1. Introduction

Figure 1. The diagram of centre error.

Figure 1. The diagram of centre error.

Figure 2. The diagram of the centre process.

Figure 2. The diagram of the centre process.

2. Framework of digital twin system for centring process

Figure 3. The digital twin system framework of high-precision lens centring process.

Figure 3. The digital twin system framework of high-precision lens centring process.

3. High-fidelity digital twin construction methods

3.1. High fidelity digital twin construction methods

1)

Geometric model

The geometric model of the centring lathe can not only provide a visual display of the structure of the equipment but also provide a basis for the construction of the subsequent physical model and behavioural model. In the process of constructing the geometric model of the centring lathe, not only the accuracy of the model should meet the requirements, but also the model should be compressed and simplified to ensure the operational efficiency of the system. In this paper, a high-fidelity geometric model of centring lathe is constructed by combining the digital twin virtual model development tool, and the process is shown in Figure 4. First of all, according to the actual geometric dimensions of the parts and the assembly relationship to draw the centring lathe CAD model, with the help of Pixyz tool plug-in import CAD files, mesh size and quality control to optimize the model, including mesh merging, normal adjustment, new UV, create materials, set lighting, and so on, and will be the model output imported into Unity3d, according to the actual relationship between the equipment's movement of the model's hierarchy planning and adjustment. The model output is imported into Unity3d, and the layers of the model are planned and adjusted according to the actual motion relationship of the device.

Figure 4. The workflow of making a geometry model.

Figure 4. The workflow of making a geometry model.

2)

Behavioral model

The interactivity of the digital twin model is improved by constructing behavioural models that provide feedback responses to internal events and external inputs[26]. The key to its construction is to accurately describe the action behaviour and sequence of the device and its components. By establishing a GameObject, the geometric model is coupled by using the Mesh component, and the spatial position and assembly hierarchy of the centring lathe and each component are mapped by using the Transform component. Create a C# script that inherits the MonoBehaviour base class, mounts it to the GameObject object, divides the different phases in the behaviour, and executes the corresponding functions. In the initialization phase, the three functions of Awake(), OnEnable() and Start() are executed sequentially. Among them, Awake() mainly performs some operations including getting components, initializing variables, etc. OnEnable() mainly enables operations such as turning on the helper program, playing sound effects, etc. After the script is instantiated, it calls OnEnable() and Start(). After the script is instantiated, Start() is called to initialize the Gameobject object and play the animation. The physical calculation stage mainly includes the FixedUpdate() function, compared with Update in the later stage; its difference is the interval of calling. FixedUpdate () is called at a fixed interval instead of once per frame, so it is often used to move the rigid body, collision monitoring and other physical functions are executed here. Logic update stage, mainly including update parameters, primarily to achieve the reading of data and the execution of the action, simulation of centring adjustment and turning machining action. Graphics rendering stage, including scene rendering OnRender() and OnGUI () rendering two parts. Finally, the selection judgment of whether to continue updating is carried out; if yes, then return to the physical calculation stage, otherwise execute OnDisable() to disable the script, and finally execute OnDestroy () to deconstruct the script to end the script's life cycle, as shown in Figure 5.

Figure 5. The workflow of the behavioural model.

Figure 5. The workflow of the behavioural model.

3)

Physical Model

The physics model describes the mechanism of motion, heat transfer, stress-strain, and processing deformation.Unity3D provides excellent management mode, i.e. Physics Manager. Physical models describe the mechanisms of motion, heat transfer, stress-strain, and processing deformation.Unity3D provides an excellent management mode, namely Physics Manager. Through the Rigidbody component in Unity3d, set the object's mass, drag, Drag, angular drag, and use gravity, and other parameters to realize the simulation of object dynamics. In addition, the physical model is constructed by combining industrial-grade simulation software. Taking Matlab as an example, the engine instance is created by determining the communication data format and protocol, then using Matlab's COM interface to create an engine instance, and then using C# to call the Matlab function in Unity to carry out the simulation calculation. According to the simulation results, the data is mapped to texture mapping, and the colours attribute is assigned a value through MeshFiltercolors to visualize the simulation results.

3.2. Digital Twin Data Mapping Methods

The ultimate goal of the digital twin is to provide real-time, efficient, and intelligent services such as monitoring, diagnosis, and decision-making, which require a large amount of data. In addition, the digital twin model is also a dynamic rather than static model and requires access to data to dynamically update the model. That is, twin data is the key to the digital twin system. In the process of constructing a digital twin system, due to the diversity of devices in hardware, software, connection mode, and communication protocols, i.e., data acquisition mode, the data has the characteristics of multi-source heterogeneity, which is eventually manifested in the phenomenon of data silo including physical level and logical level. The so-called physical data silos, that is, in the data at different stages, different departments independently of each other to store and maintain, the formation of the physical sense of the island. The logical data silo refers to the same data in the definition, and understanding will be different because of different stages, equipment, departments and different; that is, the data in the logical semantics can not interact. To solve the data silo problem of industrial equipment, this paper is based on the OPC UA information model[27] and proposes to instantiate the information model of centring turning processing according to specific application scenarios, represent the events and data of the processing process as an object, and give the object variables, events, and methods, and realize the interconnection between the objects through the referencing, and ultimately form a set of standard data parsing and organization models to realize the semantic interoperability of multi-source and heterogeneous data. Semantic interoperability of heterogeneous data. OPC UA technology is used to map the information objects to the address space, and the description and access to process data is realized through OPC DA, the description and access to vertical data is realized through OPC HAD, and OPC A&E provides the information interface of running events and alarms.

1)

Centring process information model

In this paper, based on the standard machine tool manufacturing information model is modified and extended to propose the information model of the centring turning machining process, and the tree structure is used to describe it, as shown in Figure XX. The information model has three elements: information object, attribute and attribute set. Among them, information objects are conceptualized descriptions of real or abstract entities of the machining process, such as spindles, chucks, and process documents. Attributes are textualized or digitized descriptions of the nature and characteristics of information objects. An attribute set is a collection of attributes. The information model is instantiated according to the above definition to get the centring machining system information model with practical significance, as shown in Figure 6.

Figure 6. The information model of a digital twin for high-precision lens centring process.

Figure 6. The information model of a digital twin for high-precision lens centring process.

2)

Data communication scheme based on OPC UA

OPC UA is a new generation of service-oriented communication solution for cross-platform transmission and transmission process security in the manufacturing field developed based on OPC Classic, which supports a wide variety of data semantics and information models and can unify the communication mechanism and data interaction mode of different industrial devices and solve the problem of data transmission and communication of the machining process. OPC UA mainly consists of three parts. OPC UA specifically includes three parts: OPC DA, i.e. OPC Data Access, defines the value, event and quality information of the data exchange process, which is the most important function in OPC, and is mainly used for the transmission and communication of production data, process data and factual state of the equipment; OPC HDA, i.e. OPC Historical Data Access, defines methods for querying and analyzing the data which can be applied to the historical data and time data; OPC HDA, i.e. OPC Historical Data Access, defines methods for querying and analyzing the data which can be applied to the historical data and time data. OPC HDA, OPC Historical Data Access, defines the methods that can be applied to the query and analysis of historical data and time data; OPC AE, OPC Alarms & Events, defines the exchange of alarms and event-type message information, as well as variable state and state management. C/S, i.e. Client/server architecture is used to realize the construction of the OPC UA system. The OPC UA Client includes the OPC UA client application, communication stack, and client API, and can send and receive OPC UA service requests to and from the OPC UA server side. the OPC UA Server includes the OPC UA server application, communication stack, address space, publish/subscribe entity, and server interface API. The OPC UA C/S OPC UA C/S architecture through the publish/subscribe machine to realize the interaction between the client and the server, the process is, through the client-side communication stack request to generate a session release queue, the server-side communication stack to set up the monitoring items for subscription monitoring, after accepting the session, call request the corresponding service, and in the node of the address space to perform the tasks specified in the request after sending notifications and publish the answer, as shown in Figure 7.

Figure 7. The workflow of OPC UA Client and Server.

Figure 7. The workflow of OPC UA Client and Server.

3.3. VMD-GRU Intelligent Monitoring Approach

The digital twin system provides accurate and reliable intelligent services for the stages of manufacturing, operation and maintenance, to optimise the machining and manufacturing process to achieve intelligent manufacturing. Current research on digital twins focuses on the level of model frameworks and less on the development of actual intelligent services, which is an important reason why digital twins are difficult to promote on the ground. With the machining process, the key components of the equipment change, in the wear of the tool has an important impact on the quality of the workpiece, so it is important to achieve the monitoring of the status of the tool to ensure the quality of machining and improve productivity. Tool condition monitoring methods have direct and indirect methods, while the implementation of the direct method of high cost and affects the continuity of machining, so the application has been limited, while the indirect method is through the sensor acquisition of displacement, force, acoustic emission, spindle power and other signals to indirectly monitor the amount of tool wear. In this paper, for the centring machining process, based on the digital twin system mentioned above, an intelligent monitoring service for the state of the tool, a key component of the machining system, is developed. Firstly, the time-frequency domain eigencomponents of the sensed data are extracted using the VMD variational modal decomposition, and then the input eigenvectors are constructed by normalising them, and finally the wear amount is predicted using the GRU's sequential model to predict the wear amount.

Sensor data have a low data value density due to the presence of a large amount of random background noise and repetitive redundant data, and also due to the complex coupling relationship between various signals. Therefore, the sensed data must be processed to accurately extract the effective components to construct suitable features as model inputs, which is crucial for the final effect of monitoring.

Firstly, suitable signal processing methods are chosen to convert the signals. In time series signal analysis, there are three main extraction methods commonly used, the method of time domain analysis, the method of frequency domain analysis, and the method of time-frequency domain analysis. Among them, the method of time domain analysis and frequency domain analysis is to decompose the signal in time domain and frequency domain respectively, which is suitable for dealing with smooth signals. In this paper, the monitoring of the components, due to the damage process of the components will change the frequency domain characteristics, which belong to the typical non-smooth signal. Therefore, this paper adopts the time-frequency domain analysis method commonly used for non-smooth signals. The vibration signal's inherent modal component IMF component is extracted using the variational modal decomposition VMD method[28]. The basic idea is to assume that all IMFs are bandwidth-limited components near their centre frequencies so that the sum of the estimated bandwidths is minimised, which translates into the following constrained variational problem:

It is realised as follows.

$$\min \left\{{\displaystyle \sum _{k=1}^K\left|\right|{\partial }_t[\left(\delta (t)+\frac{j}{\pi t}·u_k(t)\right)e^{-j\omega kt}]|{|}_2^2}\right\}$$

(1)

$$\mathrm{s}.\mathrm{t}.{\displaystyle \sum _{k=1}^K{u}_k=s}$$

(2)

initialise the parameters.

$$\left\{{\widehat{u}}_k^1\right\},\left\{{\omega }_k^1\right\},{\widehat{\lambda }}^1,n\leftarrow 0$$

$${\omega }_k^{n+1}\leftarrow \frac{{\displaystyle {\int }_0^{\infty }\omega {\left|{\widehat{u}}_k^{n+1}(\omega )\right|}^2}d\omega }{{\displaystyle {\int }_0^{\infty }{\left|{\widehat{u}}_k^{n+1}(\omega )\right|}^2}d\omega }$$

(3)

2. update the parameters cyclically

$${\widehat{\lambda }}^{n+1}(\omega )\leftarrow {\widehat{\lambda }}^n(\omega )+\tau (\widehat{f}(\omega )-{\displaystyle \sum _k{\widehat{u}}_k^{n+1}(\omega )})$$

(4)

3. judge whether the convergence condition is satisfied, then end and output the result, otherwise repeat step 2.

$${\displaystyle {\sum }_k\left|\right|{\widehat{u}}_k^{n+1}-{\widehat{u}}_k^n|{|}_2^2/|\left|{\widehat{u}}_k^n\right|{|}_2^2<\epsilon }$$

(5)

Then through the extraction of the statistical characteristics of the signal in the time domain, frequency domain, and geometric features, information features, to achieve the initial screening of the features of the data, to complete the dimensionality reduction of the data. Finally, the features are selected for splicing.

Figure 8. Partial time-domain features obtained by VMD extraction.

Figure 8. Partial time-domain features obtained by VMD extraction.

Figure 9. Structure diagram of GRU.

Figure 9. Structure diagram of GRU.

Recurrent neural networks can effectively capture the time-varying nature of equipment by passing the output and state of the current moment as input to the next moment and thus are widely used in the state prediction of equipment. To improve the representation ability of the model, the number of layers of the RNN is usually superimposed, but the increase of the computational depth will lead to a series of gradient problems and thus make it difficult or even impossible to train the model.LSTM uses the gating mechanism, which solves the problem of gradient to a certain extent. However, the large number of parameters in LSTM leads to a large amount of computation in the training process, and there are limitations in the real-time training and computation of the model.GRU replaces the forgetting gate and input gate in LSTM with a single forgetting gate and adds some other minor changes, which is a simplified variant of LSTM.GRU has a faster convergence speed with fewer parameters than LSTM, and the effect of GRU is not as good as that of LSTM on different tasks and datasets. and datasets are not significantly different. Therefore, GRU is used as an alternative to LSTM in this paper. The structure of GRU is shown in Fig and the calculation formula is as follows[29]:

$$z_t=\sigma (W_Z{x}_t+U_Z{h}_{t-1}+b_z)$$

(6)

$$r_t=\sigma (W_r{x}_t+U_r{h}_{t-1}+b_r)$$

(7)

$${\tilde{h}}_t=\tanh (W_h{x}_t+U_h(r_t\odot h_{t-1})+b_h)$$

(8)

$$h_t=z_t\odot h_{t-1}+(1-z_t)\odot {\tilde{h}}_t$$

(9)

4. System implementation and verification

Table 1. Development Platform Configuration Information.

Figure 10. The main interface of the digital twin system for the high-precision lens-centring process

Figure 10. The main interface of the digital twin system for the high-precision lens-centring process

Figure 11. The result VMD Decomposition.

Figure 11. The result VMD Decomposition.

Figure 12. Evaluation results.

Figure 12. Evaluation results.

Figure 13. The result of the VMD-GRU Intelligent Monitoring Approach.

Figure 13. The result of the VMD-GRU Intelligent Monitoring Approach.

5. Conclusion

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