Application of the nonlinear H∞ identification method to identify a synchronous generator model is investigated in this paper. The linear H∞ identification method has been well established in the literature for robust modeling despite noise and system uncertainties. Since many practical systems such as synchronous generators are nonlinear, linear models identified for particular operating conditions do not perform well for other operating conditions. To overcome this shortcoming, the linear H∞ identification method has been modified to cover some nonlinearities of the systems such as saturation in synchronous machines. The derived proposed algorithm is then applied to a seventh order nonlinear model of a synchronous machine with saturation effect. In this study, the field voltage is considered as the input and the active output power and the terminal voltage are considered as the outputs of the synchronous machine. Simulation results show good accuracy of the identified models.

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by Non-standard finite difference (NSFD) method. ANSFD model has been constructed for the biochemical reaction problem and numerical experiments are performed for different values of discretization parameter ‘ h’ . The results are compared with the well– known numerical scheme, i. e. RK4. Unlike RK4 which fails for large time steps, the developed scheme NSFD gives results that converge to true steady states for any time step used.

This paper deals with forecasting the tax revenues of legal entities in Iran. For this purpose, the structural natures of time series of tax revenues for Iranian legal entities are detected. Based on the separation among the resources (government and NGOs), the linearity, nonlinearity, chaotic, and random behaviors are diagnosed via the Lyapunov exponential analysis. Using Box-Jenkins and Neural Networks models with different numbers of input, output, hidden layers, learning algorithm, learning rate and etc., the performance of each model are evaluated during the years of 1381-1387. Finally, the optimal forecasting model is proposed as a multi input- multi output neural network structure with a novel algorithm. The performance of the proposed structure is evaluated during the years of 1388-1393 in the forecasting process.

This study aims to model the nonlinear dynamics of unemployment in the Iranian economy and identify the most robust determinants using Bayesian, dynamic, and selective model averaging approaches. The research is applied in nature, covering the period 1992–2021. Fifty potential determinants of unemployment were identified across ten social, economic, political, and financial domains. Bayesian Model Averaging (BMA), Dynamic Model Averaging (DMA), and Weighted Least Squares (WALS) techniques were employed to estimate the models. Based on predictive accuracy and error measures, the Bayesian model exhibited superior performance. Posterior probabilities and coefficients were calculated to determine non-fragile variables influencing unemployment. The analysis revealed 24 key variables significantly affecting unemployment, grouped into ten categories: social indicators (urbanization, poverty, human capital); real economic factors (service value-added, business environment index, Gini coefficient, capital formation, economic growth); nominal economic indicators (consumer inflation, oil revenues); openness indicators (KOF globalization index); labor market features (labor productivity, real wages, structural change index); fiscal policy (total taxes, public development expenditures); monetary policy (exchange rate, interest rate, liquidity); political factors (sanctions, privatization); financial development indicators (private sector credit share); and capital structure indices (banking sector and capital market development). Unemployment in Iran is driven by a complex interaction of structural, financial, monetary, and institutional variables. Policy interventions focused on strengthening financial systems, enhancing human capital, and improving institutional efficiency can effectively reduce unemployment and foster sustainable economic stability.

This article deals with dynamic modeling and nonlinear optimal control of an aerial vehicle taken into account nonlinear modeling of its thruster engine. To do this, nonlinear flight dynamic equations of the aerial vehicle are derived considering nonlinear equations of the thruster engine. A relation between the thrusting force and the fuel consumption of the air-breathing engine is stated and coupled with the nonlinear dynamic equations of the vehicle. Presenting the formulation of the state-dependent nonlinear optimal control, the nonlinear dynamic relations of the aerial vehicle are considered as constraint equations of the optimal control and a cost function including state and input variables is defined. Then, the Hamiltonian function of the optimal control problem is formed and optimality equations obtained. By numerical solving of the problem, various parameters like as the path angle, uncertainties, attack angle and weighting coefficients of the optimal control are considered and several simulations are presented. The results show that increasing the attack angle leads to increasing of the control time and effort of the system. Also, changing the weighting coefficients lead to various optimal paths as increasing the input weighting coefficient decreases the fuel consumption. It is seen by changing the uncertainty parameter of the model, transient response is changed but finally the optimal control method is able to track the desired path. Furthermore, by changing initial conditions and parameters, the nonlinear optimal control of the system is effectively performed which indicates the priority of the proposed method

The commonly used linear k-e turbulence model is shown to be incapable of accurate prediction of turbulent flows, where non-isotropy is dominant. Two examples of non-isotropic flows, which have a wide range of applications in marine waters, are saline water flow and the stratified flows due to temperature gradients. These relate to stratification and consequently, variation of density through vertical layers. In this paper, a nonlinear k-e turbulence model, firstly presented by Speziale (1987) and was implemented in the existing hydrodynamic model. The energy equation has been also added and solved in the hydrodynamic model. The hydrodynamic model solves the fully nonlinear Navier-Stokes equations based on an ALE (Arbitrary Lagrangian Eulerian) description. The model is an extension to WISE (Width Integrated Stratified Environments) 2DV numerical model, originally developed by Hejazi (2002). The simulated values have been compared with the experimental data and have shown acceptable agreements. The predictions are also compared with the results of the original model employing a standard buoyant k-e turbulence model, which showed the advantage of the new turbulence model in prediction of non-isotropic flows.

In this paper, a nonlinear tire model based on the elliptic concept and tire Calspan data has been developed. The effect of cornering force and aligning moment as a function of slip and camber (inclination) angles. Normal load, tire adhesion characteristics and skid number are studied. Furthermore in this model, the rolling resistant effect has been considered. Through this simple tire model, the tire behavior as well as the experimental results is represented.

In this paper, dynamic modeling of flexible links manipulators is discussed. The modeling approach is based on the Lagrange equations and finite element discretization method. In order to obtain the closed form of dynamic equations for flexible links manipulators, symbolic calculation in MATLAB's symbolic mathematics toolbox is utilized, then the non-linear dynamic equations of a single-link manipulator have been obtained and compared with the results presented in other references. In this study, the nonlinear effects of centrifugal, Coriolis and gravity are Also considered which is rarely studied in other contributions. Then the equations of motion are solved by the Runge-Kutta method for different levels of excitation torque. The simulation results show that at low levels of excitation torque, the linear and non-linear models have the same results, while with the increase of the excitation level, the difference between the linear and non-linear models is considerable and the size of the elastic components in the non-linear model becomes smaller.

Complex nonlinear unloading behavior following plastic deformation on metals has been observed by researchers. However, a constant chord modulus has been used by most of the researchers to describe the unloading behavior. In this study, a new hypoelastic model is proposed in order to describe this complex nonlinear behavior. The elastic modulus is assumed to be the initial Young’s modulus at the beginning of each loading reversal and is exponentially decreased with the elastic deformation and finally saturates to a particular value at the start of plastic deformation. The model can be easily utilized in any plasticity constitutive law. Furthermore, its numerical implementation is fairly straightforward. As an example, a simple constitutive law was developed using the von-Mises yield function, isotropic hardening law and the proposed hypoelastic model. This constitutive law was implemented into ABAQUS commercial package via a user material subroutine UMAT. A comparison between the experimental response of DP980 and its simulated response showed that the model is able to describe the material response fairly well.

This paper presents a nonlinear analytical model for silicon micromechanical ring resonators with bulk-mode vibrations. A distributed element model has been developed to describe the dynamic behavior of the micromechanical ring resonator. This model shows the nonlinear effects in a silicon ring resonator focusing on the effect of large amplitudes around the resonance frequency, material and electrical nonlinearities. Through the combination of geometrical and material nonlinearities, closed-form expressions for thirdorder nonlinearity in mechanical stiffness of bulk-mode ring resonators are obtained. Using the perturbation method and the method of harmonic balance, the expressions for describing the effect of nonlinearities on the resonance frequency and stability are derived.The results, which show the effect of varying the AC-drive voltage, initial gap spacing, DC-bias voltage and the quality factor on the frequency response and resonant frequencies, are discussed in detail. The nonlinear model introduces an appropriate method in the field of bulk-mode ring resonator design for achieving sufficient power handling and low motional resistance.