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In this work, a three layer feed-forward artificial neural network, with 24 neurons, was constructed to estimate the viscosities of a wide range of ionic liquid families, including those based on the imidazolium, ammonium, pyridinium, pyrrolidinium, phosphonium, and isoquinolinium cations, together with various anions, as well as varying lengths of alkyl side-chain lengths. The model is a function of the molecular weight and structure of the ionic liquid, and the system conditions of temperature and pressure. It covers a temperature range of (273.15 to 393.15) K and a pressure range of (0.1 to 150) MPa. Results indicated the estimated values of viscosities of pure ionic liquids to be in good agreement with the experimental data. The training (correlating) and validation coefficients (R) were 1.00000 and 0.99955, respectively, while the training and validation performances (MSE) on the training and validation datasets were 4.36 × 10 − 8 , and 1.63 × 10 − 6 , respectively. The average absolute error value on the test dataset was 1.310%.

In this study, a feed-forward artificial neural network, with three layers and seventeen neurons, was constructed to estimate the densities of a wide range of ionic liquid families including those based on the imidazolium, ammonium, pyridinium, pyrrolidinium, and isoquinolinium cations, together with various anions, as well as varying lengths of alkyl side chain lengths. The model is a function of the molecular weight and structure of the ionic liquid, and the system condition of temperature and pressure, which covers a temperature range of (273.15 to 393.17) K and a pressure range of (0.1 to 100) MPa. Therefore, no additional experimental data on the ionic liquid is required as input parameter(s), which makes this technique quite versatile. It was observed that the estimated values of densities of pure ionic liquids have very good agreement with the experimental data. The training correlating coefficient ( R ), the training performance (MSE), and the average absolute error on the training dataset were 0.99997, 6.04 × 10 −6 , and 0.019%, respectively. The average absolute error value on the test dataset is 0.014%.

A feed-forward neural network was constructed and tested to estimate the viscosities of binary mixtures of five different types of ionic liquids with various polar and non-polar solvents within a range of temperatures. The ionic liquids investigated had various anions and consisted of either the imidazolium, ammonium, pyridinium, pyrrolidinium, or isoquinolinium cations, with various cation alkyl side-chains. Together, a total of 1996 experimental data were collected from previously published literature and divided randomly into three different datasets: 1775 data points making up the training and validation datasets, and 221 data points selected as a test dataset. The molecular weight and group structure of the ionic liquid, the molecular weight and reduced boiling temperature of the solvent, and the molar composition, temperature, and pressure of the system were selected as the independent input variables. Results indicated that the network structure presented in this study is capable to estimate the viscosity of such nonideal binary mixtures, consisting of a range of ionic liquids and solvents, with an average relative error of 0.6%.

Extraction of random behavior of dynamic systems under the influence of the uncertainty associated with modeling error is a major challenge. In the present study, Random Matrix Theory (RMT) is applied to simulate this type of uncertainty in rotor shafts of high-speed rotordynamic systems. For this purpose, simulation of a random matrix is carried out based on the nonparametric approach followed by the determination of the mean model and dispersion parameters. The mean model is determined by extracting the mechanical and dimensional parameters of 15 rotor shaft samples via exact dimensional measurements and Experimental Modal Analysis (EMA). In this study, presenting the Difference Measure (DM) value, the dispersion parameters of the mass and stiffness of the rotor shafts are exploited. In this research, by minimizing the DM value as an objective function, domain variations and probability density distribution of the uncertain response (rotor shaft natural frequencies in this paper) obtained from the EMA and RMT are coincided simultaneously. The simulation process of a random matrix is fulfilled using the direct Monte Carlo simulation and minimization of the DM parameter is performed using Bee’s Algorithm (BA). It is demonstrated that this swarm intelligence-based algorithm provides an approach to extract optimal and accurate dispersion parameters in RMT implementation. The results show that the calculated dispersion parameters are in good agreement with the experimental data and the BA-based method is effective.