## 1 Introduction
The studies [22; 23; 24; 25] examine the application of wavelet transform combined with machine learning techniques to classify types of faults in electrical circuits. The authors show that the combined approach significantly improves the accuracy and sensitivity of the diagnosis. The main research directions in world science in the field of failure diagnosis include the following:  
* Developing new signal processing algorithms: Researchers are actively working on developing algorithms that combine wavelet transform with other signal processing techniques, such as filtering and machine learning. These combined approaches can improve the accuracy and sensitivity of diagnostics. For example, in [26], the authors propose a new algorithm that combines wavelet transform with an LSTM-based neural network architecture to predict faults in electrical circuits. * Machine Learning Applications: Machine learning techniques such as neural networks [27; 28; 29; 30] and random forests are used to classify failure types based on analyzing the time-frequency characteristics of signals. These methods are able to automatically train on large amounts of data and identify different types of failures with high accuracy. In [31], the authors use neural networks to diagnose faults in electrical circuits, showing a significant improvement in accuracy over traditional methods. * Integration with modern technologies: Modern technologies such as the Internet of Things (IoT) and cloud computing allow large amounts of data to be collected and analyzed in real time. The integration of these technologies with fault diagnosis techniques helps to improve the efficiency and reliability of fault diagnosis systems. In [32], the authors examine the integration of algorithms with IoT systems to monitor and diagnose failures in solar PV panels. The method suggested can be used after adaptation in agent-based modeling for complex socio-economic processes coupled with high-performance computing (HPC) [33; 34; 35; 36; 37; 38; 39; 40]. Modern approaches to data classification tasks increasingly rely on machine learning methods [41; 42; 43; 44], particularly neural network architectures. However, the use of neural networks is associated with a number of limitations, the main of which being the need to form extensive training samples. These datasets are usually collected within a specific subject area, which complicates the process of adapting the model to new applications and requires significant computational resources to retrain it. Other work in the application of wavelet transform for signal fault detection has a narrower and more specialized focus, particularly for electrical instrumentation applications [45; 46; 47]. The methods then aim to work for more specific electrical signals, which improves overall reliability and accuracy but is less applicable to general time series. The proposed method uses an alternative approach based on wavelet transform and numerical optimization techniques [48; 49; 50; 51]. The wavelet transform performs the task of localizing meaningful features in the input data, which allows for the efficient extraction of informative features. Unlike neural network methods, which require a complex training procedure, classification in our approach is based on mathematical models using libraries of basic reference signals. A key aspect of the proposed method is the application of the standard deviation metric (MSE) as a similarity criterion. This approach allows for comparing the input data with pre-formed libraries of failure (anomaly) patterns and performing classification without the need to pre-train the model on specialized samples. Thus, the flexibility of the method and its portability to different subject areas without significant adaptation costs are ensured. One of the important advantages of the proposed method is its modularity. This approach can be considered as service-oriented, which makes it possible to replace individual components of the system without disturbing its overall structure.