###### Abstract
In the case of methods based on the assessment of the change in the natural frequency or the change in the damping coefficient, they are characterized by low sensitivity to small damages, and it is difficult to locate the place where the damage occurred [73; 74; 75; 76; 77; 78; 79]. However, methods that analyze changes in frequency characteristics, filtered with respect to the selected natural frequency, do not provide information on the location of the detected damage. In the case of methods based on the assessment of natural vibration modes (modal methods), it is necessary to use a sufficiently large number of measurement points, which significantly increases the costs of using these methods. Often, due to the insufficient number of measurement points, the use of these methods is burdened with a large error and difficulty in locating the place of damage occurrence. An important aspect of assessing the condition of an object is the ability to identify and predict damage propagation. Evaluating the rate of propagation and the probability of catastrophic failure forms the basis for determining the feasibility and duration of safe operation. This enables controlled decisions regarding the timing of repairs or the moment when the object must be decommissioned. In this context, methods and algorithms are used to predict the rate and nature (direction) of damage propagation, allowing for an assessment of the object's future condition. These methods include those based on artificial intelligence (Neural Networks, Artificial Immune Systems (AIS)) [80; 81; 82; 83; 84], algorithms based on the domino effect [85; 86], experience-based methods (Case-Based Reasoning (CBR)) [87; 88], and numerical methods that enable computer simulations of damage propagation (FEM, BEM) [89]. Accurate assessment of damage propagation allows for predicting the future condition of the object, which enhances safety and reduces the costs associated with its operation. The presented research work describes the concept of a monitoring and diagnostic system based on the vibration diagnostics method with the structure of the DS system. The proposed system is a set of sensors placed on the monitored machine component and coupled with a discrete data processing model created in the Matlab/Simulink program. The discrete model serves as a digital monitoring system that, based on recorded data, transmits information about the technical state of the monitored machine component to the user. The digital monitoring system processes the acquired data in the form of the object's response to the action caused by its operating conditions. The time processes obtained in this way (system responses) are processed by a digital monitoring model and compared with the previously generated waveforms of the tested machine component. The data generated by the system (compared to the pattern) indicate the area and amount of damage in the tested object. Monitoring is continuous throughout the entire time of the facility operation, with simultaneous processing of recorded data in the DS [90; 91; 92]. Detection of ongoing changes is possible thanks to the use of a mathematical model, which determines its appropriate coupling with sensors placed on the monitored machine component. This research work formulates and formalizes the mathematical model on the basis of which the DS was built. Correct operation of the DS was verified using the model of a continuous (real) system in the form of a multi-stage machine shaft, modelled in the PLM Siemens NX program. Sensors were placed on the shaft in selected places to record data during the simulation of shaft operation. In the next stage, the data were sent to a digital monitoring system to compare them with the previously generated pattern. During the tests, various types of damage were introduced into the monitored facility, and the data were recorded and processed in DS. The data were compared with the pattern, which allowed us to detect the location and extent of damage to the monitored object.