Class Of Nonlinear Models Research Articles

A New Fractional Gradient Representation of Birkhoff Systems

A fractional generalization of the gradient system to the Birkhoff mechanics, that is, a new fractional gradient representation of the Birkhoff system is investigated, in this paper. The definitions of the fractional gradient system are generalized to Birkhoff mechanics. Based on the definition, a general condition that a Birkhoff system can be a fractional gradient system is derived, the former studies for fractional gradient representation of the Birkhoff system are special cases of this paper. As applications of the results, the Birkhoff equations and fractional gradient expression of several classical nonlinear models are derived, such as the Hénon–Heiles equation, the Duffing oscillator model, and the Hojman–Urrutia equations. The results indicate, different from the former studies, that only gave the second-order gradient (integer order) expression for the Birkhoff system, an arbitrary fractional order gradient representation, exists for the Birkhoff system. The fractional potential function obtained from the general condition can determine the stationary states of these models in Birkhoffian expression.

Modeling, Control, and Simulation of a 3-Degrees of Freedom Mechanism Actuated by Pneumatic Artificial Muscles for Upper Limb Prosthesis Application

Abstract This work reports advances in enabling the use of pneumatic artificial muscles (PAM) as an alternative to electromechanical actuators in upper-limb prostheses to take advantage of their low weight, clean, renewable energy source, and force compliance, which is especially suitable for interactions between machines and humans. It describes the model, simulation, and control of a 3-degrees of freedom (DOF) mechanism representing a prosthetic finger using PAM actuators. Its main contribution is the combination and expansion of classic nonlinear models and control methods for robotic systems to allow PAM actuators in the intended application, especially regarding transient effects in the generation of PAM forces. The effectiveness of the proposed mechanism and its associated controller is verified through both numeric simulations and experimental results.

Forecasting tourism growth with State-Dependent Models

We introduce two forecasting methods based on a general class of non-linear models called ‘State-Dependent Models’ (SDMs) for tourism demand forecasting. Using a Monte Carlo simulation which generated data from linear and non-linear models, we evidence how estimations from SDMs can capture the level shifts pattern and nonlinearity in data. Next, we apply two new forecasting methods based on SDMs to forecast tourism demand growth in Japan. The forecasts are compared with classical recursive SDM forecasting, Naïve forecasting, ARIMA, Exponential Smoothing, Neural Network models, Time varying parameters, Smooth Transition Autoregressive models, and with a linear regression model with two dummy variables. We find that improvements in forecasting with the proposed SDM-based forecasting methods are more pronounced in the longer-term horizons.

Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1<d<2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t−1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model.

Input/output reduced model of a damped nonlinear beam based on Volterra series and modal decomposition with convergence results

This paper addresses the model reduction and the simulation of a damped Euler–Bernoulli–von Kármán pinned beam excited by a distributed force. This nonlinear problem is formulated as a PDE and reformulated as a well-posed state-space system. The model order reduction and simulation are derived by combining two approaches: a Volterra series expansion and truncation and a pseudo-modal truncation defined from the eigenbasis of the linearized problem. The interest of this approach lies in the large class of input waveshapes that can be considered and in the simplicity of the simulation structure. This structure only involves cascades of finite-dimensional decoupled linear systems and multilinear functions. Closed-form bounds depending on the model coefficients and the truncation orders are provided for the Volterra convergence domain and the approximation error. These theoretical results are generalized to a large class of nonlinear models, and refinement of bounds are also proposed for a large sub-class. Numerical experiments confirm that the beam model is well approximated by the very first Volterra terms inside the convergence domain.

Comparative Analysis of Nonlinear Viscoelastic Models Across Common Biomechanical Experiments

Biomechanical modeling has a wide range of applications in the medical field, including in diagnosis, treatment planning and tissue engineering. The key to these predictive models are appropriate constitutive equations that can capture the stress-strain response of materials. While most applications rely on hyperelastic formulations, experimental evidence of viscoelastic responses in tissues and new numerical techniques has spurred the development of new viscoelastic models. Classical as well as fractional viscoelastic formulations have been proposed, but it is often difficult from the practitioner perspective to identify appropriate model forms. In this study, a systematic examination of classical and fractional nonlinear isotropic viscoelastic models is presented (consider six primary forms). Consideration is given for common testing paradigms, including varying strain or stress loading and dynamic conditions. Models are evaluated across model parameter spaces to assess the range of behaviors exhibited in these different forms across all tests. Similarity metrics are introduced to compare thousands of models, with exemplars for each type of model presented to illustrate the response and behavior of different model variants. The parameter analysis does not only identify how the models can be tailored, but also informs on the model complexity and fidelity. These results illustrate where these common models yield physical and non-physical behavior across a wide range of tests, and provide key insights for deciding on the appropriate viscoelastic modeling formulations.

Optimization of infrastructure projects parameters in the program

The object of research is infrastructure projects as part of the program. The products of infrastructure projects are various infrastructural objects that together provide a certain value for stakeholders, for example, a certain bandwidth of the transport network or the capacity of a port, channel, etc. Identification of the parameters of project products is carried out at the stage of program development. For most projects, these parameters allow for variability within certain limits. The interconnection of infrastructure projects is determined not only by general financing and management, but, above all, by the consistency of the properties of goods. Therefore, the optimization of the parameters of the products of such projects is carried out integrally, within a single model. Coordination of the parameters of the products of infrastructure projects as part of the program requires formalized methods that allow them to be optimized taking into account both local constraints for each project and the global conditions for implementing the program. As a result of the study, a concept has been formed and an appropriate model has been developed, which allows setting the optimal parameters of the products of infrastructure projects as part of the program. Modeling is based on the ability to vary the parameters of project products and their relationship with the characteristics of projects and the program as a whole, such as value, costs, and the magnitude of risks. Since the program and the projects included in it can be of a non-commercial nature, therefore, the main criterion of optimality for the parameters of the products of projects and programs is a universal category – value, and it is considered for all stakeholders. The use of this model in the development of the program and the infrastructure projects included in it ensures the optimization of the required result while meeting certain requirements and limiting conditions. The model belongs to the class of nonlinear models and is developed for a situation where a so-called «main» project (or their combination) can be distinguished, which form(s) the requirements for the products of other projects interconnected with it, which is typical for infrastructure programs.

R kullanarak Mars Veri Madenciliği Algoritması ile Yumurta Ağırlığı Tahmini

Internal and external quality characters of poultry eggs are quitely important to determine egg weight. Also, the quality of eggs is important for both hatching and egg production. The purpose of this study was modelling of egg weight with the MARS (Multivariate Adaptive Regression Splines) method using inner and outsider quality characters of egg in Lohmann LSL Classic white hybrit flock. For this purpose, the eggs of the Lohmann LSL Classic white hybrid flock (n=60) were used. Weekly egg yields were evaluated from the 22nd week to the 62nd week. In the research, for the prediction of dependent and continuous variable egg weight; shape index (SI), shell breaking resistance (SBS), shell weight (SW), shell thickness (ST), yolk diameter (YD), yolk width (YW), yolk height (YH), color (YC ), albumen length (AW), albumen height (AL) and albumen height (AH) were used. In order to obtain perfect goodness of fit, in the “earth” package of the R program, the definitions of penalty -1, degree = 2, nprune = 10 and nk = 60. The research, the mars prediction model was determined such as EW = 63.1-0.906 * max (0,75-SI)-0.32 * max (0, SI-75) -62.4 * max (0,0.57-ST) -354 * max (0, ST-0.57) + 1.13 * Groupa2 * max (0, 75-SI) + 1.49 * (0.0.57-ST) max * YD + 8.2*max(0, ST 0.57) * YD-0.02*(0 YD-38.5)max* YC-0.0366*YH * max(0,13-YC). As a result, some quality variables were found to be important in determining egg weight. Variables such as group a2, SI, YC, ST, YD, YH to estimate the weight of the egg determined as the dependent variable were used. Other variables are not included in this equation. In the poultry, the MARS prediction model may be a better alternative to classical nonlinear models in predicting egg weight since that it is easier and has higher accuracy.

Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models

The paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.

Signal Smoothing with Time-Space Fractional Order Model

Abstract The time-space fractional-order model (TSFOM) is a generation of the classical diffusion model which is an excellent smoothing method. In this paper, the fractional-order derivative in the model is found to have good performance for peak-preserving. To check the validity and performance of the model, some noisy signals are smoothed by some commonly used smoothing methods and results are compared with those of the proposed model. The comparison result shows that the proposed method outperforms the classical nonlinear diffusion model and some commonly used smoothing methods.

A Data-Driven Method for Hybrid Data Assimilation with Multilayer Perceptron

Abstract Accurate and timely weather prediction is of significance for autonomous vehicles, such as designing more appropriate sensors or other configurations and developing safer driving strategies. Generally, as the mainstream weather prediction method, numerical weather prediction (NWP) relies on high-quality spatio-temporal observations. However, the precise state of the real world is not measurable. Thus, how to obtain a proper initial condition estimation based on big geospatial-temporal data is a crucial procedure for NWP. Data assimilation (DA) has been a traditional solution to the problem, for the better performance of which various mathematical-physics models have been used. However, the computational effectiveness and efficiency are still largely compromised by the complicated and nonparallel integration process in existing DA methods. In this paper, we propose a novel data-driven method named HDA-MLP to address the DA problem. We first constructed a customized MLP by introducing the temporal peculiarities of the state variables to simulate and optimize pure 3DVar and EnKF. Then we blended the optimized analysis fields directly by implicitly updating the background error covariance matrix through another neural network model to alleviate the dependence on traditional DA methods. We conducted extensive experiments to investigate the effectiveness and efficiency of the proposal by utilizing two classical nonlinear dynamic models. Results reveal that our approach has better robustness and enhanced capability to capture the variation of state variables. Notably, the analysis quality and computational efficiency are significantly improved.

Volterra-series approach to stochastic nonlinear dynamics: Linear response of the Van der Pol oscillator driven by white noise.

The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation oscillations in a real system are usually coupled to environmental noise, which further enriches their dynamics, but makes theoretical analysis of such systems and determination of the equation parameter values a difficult task. In a companion paper we have proposed an analytic approach to a similar problem for another classical nonlinear model-the bistable Duffing oscillator. Here we extend our techniques to the case of the Van der Pol equation driven by white noise. We analyze the statistics of solutions and propose a method to estimate parameter values from the oscillator's time series. We use experimental data of active oscillations in a biophysical system to demonstrate how our method applies to real observations and can be generalized for more complex models.

Group classification for a class of non-linear models of the RAPM type

A class of non-linear equations of RAPM (risk-adjusted pricing methodology) model type with a free element, depending on the second derivative with respect to the underlying asset, is studied. This class contains the Jandačka–Ševčovič model of the option pricing with taking into account transactions costs. The equivalence transformations continuous group of the equations class is found and is applied to the group classification obtaining for the model. The symmetries of the found free element specifications in the considered model are used for the deriving multi-parameter exact solutions.

Comparing generic and vectorial nonlinear manoeuvring models and parameter estimation using optimal truncated least square support vector machine

An optimal truncated least square support vector machine (LS-SVM) is proposed for the parameter estimation of nonlinear manoeuvring models based on captive manoeuvring tests. Two classical nonlinear manoeuvring models, generic and vectorial models, are briefly introduced, and the prime system of SNAME is chosen as the normalization forms for the hydrodynamic coefficients. The optimal truncated LS-SVM is introduced. It is a robust method for parameter estimation by neglecting the small singular values, which contribute negligibly to the solutions and increase the parameter uncertainty. The parameter with a large uncertainty is sensitive to the noise in the data and have a poor generalization performance. The classical LS-SVM and optimal truncated LS-SVM are used to estimate the parameters, and the effectiveness of optimal truncated LS-SVM is validated. The parameter uncertainty for both nonlinear manoeuvring models is discussed. The generalization performance of the obtained numerical models is further tested against the validation set, which is completely left untouched in the training. The R2 goodness-of-fit criterion is used to demonstrate the accuracy of the obtained models.

On the double resonance activation of electrostatically actuated microbeam based resonators

Electrostatically actuated microelectromechanical system (MEMS) devices have shown prominent potential in various applications. However, despite their low power consumption, they do require high input voltages to be actuated. This is even worse if these devices are driven around their mechanical resonant state. Assuming a double resonance excitation scheme, both electrically and mechanically, activates the system’s mechanical and electrical resonances simultaneously. This double resonance activation was recently verified experimentally to alleviate the problem of high actuating voltage/displacement near the resonant state. Therefore, in this work, an analytical electro-mechanical coupled model for a double-resonance-driven microbeam, assuming a classical nonlinear beam model combined with an RLC electric circuit model is first proposed and then numerically examined. Good match among the numerical simulations and the experimental data when the electrical resonance frequency band is sufficiently high is demonstrated. The suggested model can be used to further optimize certain MEMS designs and therefore fully benefit from this double resonance activation scheme in improving MEMS sensors and actuators.

Human Immunoglobulin G Adsorption in Epoxy Chitosan/Alginate Adsorbents: Evaluation of Isotherms by Artificial Neural Networks

Abstract This work aimed to evaluate the interaction of human IgG in non-conventional adsorbents based on chitosan and alginate in the absence and presence of Reactive Green, Reactive Blue and Cibacron Blue immobilized as ligands. The adsorption was evaluated at 277, 288, 298 and 310 K using sodium phosphate buffer, pH 7.6, at 25 mmol L−1. The highest adsorption capacity was observed in the experiments performed with no immobilized dye, although all showed adsorption capacity higher than 120 mg g−1. Data modeling was done using Langmuir, Langmuir-Freundlich and Temkin classical nonlinear models, and artificial neural networks (ANN) for comparison. According to the parameters obtained, a possible adsorption in multilayers was observed due to protein-adsorbent and protein-protein interactions, concluding that IgG adsorption process is favorable and spontaneous. Using an ANN structure with 3 hidden neurons (single hidden layer), the MSE (RMSE) for training, test and validation were 13.698 (3.701), 11.206 (3.347) and 7.632 (2.763), respectively, achieving correlation coefficients of 0.999 in all steps. ANN modeling proved to be effective in predicting the adsorption isotherms in addition to overcoming the difficulties caused by experimental errors and/or arising from adsorption phenomenology.

An Improved Data Assimilation Localization Method Based on Fuzzy Logic Control

To determine the best estimates of the ocean or atmospheric state, Data Assimilation (DA) is a methodology to combine all available information from numerical models and observation information. With small ensemble numbers in the Ensemble Kalman filter, the more effective utilization the observation data are, the higher the assimilation performance become. In this study, we proposed a new fuzzy control-based data assimilation system, named FA (fuzzy analysis) and CF (covariance fuzzy), which coupled with fuzzy logic control algorithms to improve assimilation performance. A number of numerical experiments are designed using a classical nonlinear model (the Lorenz-96 model) to explore the effects of the new algorithms on the ensemble transform matrices. The experiments show that the FA algorithm can be selected when the system is in weak assimilation, whereas both algorithms can be implemented in medium assimilation situations. If the system is strongly assimilated, the CF algorithm has demonstrated more robust performance.

A Comparative Study of Localization Methods in EnkF Data Assimilation

This study investigates the relation between some common localization methods in ensemble Kalman filter (EnKF) systems including covariance localization (CL) and local analysis (LA), which are popular used in large-scale Geo-science applications. Two fuzzy-based localization methods, named covariance fuzzy (CF) and fuzzy analysis (FA), are formulated in terms of tapering of ensemble covariance in a fuzzy logic way. To explore the effects of all algorithms on the error covariance matrix, numerical experiments are designed using a classical nonlinear model (i.e., the Lorenz-96 model) by determining the Power Spectrum Density (PSD) of the corresponding systems. The experiments show that the new algorithms can eliminate spurious correlation of the background error covariance matrix. The results of PSD demonstrate that the new fuzzy based methods have more robust performance than the CL or LA algorithm.

On the use of LES-based turbulent thermal-stress models for rod bundle simulations

An alternative methodology is proposed here to overcome the excessive cost of large eddy simulations (LES) of full-length heated rod bundle calculations, while improving the inaccurate results typically obtained with Reynolds-averaged Navier–Stokes equations (RANS). While the cost of the full-length LES is generally too high, LES of a small section of a single rod is usually affordable. The idea presented here consists of using the information granted by the small LES calculation to determine the appropriate turbulence viscosity or turbulent thermal diffusivity that can be used to solve only for the temperature field in a pseudo-RANS approach. The study has been performed with single-rod simulations with a P/D of 1.12 and 1.24, considering rod lengths that are representative of reactor applications, for the cases of uniform heat flux and a more realistic cosine-like axial heat distribution. The spectral element code Nek5000 has been used for all LES, RANS, and pseudo-RANS simulations. The recently proposed Nek5000 steady-state solver has been used for solving the temperature field in the pseudo-RANS approach and has proved significantly faster than transient schemes. Prediction of thermal quantities is compared with classical linear and nonlinear RANS models. LES for the full-length rods has also been performed and is used as a reference. Results of the proposed method show significant improvements with respect to those obtained with RANS.

Solitary waves in a granular chain of elastic spheres: Multiple solitary solutions and their stabilities.

A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single- and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.