###### Abstract  
The monitoring and diagnostic system has been suggested as a non-destructive diagnostic method. The structure and operation of the suggested system can be described by the concept of digital shadow (DS). One of the main DS subsystems is a set of sensors properly placed on the monitored object and coupled with a discrete data processing model created in Matlab/Simulink. The discrete model, as another important DS subsystem of the monitored facility, transfers information about its technical condition to the operator based on data recorded by the sensor system. The digital monitoring model processes the recorded data in the form of the object's response to actions caused by its operating conditions. This work formalized a mathematical model determining the coupling of the digital model with the sensors placed on the monitored object. The formulated method using DS, due to its sensitivity, enables the detection of the damage in the object at an early stage. The tests allowed for detecting the regularities enabling the determination of the area of damage to the shaft and its size. monitoring and diagnostic system; digital shadow; mathematical model; synthesis of vibration systems +
Footnote †: journal: Applied sciences  
Article  
Development and Validation of Concept of Innovative Method of Computer-Aided Monitoring and Diagnostics of Machine Components  
[PERSON]  
1 Department of Engineering Processes Automation and Integrated Manufacturing Systems, Silesian University of Technology, 44-100 Gliwice, Poland; and [EMAIL_ADDRESS] (A.D.); [EMAIL_ADDRESS] (P.O. ); [EMAIL_ADDRESS] (T.D. ); [EMAIL_ADDRESS] (C.G. ); [EMAIL_ADDRESS] (K.B. ); [EMAIL_ADDRESS] (Z.M.) Intelligent sensors, state-of-the-art measuring equipment, the IOT concept, digital modelling technology and cloud data processing have allowed the development of new methods of creating the virtual equivalents of real machine components, namely, the concepts of \"digital twin\" (DT) and \"digital shadow\" (DS). Based on the literature review, from [9; 10; 11; 12; 13; 14; 15; 16], it can be concluded that DT is a virtual representation of a real object (entity), created to optimize the processes related to it. DT is a virtual model of a product, process or service ensuring a two-way flow of information between the virtual and physical models. It enables analyzing the data and monitoring systems to avoid problems before they occur. In the case of the DT system concept, the integration of four basic elements, i.e., a graphical representation of the object, a mathematical model of the object (representing important behavior or states of the considered object or process), state monitoring system or process data, and a two-way flow of information between the virtual model and the real object, is required. The integration of these four elements makes DT an IT tool that allows for comprehensive control and optimization of the functioning of devices or processes. The DS concept, unlike the DT concept, does not have automatic feedback between the virtual model and the real object. In the DS model concept, data from a real object allow for mapping its operation and related processes, while the impact on the real object is manual. Areas of industry in which the concepts of DT and DS are used are the processes of monitoring and diagnosing the state of the machines and the processes they perform. Correct assessment of the machine state is the basis for eliminating the failures, which are one of the main causes of disruptions in manufacturing processes. They cause downtime, which negatively affects production. The use of predictive control methods, which enable predicting the current and future state of a machine or process, is important. Minimizing the costs associated with planning inspections and servicing the machines is another important aspect [17; 18; 19]. In the process of machine state control, a distinction can be made between monitoring and diagnostics.