# Time Scale Control Using Dynamic GMDH Neural Network Forecasting Based on Real Measurement Data
## 1 Introduction
Furthermore, ensuring the best possible compliance provides a reliable source of measurement traceability in regard to the time and frequency domains for the UTC(k) scale, as well as the possibility of precise synchronization and independence from less reliable external sources. In recent years, neural networks, inspired by the human brain, have revolutionized many fields of science and engineering, from image and speech recognition to natural language processing. Their ability to learn complex relationships from data and adapt to changing conditions opens up new possibilities for intelligent control. In this context, the application of neural networks for the dynamic control or forecasting of the national time scale, UTC(k), has become a promising direction of research and development. The Polish Time Scale UTC(PL) is implemented by the Time and Length Department of the Central Office of Measures (GUM) in Warsaw, using the active hydrogen maser VCH-1003M. Until 2016, UTC(PL) forecasting was performed based on the aforementioned statistical method of linear regression. At the same time, research has been conducted at the Institute of Metrology, Electronics and Computer Science at the University of Zielona Gora (IMEI UZ) on the application of various types of neural networks to forecast the Polish Time Scale. The possibility of using neural networks for forecasting results from their properties. Neural networks are a very good mathematical tool to solve very complex non-linear problems [13]. The main goal of these research works was to obtain a better quality of UTC(PL) forecasting in relation to the previously used linear regression method [14,15,16]. The research results presented in these works, based on historical data, showed the possibility of achieving a significantly better quality of UTC(PL) forecasting using the GMDH (group method of data handling) neural network [17], in comparison to other methods that were compared using the same input data. The results of the research clearly showed that the GMDH neural network has the best forecasting properties [18]. GMDH neural networks are an innovative category of self-organizing networks. Their key feature is the use of the group method of data handling, which is widely used in various areas, such as data acquisition, prediction, the modelling of complex systems, and process optimization [17]. They have the ability to automatically optimize the networks during the training process. This includes the precise adjustment of the number of hidden layers and the number of neurons in each of these layers. The activation functions that drive the neurons in these networks most often take the form of polynomials, which allows for the effective modelling of non-linear dependencies in the data. In addition, the good forecasting properties of the GMDH-type neural networks enable the quick adaptation of these neural networks to the nature of the data used as input. As a result of the conducted research work, a procedure for forecasting the national UTC(k) time scale has been developed using a GMDH-type neural network [19]. First, the correctness of the developed procedure has been verified for time scales implemented based on commercial caesium atomic clocks, hydrogen masers, and hydrogen masers supervised by the primary frequency standard in the form of a caesium fountain [20,21]. The research results presented in the cited publications showed that the developed procedure is universal and enables the achievement of very good quality UTC(PL) forecasting [22], as well as other national UTC(k) time scales. This has resulted in a forecasting procedure based on a GMDH-type neural network being used to control the Polish Time Scale UTC(PL) by the Time and Length Department of the Central Office of Measures, since 2016, which enables the dynamic forecasting of the UTC(PL) based on real measurement data.