The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.
Doubly stochastic point processes driven by non-Gaussian Ornstein-Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.
In this paper we attempt to form a neural network to code nonlinear iterated function system. Our approach to this problem consists of finding an error function which will be minimized when the network coded attractor is equal to the desired attractor. First, we start with a given iterated function system attractor, with a random set of weights of the network. Second, we compare the consequent images using this neural network with the original image. On the basis of the result of this comparison, we can update the weight functions and the code of the nonlinear iterated function system (NLIFS). A common metric or error function used to compare between the two image fractal attractors is the Hausdorff distance. The error function gives us good means to measurement the difference between the two images.
This work is focused on determninig a nonlinear output error (OE) model, i.e., a dynamic system, by training a two layer neural network with a Levenberg-Marquardt method. Selected as a case study is application of a dynamic model to predict cutting force in machining processes. A model crated by using Artificial Neural Networks (ANN), able to predict the process output, is introduced in order to deal with the characteristics of such an ill-defined process. This model describes the dynamic response of the output before the changes in the process input command (feed rateú and the process parameters (depth of cut). The model provides a sufficiently accurate predition of cutting foce, since the process-dependent specific dynamic properties are adequately reflected.
This paper deals with neural-predictive algorithm for some nonlinear
processes in the industry. Neural model predictive control (NMPC) uses artificial neural networks (ANN) for modeling the process and for configuration of the optimizer. The optimizer sets up on-line controller parameters by predicting next control action signals. Depending on the number of prediction steps, the optimizer can predict the process behavior in the future. Therefore this type of predictive control is very useful for the control of the highly nonlinear processes, which are known for their various behaviors. One practical example is the isothermal polymerization reactor where the NMPC Controls the oiitput variable very robustly. Finally, this control method is compared with the linear PID controller designed to solve this problém using a genetic algorithm.
This paper presented 2D numerical linear and nonlinear site response analyses based on the scaled boundary finite-element method (SBFEM) and compared their results with those of the DEEPSOIL software. In linear time-domain analysis, the seismic boundary traction was applied to lines in the near-field with the same vertical coordinates using seismic time history load. The far-field was modeled utilizing an improved continued-fraction-based high-order transmitting boundary. The constitutive relationship of the boundary was determined utilizing the SBFEM equation in the dynamic stiffness model. It was shown that the results of the SBFEM had a good agreement with those obtained from the DEEPSOIL software. The results of spectral acceleration demonstrated period lengthening. The nonlinear site responses were analyzed using both the DEEPSOIL software and the coupling of SBFEM/FEM. The one-dimensional nonlinear site response was analyzed using the tools in the DEEPSOIL software including the strength correction, pressure-dependent modulus reduction, and the damping ratio curve of sand. In the nonlinear-coupled analysis, the bounded domain was also modeled in OpenSees using a pressure-dependent multi-yield plasticity soil model. The comparison of the results demonstrated the accuracy of the nonlinear analysis using the coupled SBFEM/FEM. The coupling method underestimated spectral acceleration in low periods compared with the DEEPSOIL software. The absolute residual was also obtained less than 0.2.
The paper deals with a filter design for nonlinear continuous stochastic systems with discrete-time measurements. The general recursive solution is given by the Fokker-Planck equation (FPE) and by the Bayesian rule. The stress is laid on the computation of the predictive conditional probability density function from the FPE. The solution of the FPE and its integration into the estimation algorithm is the cornerstone for the whole recursive computation. A new usable numerical scheme for the FPE is designed. In the scheme, the separation technique based on the upwind volume method and the finite difference method for hyperbolic and parabolic part of the FPE is used. It is supposed that separation of the FPE and choice of a suitable numerical method for each part can achieve better estimation quality comparing to application of a single numerical method to the unseparated FPE. The approach is illustrated in some numerical examples.
In this paper, the problem of nonlinear viscoelastic rectangular thin plate subjected to tangential follower force is examined. The nonlinear strain-displacement relation is used to express non-linearity. After obtaining the equilibrium equation of the system in Laplace domain and performing the Laplace inverse transformation, the nonlinear differential equation of plate constituted by Kelvin-Voigt model and subjected to tangential follower force in time domain is obtained. Multi-scales method is firstly used to solve the governing equation, and the influence of the initial amplitude on the nonlinear frequency ratio is studied. Secondly, the differential quadrature method (DQM) is employed to confirm the obtained results. and Obsahuje seznam literatury