# Comparing Polynomials and Neural Network to Modelling Injection Dosages in Modern CI Engines
Injection delay is the time from the moment the fuel injector is actuated to the moment the fuel is fed to the combustion chamber. This parameter is very important because too long times will result in incorrect engine operation. On average, in the injectors of the CR system, the fuel injection delay is 200-300 us at the pressure of 80 MPa. In the studies by [PERSON] et al. [4] the operating parameters of an electromagnetic and piezoelectric fuel injector were compared. Both injectors were mounted on the same CI engine and its emission of pollutants into the atmosphere and fuel consumption were examined. The differences between the operation of the engine on electromagnetic and piezoelectric fuel injectors are minimal. An important difference between electromagnetic and piezoelectric fuel injectors is their production costs. One of the causes of knocking combustion in the engine is deficiency in the fuel injector. The authors in Taghizadeh--Alisaraei et al. [5] presented a method of diagnosing fuel injectors by reading the vibrations that occur in damaged components. The analysis showed that the damaged elements emit greater vibrations during operation, which affects the size of injection doses. Similar studies were presented by the authors of [PERSON] et al. [6]. Four fuel injectors were subjected to the analysis. The damaged ones caused a pressure drop in the system due to the higher value of the overflow and additional vibrations. [PERSON] et al. [7] developed an optical method for diagnosing fuel injectors used in marine CI engines. The method consists in analyzing the quality parameters of the fuel stream. The analysis of the shape of the injected fuel stream may help to assess the technical condition of the atomizer. Assessment of the condition of individual components can be performed using neural network algorithms. In the study by [PERSON] [8], an algorithm to calculate the mass of air supplied in a turbocharged engine was developed. The analysis of the test results and calculations has shown that it is possible to apply the above solution in estimating the amount of air supplied to the CI engine. The article by [PERSON] et al. [9] presented the possibilities of using linear regression and neural network in order to model the operating characteristics of the engine and the emission of toxic substances in exhaust gases. The engine was powered by standard diesel and various types of biofuel. The analysis of the test results showed that the very accurate mapping of the measurements was made with the use of a neural network. In the Matlab environment, using the Neural Network Toolbox add-on, a neural network which tested the operation of the engine was implemented, [PERSON] et al. [10]. Based on parameters such as engine speed, intake air temperature, boost pressure, exhaust gas temperature, engine coolant temperature and fuel consumption, it has been trained for turbocharger diagnostics. The Levenberg-Marquardt algorithm with a square error value of 0.001 was used in the network. The same algorithm was used in the works [11; 12; 13] to implement neural networks. The research carried out in the work of [PERSON] [14; 15] describes the possibilities of using statistical methods in a spreadsheet in order to forecast the fuel injector injection doses. When analyzing the results of the conducted experiment, it can be concluded that the use of simple calculation methods and a spreadsheet is inaccurate and limits the number of input variables. The authors of the work [16] used a neural network to estimate the vibration of the engine powered by sunflower oil mixtures. The proposed algorithm was compared with the measurement results and a very high degree of matching was obtained. Also in [17], a model of a neural network was used to determine the vibration for engine diagnostics and compared with the measurement results. The results of the analysis showed a high degree of alignment of the algorithm with the values obtained during the measurements.