建模、数据连接、属性定义、语义建模、信息连接和参数验证。实时运行中的传感器数据被用来与 DT 模型中的相应数据进行比较，而 DT 模型中的数据很容易受到噪声数据的影响。Semenkov 等人[8]提出了一种混合数字模型，包括虚拟机、仿真器和实际硬件，用于验证大型控制系统。此外，Qian 等人[22]提出了一种基于数据特征的 DMW 模型验证方法，以验证 DT 模型的建模精度。但提出的布局相似度和模型相似度指标采用专家打分法，具有使用简单、直观性强的特点，但忽略了其理论性和系统性，有时难以保证评价结果的客观性和准确性。Jiang 等人 [23]利用区块链提出了一种新的数字孪生边缘网络框架，以实现灵活、安全的数字孪生构建，并提出了一种基于区块链和合作联合学习的DT模型更新与验证方法，该方法在数据量较小的情况下效率较高，但由于区块链的特性（如历史数据的追溯、交易的延迟等），在大数据环境下可能并不适用。Zhang 等人[24]提出了一种针对 DT 车间模型的一致性评价框架，主要包含两个阶段：模型组装前后和模型融合。具体来说，在模型组装和模型融合之前，主要考虑几何模型、物理模型、行为模型和规则模型。在模型组装和融合之后，则更加关注组装模型和融合模型的整体性能。但分析层次过程用于形成 DT 车间模型的综合一致性评价结果、
which may be easily influenced by subjective factors, resulting in inaccurate evaluation.
这很容易受到主观因素的影响，导致评估不准确。

Obviously, previous studies have shown it is feasible to evaluate the effectiveness of DT model in terms of its behavior, process and result, etc. However, there are some indicators (e.g., consistency index of geometry model, behavior model and logic model, etc.) that are difficult to quantify, moreover, the evaluation result are easily affected by subjective factors and thus result in poor enforceability.
显然，以往的研究表明，从行为、过程和结果等方面评价 DT 模型的有效性是可行的。但有些指标（如几何模型、行为模型和逻辑模型的一致性指标等）难以量化，而且评价结果容易受主观因素影响，可执行性差。

The DT model synchronous evolution of DMW requires DT model to be qualified for tracking the performance degradation state of workshop and realizing the synchronization of the performance of physical workshop in industrial environment. Qian et al. [6] presented a representation model of performance degradation and a synchronous update model with competitive election mechanism to enhance the accuracy of production progress prediction with time in industrial environment. Zheng et al. [9] explored an application framework of DT, and described the implementation process of full parametric virtual modeling and the construction idea for DT application subsystems. In this work, the model of DT for product lifecycle management is analyzed, and the implementation process of full parametric virtual modeling is described. However, there are drawbacks in practical application mode of DT. Wang et al. [25] put forward a big data driven hierarchical DT predictive remanufacturing paradigm, and developed a big data driven layered architecture and the hierarchical digital-twin reconfiguration control mechanism respectively, which makes it possible to predict rapid reconfiguration optimization of sustainable products and remanufacturing processes. But it still lacks detailed reconstruction and evolution methods. Liu et al. [26] proposed an adaptive evolutionary framework for the decision-making models of DT machining system, focusing on insufficient robustness of the DT system in specific scenarios. This framework endows different decision-making models with evolutionary characteristics and can adaptively improve system’s machining quality requirements with product development. However, this research needs to be further in-depth application validated in complex industrial environments. Besides, Liu et al. [27] presented a multi-scale evolution mechanism of DT mimic model and explained the evolution mechanism from data to knowledge. The method can generate product quality knowledge models from product data, explore the relationships between quality indicators and reveal evolution mechanism during machining processes. But it may not be able to adapt to the dynamic evolution process in industrial environments, as it is considered from a multi-scale perspective and not from an adaptive dynamic perspective. Zhang et al. [10] explored an online training DT model method, established a DT model including state attributes, static performance attributes and fluctuating performance attributes, and realized the DT model training online by using real-time data. It facilitates data sharing and reuse to meet the dynamic update requirements of DT model and mainly focuses on the theoretical framework. However, the specific evolution and application technique are not clear to reflect production process, entities status dynamically.
DMW 的 DT 模型同步演化要求 DT 模型具备跟踪车间性能退化状态的能力，实现工业环境下物理车间的性能同步。Qian等[6]提出了一种性能退化表示模型和具有竞争选举机制的同步更新模型，以提高工业环境下生产进度随时间变化预测的准确性。Zheng 等[9]探讨了 DT 的应用框架，阐述了全参数虚拟建模的实现过程和 DT 应用子系统的构建思路。本文分析了 DT 在产品生命周期管理中的模型，阐述了全参数化虚拟建模的实现过程。然而，DT 在实际应用模式中存在缺陷。Wang等[25]提出了大数据驱动的分层DT预测再制造范式，并分别开发了大数据驱动的分层体系结构和分层数字-双子重构控制机制，使得预测可持续产品和再制造过程的快速重构优化成为可能。但它仍然缺乏详细的重构和演化方法。Liu 等人[26]针对 DT 系统在特定场景下鲁棒性不足的问题，提出了针对 DT 加工系统决策模型的自适应进化框架。该框架赋予不同的决策模型以进化特性，并能随着产品的发展自适应地提高系统的加工质量要求。不过，这项研究还需要在复杂的工业环境中进一步深入应用验证。 此外，Liu 等人[27] 提出了 DT 模拟模型的多尺度演化机制，并解释了从数据到知识的演化机制。该方法可以从产品数据中生成产品质量知识模型，探索质量指标之间的关系，揭示加工过程中的演化机理。但由于该方法是从多尺度角度考虑问题，而不是从自适应动态角度考虑问题，因此可能无法适应工业环境中的动态演化过程。Zhang 等人[10]探索了一种在线训练 DT 模型的方法，建立了包括状态属性、静态性能属性和波动性能属性的 DT 模型，并利用实时数据实现了 DT 模型的在线训练。它促进了数据共享和重用，满足了 DT 模型的动态更新要求，主要集中在理论框架上。但在动态反映生产过程、实体状态等方面的具体演化和应用技术还不明确。

Obviously, previous studies have shown the success in DT model evolution framework, parameter evolution, etc. However, the dynamic updating mechanism of DT model in application of a manufacturing system has not yet been established, which may result in the decline of DT model accuracy and even failure.
显然，以往的研究已经在 DT 模型演化框架、参数演化等方面取得了成功。然而，DT 模型在制造系统应用中的动态更新机制尚未建立，这可能会导致 DT 模型精度下降，甚至失效。

To sum up, some challenges including modeling, verification and evolution of DT model still exist in DMW. Thus, taking “model modelingmodel verification-model evolution” as the main line, we begin with the concept and characteristics of DT model in DMW, then propose three key technologies of DMW, and verify the actual scenarios application effect, providing guide for the development of DT in discrete manufacturing workshop.
综上所述，在DMW中，DT模型的建模、验证和演进仍然存在一些挑战。因此，我们以 "建模-验证-演进 "为主线，从离散制造车间 DT 模型的概念和特点入手，提出离散制造车间 DT 的三大关键技术，并验证实际场景应用效果，为离散制造车间 DT 的发展提供指导。

Definition 1. The discrete manufacturing workshop (DMW) is a type of workshop (system) that produces according to discrete tasks and work units. For each order or product, the workshop needs to dispatch and arrange processes, operations and resources, etc. to meet different production needs. In the current multi-variety, variable-batch, and highly complex production environment, it has characteristics such as diversity, multi-disturbance, uncertainty and dynamic variability [2,11], which are described in more detail as follows.
定义 1.离散制造车间（DMW）是一种按照离散任务和工作单元进行生产的车间（系统）。针对每个订单或产品，车间需要调度和安排工序、作业和资源等，以满足不同的生产需求。在当前多品种、变批量、高复杂度的生产环境下，它具有多样性、多干扰性、不确定性和动态多变性等特点[2,11]，下面对这些特点进行详细介绍。

With the in-depth research and application of DT in various industries, the understanding of DT tends to be diversified. It is widely acknowledged that the terminology was first introduced as “digital equivalent to a physical product” by Michael Grieves at University of Michigan in 2003 [28]. After then, the terminologies such as digital replication [29], dynamic virtual representation [30] and information mirroring model [31] emerged. Although the terminology has changed, the core concept remains, namely, establishing the mirroring model of physical object in digital space, and then mirroring model-based to enhance management ability and application effect.
随着 DT 在各行各业的深入研究和应用，人们对 DT 的理解也趋于多元化。众所周知，2003 年密歇根大学的 Michael Grieves 首次提出了 "数字等同于实体产品 "的术语[28]。此后，又出现了数字复制[29]、动态虚拟表示[30]和信息镜像模型[31]等术语。虽然术语发生了变化，但核心理念没有变，即在数字空间建立实物的镜像模型，然后基于镜像模型提高管理能力和应用效果。

DMW is a large, dynamic and complex system, and its virtual workshop should be completely consistent and synchronized with physical workshop in the explicit and implicit characteristics such as geometry, behavior, logic and performance of DT model. The concept of DT in DMW is defined as follows.
DMW 是一个庞大、动态和复杂的系统，其虚拟车间在 DT 模型的几何、行为、逻辑和性能等显性和隐性特征方面应与物理车间完全一致和同步。DMW 中 DT 的概念定义如下。

Definition 2. The DT of DMW is a technology system that is supported by manufacturing technologies such as Internet of things, Big data, artificial intelligence etc. It makes virtual replication of the characteristics, behavior, logic, and performance of manufacturing elements of DMW, performs the operations of description, monitoring, simulation, prediction, optimization and control of DMW, and enables visible status, measurable performance, optimized scheme, and controllable process [32,33].
定义 2.DMW 的 DT 是以物联网、大数据、人工智能等制造技术为支撑的技术系统。它对 DMW 制造要素的特征、行为、逻辑和性能进行虚拟复制，对 DMW 进行描述、监测、仿真、预测、优化和控制等操作，实现状态可视、性能可测、方案可优、过程可控[32,33]。

The word “twin” is interpreted as ‘the same or very similar metaphor’ in the dictionary, so it means that physical system and DT model have the same gene, and should have very similar or the same physical laws and operating mechanism. Moreover, DT model should have ability to simulate, track physical system performance changes, and optimize the physical system constantly. Thus, the DT in discrete manufacturing workshop also needs to have the following characteristics.
在字典中，"孪生 "一词被解释为 "相同或非常相似的比喻"，因此它意味着物理系统和 DT 模型具有相同的基因，应该具有非常相似或相同的物理规律和运行机制。此外，DT 模型还应具备模拟、跟踪物理系统性能变化并不断优化物理系统的能力。因此，离散制造车间的 DT 还需要具备以下特征。