PULSE METHOD FOR DETERMINATION OF TIME PARAMETERS THERMAL FIRE DETECTOR

For thermal fire detectors with a thermoresistive sensitive element, the method of determining its time parameters is justified. The time parameters of operation and the time constant of the thermal fire detector are considered as time parameters. The method is based on the use of the Joule-Lenz effect, for the implementation of which single pulses of electric current are passed through the thermoresistive sensitive element of the fire detector. Pulses having the shape of a quarter sinusoid or a quarter cosinusoid are used as such test signals. Using the Laplace integral transformation, analytical expressions are obtained, which represent the formalization of the reaction of the thermoresistive sensitive element of the fire detector to the corresponding test signals. These analytical expressions are used to obtain the functional dependences of the fire detector time constants on the pulse duration of the electric current and the auxiliary parameter. The auxiliary parameter is the ratio of the values ​​of the output signal of the thermal fire detector at two fixed points in time. This choice of auxiliary parameter allows to ensure invariance with respect to the transfer coefficient of the thermal fire detector with a thermoresistive sensing element. The fixed moments of time are chosen to be equal to half and three quarters of the duration of the pulses of electric current flowing through the thermoresistive sensitive element of the fire detector. The time of operation of the thermal fire detector is determined in the form of two additive components, one of which is a time constant of the fire detector, and the other is determined by the values ​​of normalized parameters in accordance with existing regulations. A sequence of procedures is given, which together represent a method of determining the time parameters of thermal fire detectors of this type.

Numerical solution to the Falkner-Skan equation: a novel numerical approach through the new rational a-polynomials

The new rational a-polynomials are used to solve the Falkner-Skan equation. These polynomials are equipped with an auxiliary parameter. The approximated solution to the Falkner-Skan equation is obtained by the new rational a-polynomials with unknown coefficients. To find the unknown coefficients and the auxiliary parameter contained in the polynomials, the collocation method with Chebyshev-Gauss points is used. The numerical examples show the efficiency of this method.

THE ASYMPTOTICS OF A SOLUTION OF THE MULTIDIMENSIONAL HEAT EQUATION WITH UNBOUNDED INITIAL DATA

For the multidimensional heat equation, the long-time asymptotic approximation of the solution of the Cauchy problem is obtained in the case when the initial function grows at infinity and contains logarithms in its asymptotics. In addition to natural applications to processes of heat conduction and diffusion, the investigation of the asymptotic behavior of the solution of the problem under consideration is of interest for the asymptotic analysisof equations of parabolic type. The auxiliary parameter method plays a decisive role in the investigation.

An Adaptive Filter for Nonlinear Multi-Sensor Systems with Heavy-Tailed Noise

Aiming towards state estimation and information fusion for nonlinear systems with heavy-tailed measurement noise, a variational Bayesian Student’s t-based cubature information filter (VBST-CIF) is designed. Furthermore, a multi-sensor variational Bayesian Student’s t-based cubature information feedback fusion (VBST-CIFF) algorithm is also derived. In the proposed VBST-CIF, the spherical-radial cubature (SRC) rule is embedded into the variational Bayes (VB) method for a joint estimation of states and scale matrix, degree-of-freedom (DOF) parameter, as well as an auxiliary parameter in the nonlinear system with heavy-tailed noise. The designed VBST-CIF facilitates multi-sensor fusion, allowing to derive a VBST-CIFF algorithm based on multi-sensor information feedback fusion. The performance of the proposed algorithms is assessed in target tracking scenarios. Simulation results demonstrate that the proposed VBST-CIF/VBST-CIFF outperform the conventional cubature information filter (CIF) and cubature information feedback fusion (CIFF) algorithms.

EFFECT OF FRACTIONAL DERIVATIVE PROPERTIES ON THE PERIODIC SOLUTION OF THE NONLINEAR OSCILLATIONS

A periodic solution of the time-fractional nonlinear oscillator is derived based on the Riemann–Liouville definition of the fractional derivative. In this approach, the particular integral to the fractional perturbed equation is found out. An enhanced perturbation method is developed to study the forced nonlinear Duffing oscillator. The modified homotopy equation with two expanded parameters and an additional auxiliary parameter is applied in this proposal. The basic idea of the enhanced method is to apply the annihilator operator to construct a simplified equation freeness of the periodic force. This method makes the solution process for the forced problem much simpler. The resulting equation is valid for studying all types of possible resonance states. The outcome shows that this alteration method overcomes all shortcomings of the perturbation method and leads to obtain a periodic solution.

Neuro-fuzzy iterative learning control for 4-poster test rig

In this paper, a new control method is presented for the 4-poster test systems. The primary aim of the paper is to improve the convergence speed and decrease the error rate for model-based iterative learning control (ILC), a widely used method as a tracking control. First, the dynamic equations of the system are generated, and the control problem is formulated. Then, an inverse model of the system is established directly through the adaptive neuro-fuzzy inference system (ANFIS) with auxiliary parameter (piston position) as a serial combination of two sub-models. In order to construct a neuro-fuzzy ILC (NFILC) structure, these sub-models are integrated into the neuro-fuzzy inverse controller (NFIC). Because of this new structure, the modified ILC rule has two layers. In the first layer, the controlled parameter, namely, the acceleration is iterated, whereas, in the second layer, the auxiliary parameter is iterated. The outcomes of the proposed control method are scrutinized by testing through a numerical simulation. Finally, it is demonstrated that the modified ILC rule dramatically increase the convergence speed and reduce the final error rate.

Variational Iteration Algorithm-I with an Auxiliary Parameter for Solving Boundary Value Problems

In this article, the variational iteration algorithm-I with an auxiliary parameter (VIA-I with AP) is elaborated to initial and boundary value problems. The effectiveness, absence of difficulty and accuracy of the proposed method is remarkable and its tractability is well suitable for the use of these type of problems. Some examples have been given to show the effectiveness and utilization of this technique. A comparison of variational iteration algorithm-I (VIA-I) along VIA-I with AP has been carried out. It can be seen that this technique is more appropriate than as VIA-I.

Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems

In this article, variational iteration algorithm I with an auxiliary parameter is used for simple and damped mass–spring systems that undergo forced vibrations and transverse vibration of uniform and variable beams with simply supported analytical treatment. In addition, common vibration problems are classified and the values of Lagrange multipliers are identified for each type of problem. Examples are given at the end, which shows that this modification demonstrated the high efficiency and attained very good agreement in illustrated models and might be promptly reached out to other nonlinear differential and partial differential equations.

Solitons for the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid via the Pfaffian technique

Fluids are common in nature, the study of which helps the design of the related industries. Under investigation in this letter is the (2[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid. Pfaffian solutions have been obtained based on the Pfaffian technique with the assistance of the real auxiliary function [Formula: see text]. N-soliton solutions with [Formula: see text] are constructed, where y is the scaled space coordinate and [Formula: see text] is the steady stream function in the irrotational incompressible flow. Background shapes of the solutions are affected by [Formula: see text], but the structures of the solutions are affected by the derivative of the log terms in the solutions. Neighborhoods at the origins of the solitons are different in consequence of the different values of the real auxiliary parameter a. One- and two-soliton solutions are illustrated, which are the superpositions of the two kink solitons and different forms of [Formula: see text]. Interactions of the two solitons are presented, from which we see that the velocities, amplitudes and shapes of the two solitons remain unchanged before and after each interaction.