Summary
It is significant to fit a Gaussian function with the observation data for artificial intelligence or other engineering fields. Considering the influence of noises, this article proposes a ...nonlinear optimization method for fitting the Gaussian activation functions. By means of the gradient search and the Newton search, a direct gradient‐based iterative algorithm and a direct Newton iterative algorithm are presented for identifying the Gaussian functions. Considering the computational cost, the authors develop a multi‐innovation stochastic gradient algorithm for the noisy Gaussian functions. After introducing a forgetting factor, the parameter estimation accuracy can be further improved. The simulation results indicate that the proposed nonlinear optimization method and gradient‐based algorithms can fit the noisy Gaussian functions very well.
In this paper, we consider the parameter estimation problem of dual-frequency signals disturbed by stochastic noise. The signal model is a highly nonlinear function with respect to the frequencies ...and phases, and the gradient method cannot obtain the accurate parameter estimates. Based on the Newton search, we derive an iterative algorithm for estimating all parameters, including the unknown amplitudes, frequencies, and phases. Furthermore, by using the parameter decomposition, a hierarchical least squares and gradient-based iterative algorithm is proposed for improving the computational efficiency. A gradient-based iterative algorithm is given for comparisons. The numerical examples are provided to demonstrate the validity of the proposed algorithms.
This paper studies the problem of parameter estimation for the multifrequency sine signals, which have multiple characteristic parameters such as the amplitudes, phases, and frequencies. It is noted ...that the signal output is nonlinear with respect to the phase and frequency parameters while it is linear with respect to the amplitude parameters. This feature inspires us to separate all of the characteristic parameters into a linear parameter set and a nonlinear parameter set, where the linear set is composed of the amplitude parameters and the nonlinear set is composed of the phase parameters and the frequency parameters. After the parameter separation, two identification submodels are constructed for optimizing the linear parameter set and the nonlinear parameter set. Then the nonlinear identification model becomes a linear identification submodel and a nonlinear identification submodel. Therefore, the nonlinear optimization for minimizing the objective function is converted into the combination of the quadratic optimization and nonlinear optimization. Based on the separable identification submodels, a recursive least squares subalgorithm and a recursive gradient subalgorithm are proposed for identifying the linear parameters and nonlinear parameters, respectively. Moreover, an interactive estimation algorithm is designed to remove the related parameter sets between the subalgorithms and a hierarchical identification method is presented by combining the subalgorithms. For the purpose of tracking the time‐varying, a forgetting factor is introduced to improve the convergence speed. The numerical examples are provided to qualify the performance of the proposed method based on some performance measures.
This paper studies the problem of parameter estimation for frequency response signals. For a linear system, the frequency response is a sine signal with the same frequency as the input sine signal. ...When a multi-frequency sine signal is applied to a system, the system response also is a multi-frequency sine signal. The signal modeling for multi-frequency sine signals is very difficult due to the highly nonlinear relations between the characteristic parameters and the model output. In order to obtain the parameter estimates of the multi-frequency sine signal, the signal modeling methods based on statistical identification are proposed by means of the dynamical window discrete measured data. By constructing a criterion function with respect to the model parameters to be estimated, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition. Moreover, the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm. The simulation results show the effectiveness of the proposed methods.
Synapse coupling can benefit signal exchange between neurons and information encoding for neurons, and the collective behaviors such as synchronization and pattern selection in neuronal network are ...often discussed under chemical or electric synapse coupling. Electromagnetic induction is considered at molecular level when ion currents flow across the membrane and the ion concentration is fluctuated. Magnetic flux describes the effect of time-varying electromagnetic field, and memristor bridges the membrane potential and magnetic flux according to the dimensionalization requirement. Indeed, field coupling can contribute to the signal exchange between neurons by triggering superposition of electric field when synapse coupling is not available. A chain network is designed to investigate the modulation of field coupling on the collective behaviors in neuronal network connected by electric synapse between adjacent neurons. In the chain network, the contribution of field coupling from each neuron is described by introducing appropriate weight dependent on the position distance between two neurons. Statistical factor of synchronization is calculated by changing the external stimulus and weight of field coupling. It is found that the synchronization degree is dependent on the coupling intensity and weight, the synchronization, pattern selection of network connected with gap junction can be modulated by field coupling.
This paper investigates the recursive parameter and state estimation algorithms for a special class of nonlinear systems (i.e., bilinear state space systems). A state observer-based stochastic ...gradient (O-SG) algorithm is presented for the bilinear state space systems by using the gradient search. In order to improve the parameter estimation accuracy and the convergence rate of the O-SG algorithm, a state observer-based multi-innovation stochastic gradient algorithm and a state observer-based recursive least squares identification algorithm are derived by means of the multi-innovation theory. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms.
The presence of heavy metals in the industrial effluents has recently been a challenging issue for human health. Efficient removal of heavy metal ions from environment is one of the most important ...issues from biological and environmental point of view, and many studies have been devoted to investigate the environmental behavior of nanoscale zerovalent iron (NZVI) for the removal of toxic heavy metal ions, present both in the surface and underground wastewater. The aim of this review is to show the excellent removal capacity and environmental remediation of NZVI-based materials for various heavy metal ions. A new look on NZVI-based materials (e.g., modified or matrix-supported NZVI materials) and possible interaction mechanism (e.g., adsorption, reduction and oxidation) and the latest environmental application. The effects of various environmental conditions (e.g., pH, temperature, coexisting oxy-anions and cations) and potential problems for the removal of heavy metal ions on NZVI-based materials with the DFT theoretical calculations and EXAFS technology are discussed. Research shows that NZVI-based materials have satisfactory removal capacities for heavy metal ions and play an important role in the environmental pollution cleanup. Possible improvement of NZVI-based materials and potential areas for future applications in environment remediation are also proposed.
In this paper, we develop and study a stochastic predator–prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic ...Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.
Heat transportation advancement in liquid is a crucial work which can be easily obtained via utilization of hybrid nanoparticles. Therefore, main concern of the current article is to address the ...entropy aspects in Dracy-Forchheimer flow of hybrid nanomaterials (kerosene oil, SWCNT and MWCNT). The novel features of Xue's which is modified and implemented for flow physical empirical relations (thermal conductivity, density and specific heat). Furthermore, entropy concept is utilized to estimate the frame of analysis disorderness. The transformed expressions have been computed through numerical scheme after conversion to ODEs by dimensionless variables. Graphical illustrations and tables are made to investigate the effects of noteworthy embedding variables on various distributions. Moreover, detailed analysis for temperature and velocity gradients against pertinent parameters at the surface is provided. Obtained findings reflect that temperature upgraded for both nanoliquid and hybrid nanoliquid by rising Eckert number and heat source parameter, whereas an opposite features is pointed out for gradient of temperature. It is also perceived that skin friction escalates for inertia coefficient, rotation parameter and porosity parameter. There is remarkable increase for SWCNT-MWCNT/kerosene oil hybrid nanofluid when compared with SWCNT/kerosene oil nanoliquid. Overall, hybrid nano phase has an incredible effect in comparison to nanomaterials.
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