Digital twins creation based on discrete modelling of non-destructive evaluation objects

. Nowadays, the implementation of digital industrial technologies for maximal industrial processes automation and unmanned technologies creation is the main direction of technological development in the key of Industry 4.0 and NDE 4.0 paradigms. Service-oriented approach is proposed for the implementation of digital non-destructive evaluation as an effective solution for obtaining, processing and storing data and testing results. The model of industrial radiography laboratory simulator is considered, discrete models of digital twin objects are built when obtaining an image, for which the basic statements and tools of set theory are used. Examples illustrating the correspondence of digital twins’ mathematical models to their graphical analogues as well as the image generated on the detector are presented. The subject of extending CAD systems tools in the context of practical design of digital twins geometric image is considered. It is noted that virtualization of such a complex technical object as industrial radiography laboratory allows to check feasibility of technical solutions and engineering hypotheses with regard to real industrial conditions and needs in a short period of time and with minimum costs, thus providing, variability in implementation of process steps, and increasing the number of trained qualified specialists in radiation kind of non-destructive evaluation.


Introduction
The modern stage of society development is characterized by a significant influence on it of information and telecommunication technologies, which penetrate more and more actively and deeply into all spheres of human activity without exception, provide distribution of information in society, thus forming a global information space.An integral and important part of these processes is the penetration of modern information and communication technologies into the sphere of industrial production.At present, many countries are rapidly forming new approaches and principles of economy functioning, "Digital Economy", and industrial production, "Digital Production", oriented toward entering the world scientific, educational, economical and informational environment.This process is accompanied by significant changes in the system of engineering education itself, associated with the implementation of significant adjustments in the content of teaching technologies, first of all, practice-oriented.This corresponds to the modern challenges of Industry 4.0, non-destructive evaluation (NDE) 4.0 era and is ensured by technical software and hardware capabilities involved directly in the implementation of training, which contribute to harmonious entry of an individual into the dynamically changing information industrial society.Application of modern approaches in information and communication field, including the use of virtual and augmented reality, digital twins, provides rapid development of new knowledge-intensive technologies in the field of industry and machine building production, as well as in the field of effective training tools for specialists in various kinds and techniques of products and materials non-destructive testing (NDT), in particular -radiation evaluation.
2 Industrial informatics, Industry 4.0 and NDE 4.0 Industrial informatics, as an independent scientific and engineering branch, emerged at the junction of and as a result of the rapid development of science, technology and information technology.The term "industrial" refers to the creation of real production software applications, and "informatics" refers to the infrastructure that ensures their development, implementation and maintenance throughout their lifecycle.Moreover, informatics, as a science, offers tools and methods for analyzing, processing, transforming, and transferring information.Industrial informatics focuses primarily on knowledge-based automation as a means of reengineering and modifying technological processes and operations in industry, including control operations related to non-destructive impact on the control object [1].Industrial informatics is not limited to the fields of metalworking, it includes, for example, fields of knowledge such as: computer control systems, robotics, materials science, intelligent systems of video surveillance and image processing, as well as data collection of various nature and processing of multidimensional signals, where mathematical methods and informatics tools are most widely used.Industrial informatics has a set of methods and practices that uses the analysis, processing and distribution of information towards more significant results in terms of efficiency, reliability and/or safety in an industrial environment.The field of industrial informatics has become a one of the keystones for intelligent control and digital manufacturing technologies.Information technology (IT) design tools for different industries differ depending on the specifics of how a particular industry functions.For example, IT applications for the manufacturing industry include process modeling, production planning and management, distributed material requirements planning and knowledge management information systems for applied scientific research.
Industrial informatics has been formed and developed on the foundation of "classical" informatics using algorithm theory, fuzzy logic, artificial neural networks, artificial immune systems, evolutionary algorithms, industrial approach in information systems design, as well as accumulated significant practical experience in the field of theoretical and applied informatics.Industrial design processes are defined as a set of logically related tasks performed to achieve the required result, with the industrial production process defined based on customer requirements and their business interests [1].
Today, application of digital industrial technologies for maximal automation of various manufacturing processes and creation of unmanned technologies is the main direction of manufacturing technological development in the key of Industry 4.0 paradigm all over the world, which determines their efficiency and competitiveness in the international innovative technology market.
The fourth industrial revolution (Industry 4.0) is the continuous automation of traditional manufacturing processes using modern intelligent computer technologies.Large-scale machine-to-machine communication and the Internet of Things are integrated for increased automation, enhanced communication and self-monitoring, and intelligent machine manufacturing that can analyze and troubleshoot problems without the need for human intervention [2].
The list of key technologies underlying Industry 4.0 includes the Internet of Things, Big Data, Artificial Intelligence, Virtual Reality and Augmented Reality technologies.
Internet of Things -a system of data exchange between devices, which unites devices into a computing network and allows them to analyze data, as well as to transfer them to other devices included in this network by means of software applications.
Big Data -structured or unstructured data arrays of large volume.Their processing is performed using special software and algorithmic tools.Through Big Data, stimulation models are developed to test various engineering solutions, hypotheses, and products.
Artificial Intelligence is able to solve many problems of industrial manufacturing, at the same time excluding the human factor, and is used to support decision-making, automation of technological processes and manufactures.
Virtual and Augmented Reality technologies allow us to take a new look at the process of training and assessment of industrial enterprises and machine-building production specialists, significantly improve quality and efficiency of their practical training in terms of their practical skills specific to their subject areas of activity [3,4,13].
The technologies used in Industry 4.0 open up new horizons for quality control in production, including safety in manufacturing and exploitation of physical objects.In modern conditions, the line between non-destructive testing/non-destructive evaluation and Industry 4.0 becomes vague, as both research-and-engineering approaches are based on the use of multidimensional data supplied by various industrial sensors [2].
This "synergistic" approach has led to the birth of a new paradigm -NDE 4.0 with pervasive use of information and communication technologies in monitoring, automated acquisition and analysis of information about the condition of objects with various nature and functional purpose.All this is a prerequisite and serves as some kind of trigger for consistent generation and operating with digital twins of objects used in nondestructive testing [2].
Digital Twin is a software analogue of a physical object that simulates internal processes, technical characteristics and behavior of a real object under environmental conditions.It can include geometric and structural model of the object, a design data collection for parts, units and entire product, mathematical models describing all ongoing physical processes within the product, information on the manufacturing and assembly technological processes of specific elements and entire product [5].The use of digital twins makes it possible to reduce material expenses on process equipment and accessories, to avoid the harmful effects of industrial factors both on people and on the environment [6].

Digital platform collecting and processing of non-destructive testing results
One of the main evolution trends of application software in the structure of digital manufacturing and digital non-destructive testing (NDE 4.0) was the transition from monolithic structure of information systems design to modular, which greatly facilitates software scaling [7].
The recent stage in the development of modular programming has become the serviceoriented architecture of information systems (SOA) [8].SOA is primarily a modular approach to software development, relying on the use of distributed, loosely connected standardized components (services).Services are characterized by compatibility, flexibility and reusability.Accordingly, all system functionalities are implemented in components that are designed in such a way that they almost fully independent from each other.With the growth of data scale and calculation volumes, the implementation of SOA-based information systems becomes preferable [10].
The developed digital platform prototype for collecting and processing of NDT data is based on Industrial Internet of Things (IIoT) technologies, artificial intelligence for data analysis and service-oriented architecture of software solutions (Fig. 1).It represents one of information subsystems in the structure of integrated digital production [9].
Services perform various practical tasks (e.g., image recognition for radiation kind of nondestructive testing, generation of expert reports, etc.) and are incorporated with each other exclusively for solving certain tasks determined by their respective application, shown on the model.
It is worth noting that business processes serve as a mechanism for ensuring interaction between services.A business process is a set of interrelated tasks that controls an event stream, which calls and coordinates services, and creates a context for their interactions.A business process is an abstract mechanism that is independent of services' implementation and their business logic.The main task of a business process is to organize services for its efficient implementation [1].The orchestration module is designed for selecting a particular business process that interacts with various services.It specifies the interaction mechanism of the service based on the business process logic and represents the sequence of service performed actions.A service bus (in this case, ESB) provides an environment for service interaction.One of the most rational ways to implement a service-oriented approach is via web services, where a service-oriented model covers all levels of data management in a SOAbased software platform.It also avoids division into providers and consumers, because all the necessary services' information is located in a registry.For more complex and in-depth data analysis, there are public, private or hybrid cloud-based services [4,9,10].
For digital software platform implementation, the enterprise service bus Open ESB is used [11].The services are implemented in the form of web services, the functional part of which is written with high-level languages supported by the enterprise service bus.The system elements of the digital platform communicate with each other using SOAP protocol [12].A cloud-based relational database management system with open-source software code is used to store data and calculation results.These technologies provide data analysis and filtering capabilities, which are also available in basic Microsoft Office software or in "open source" software analogues' environments.
Application of an automated universal digital platform based on SOA technologies with an extended set of software services for data collection and analysis during nondestructive testing allows to reduce the influence of human factor, increase reliability of informationmeasuring subsystem and accuracy of data analysis, provide transition to automated digital production.Moreover, cloud migration of services and their SaaS implementation [9,10] expand the applicability range of applied software solutions, particularly for Big Data processing in various kinds of nondestructive testing, and allow to invite independent developers for invariance and greater intellectualization of such solutions.

Industrial radiography laboratory simulator
Simulator of industrial radiography laboratory (Fig. 2) represents a laboratory made in virtual reality environment with digital twins of testing objects, process and auxiliary equipment, instruments and tools for obtaining radiographic or radioscopic image on analogue or digital information carrier (detector) [4].
Industrial radiography laboratory simulator executed in the virtual reality environment includes models of three rooms: Room №1 -operator's room, where preparation, examination of testing samples and interpretation of obtained radiographs take place; Room №2 -X-ray laboratory, where testing object irradiation and image acquisition on digital or analog carrier is performed; Room №3 -photo laboratory, where photosensitive film is chemically processed after its exposure.
Room specification is given in the text to Fig. 2. Process equipment, testing objects, detector for fixing the results of testing object radiation exposure, information and auxiliary equipment for producing radiographic images are presented in Fig. 3 Specification of the objects involved in producing radiographic images is presented in the text to the Fig. 3.
As a result of industrial radiography laboratory simulator (Fig. 4) usage together with information software, digital twins of testing objects and process equipment, as well as measuring and testing instruments, each person is trained in virtual reality environment individually with intermediate and final results being recorded in the database in order to use them later for optimization of training process and intellectualization of knowledge check, as well as to expand the range of industrial radiography laboratory simulator hardware and software solutions applicability in its implementation as a part of telecommunication solutions [4].Fig. 2. Model of industrial radiography laboratory. 1 -negatoscope, 2 -negatoscope control panel, 3information board with testing parameters, 4 -table for radiographic testing, 5 -table for equipment storage, 6 -industrial X-ray machine, 7 -safety indication and alarm system, 8 -table for measuring and auxiliary instruments, 9 -table with the control panel of the X-ray machine, 10 -x-ray machine control desk, 11 -cabinets for storing digital twins of testing samples, 12 -information board with technical data, 13 -information board for task display and results verification, 14 -development machine, 15 -lighting control unit for room № 3, 16 -table for operation with radiographs, 17 -nonactinic lamp, 18 -daylight lamps.

Models of objects' digital twins in industrial radiography
Creation of digital twins of physical objects for nondestructive testing execution in the virtual environment of industrial radiography simulator involves the following sequential steps and actions: -aggregation of retrospective information of the NDT results in the database under the control of the industrial DBMS of the digital software SOA-platform according to applied physical techniques of welded joints testing of structural or alloyed steel products; -designing the geometry of a digital twin with a welded seam; -designing the texture of the digital twin; -providing the twin with physical properties necessary and sufficient for testing execution in a virtual environment; -designing of weld structure, weld zone and base metal defects.
-designing and verification of indication and non-destructive testing results measurement instruments; -defining the parameters of NDT object's digital twin; -development of models and algorithms for testing simulation; -adjustment of X-ray exposure parameters for testing object's digital twin, considering screens and amplifiers of X-ray exposure; -receiving the result of corresponding digital twins interaction -digital twin of the X-ray image; -evaluation of the radiographic inspection results; -acquisition of a physical/electronic copy of a virtual X-ray image.Creation of digital twins of physical objects for nondestructive testing execution in the virtual environment of industrial radiography simulator involves the following sequential steps and actions: -aggregation of retrospective information of the NDT results in the database under the control of the industrial DBMS of the digital software SOA-platform according to the applied physical techniques of welded joints testing of structural or alloyed steel products; -designing the geometry of a digital twin with a welded seam; -designing the texture of the digital twin; -providing the twin with physical properties necessary and sufficient for testing execution in a virtual environment; -defining the parameters of NDT object's digital twin; -development of models and algorithms for testing simulation; -adjustment of X-ray exposure parameters for testing object's digital twin, considering screens and amplifiers of X-ray exposure; -receiving the result of corresponding digital twins interaction -digital twin of the X-ray image; -evaluation of the radiographic inspection results; -acquisition of a physical/electronic copy of a virtual X-ray image.
To develop models of industrial radiography digital twin objects for obtaining final Xray image we shall use information stored in the database of digital platform, physical principles of radiation nondestructive testing [10], developed plug-ins, as well as basic statements and methods of set theory [13].
Let's represent the digital twin of testing with welding seam D of nondestructive testing object (Fig. 5) in the form of a tuple.

𝐷 = ⟨𝐺, 𝐹, 𝑊⟩ (1)
where G -set of geometrical parameters of testing object's digital twin, F -set of testing object's base material physical parameters, W -set of digital twin's welding seam parameters.
The set of geometrical parameters of testing object's digital twin G is presented by the following set  = {  ,   ,   ,   } (2) where gi -linear parameter, i ∈ where f1 -is the material density parameter; f2 -X-ray transparency parameter of the base material of the testing object's digital twin; E -set of chemical elements included in the base material.W -tuple of weld parameters of the digital twin of the object of control (Fig. 6) Gw -set of geometrical parameters of the weld where gwi -linear parameter where fw1 -weld material density parameter; fw2 -X-ray transparency parameter of the weld material; Ew -set of chemical elements of weld material composition.I -set (tuple) of parameters of indicating means (Fig. 7).where Gi is the set of geometric parameters of indicating means; Fi -the set of physical parameters of indicating means, ⅈ ∈ [1,n],n ∈ N.
where g1i -indicating means' linear parameter, i ∈ where f1 -indicating means' density parameter; f2 -X-ray transparency parameter of indicating means; Ef -set of chemical elements of indicating means composition.Ds -set (tuple) of weld structure defects (Fig. 8) where Gd is the set of geometric parameters of weld structure defects; = {  ,   ,   ,   } (11) where gdi -shape parameter of weld structure defect, i ∈ where fd1 -density parameter of weld structure defect; fd2 -X-ray transparency parameter of weld structure defect; Ed -set of chemical elements of weld structure defect.where ro1 -distance between the x-ray source and the detector surface; ro2 -rotation angle of the X-ray source; ru -anode voltage; ri -anode current; rt -exposure time.
Fig. 9. X-ray machine for performing NDT operations S -set (tuple) of X-ray intensifying screens parameters (Fig. 10) where Gs -set of geometric parameters of X-ray intensifying screens where gsi -linear parameter, i ∈ [1,n], n ∈ N; gst -texture parameter, t ∈ [1,n], n ∈ N. Fs -set of physical parameters of X-ray intensifying screens' material where fs1 -density parameter of intensifying screen's material; fs2 -X-ray transparency parameter of intensifying screen's material; Es -set of chemical elements of intensifying screen's material.Image -image (Fig. 11), formed on the detector during radiographic inspection [4,14], can be represented as a structure consisting of a set of components used in its implementation  ⊆  ×   ×  ×  × , (13) where D -the digital twin of the testing object with the welding seam; DS -set of defects in the weld structure; I -set of indicating means parameters; Ro -set of X-ray machine parameters for the inspection performing; S -set of X-ray intensifying screens parameters.The modern development of 3D graphics modeling technologies has led to the need for creating auxiliary software for a wide variety of functional purposes.The main purpose of such software is to simplify some, usually operations for users of 3D modeling and animation tools.Despite all the advancement of modern 3D-modeling software, there are cases when available software functionality is not enough or performing a particular modeling related task with its help is inefficient or simply inconvenient.
To handle such cases, popular 3D graphics software allows for creation of plug-ins that significantly extend functionality of CAD systems or modify existing functionality.Creating software modules or "plug-ins" is a common practice, which is often resorted to by both individual 3D modeling specialists and large computer graphics studios that need specialized functionality to effectively develop and maintain their products.The Blender software used in VR development [15] is a professional freeware and open-source software for creating 3D computer graphics, including modeling, sculpting, animation, simulation, rendering, postprocessing, etc.
The plug-in system in Blender provides a wide range of options for simplifying and speeding up workflow, allowing routine or laborious operations to be delegated to the CAD system, and expanding work possibilities through access to the now popular Python scripting language.Scripts provide for making interactive user input in the form of windows and fields with editable parameters.By transforming the scripts into a full-featured "plug-in," it is possible to give them enhanced functionality and connect them to the Blender interactive graphics software add-in system, but you must follow the mandatory requirements of the Blender API.For example, different types of welds with different configurations are generated using pre-designed parametrized surface elements, which, when multiplied, provide a holistic picture of a 3D weld image.In the course of its generation, typical for the given technological process defects and artifacts are embedded into the weld joint, which finally gives the finished and edited weld joint the appearance of a digital twin.Quantitative and qualitative values of surface elements, defects and artifacts are set by the user in the "plug-in" configuration when the plug-in is activated.
This approach significantly reduces the labor content of creating 3D-models of both the welded joints themselves and their surfaces.At the same time digital twin qualitative parameters are improved, which affects the behavior of the testing object during radiographic image generation in the industrial radiography simulator.

Conclusion
Digital twin technologies are now being successfully developed and used at all stages of product life cycle: from its design and engineering, to manufacturing and maintenance, including its non-destructive testing and technical diagnostics.
Through the combined application of modeling techniques, data collection and analysis using the Industrial Internet of Things, artificial intelligence and machine learning methods, digital twins provide simulation of product manufacturing operations, including nondestructive testing operations, production and laboratory environment interaction, and many other factors that affect overall production efficiency and product quality assurance.Digital twin usage reflects the NDE 4.0 paradigm, as an integral part of product lifecycle management involving the results of objects modeling and digitalization with wide application of modern information and communication technologies for increasing the quantitative and qualitative characteristics of both the target object and the process itself.
The main purpose of developing an X-ray industrial radiography laboratory digital twin is virtualization of a complex technical object and providing an opportunity to check the feasibility of even the most ambiguous ideas and hypotheses with minimal costs in a short period of time in realistic conditions.This allows, on the one hand, to increase the variability in the implementation of technological operations and, on the other hand, to rapidly increase the number of trained skilled specialists.

Fig. 4 .
Fig. 4. Graphic model of industrial radiography laboratory simulator in virtual reality environment

Fig. 5 .
Fig. 5. Digital twins of weld NDT samples F -a physical parameters set of digital twin of testing object's base material

Fig. 6 .
Fig. 6.Digital twins of the weld and the weld-affected zone of NDT objects Fw -set of physical parameters of testing object's digital twin  = { 1 ,  2 , }(6)

Fig. 10 .
Fig. 10.Intensifying screens used in the radiation kind of NDT

Fig. 11 .
Fig. 11.Image generated on the detector during the radiation kind of NDT