Nonlinear Model Problem Research Articles

LabVIEW Venus Flytrap ANFIS Inverse Control System for Microwave Heating Cavity

Growing interests in nature-inspired computing and bio-inspired optimization techniques have led to powerful tools for solving learning problems and analyzing large datasets. Several methods have been utilized to create superior performance-based optimization algorithms. However, certain applications, like nonlinear real-time, are difficult to explain using accurate mathematical models. Such large-scale combination and highly nonlinear modeling problems are solved by usage of soft computing techniques. So, in this paper, the researchers have tried to incorporate one of the most advanced plant algorithms known as Venus Flytrap Plant algorithm (VFO) along with soft-computing techniques and, to be specific, the ANFIS inverse model-Adaptive Neural Fuzzy Inference System for controlling the real-time temperature of a microwave cavity that heats oil. The MATLAB was integrated successfully with the LabVIEW platform. Wide ranges of input and output variables were experimented with. Problems were encountered due to heating system conditions like reflected power, variations in oil temperature, and oil inlet absorption and cavity temperatures affecting the oil temperature, besides the temperature's effect on viscosity. The LabVIEW design followed and the results figure in the performance of the VFO- Inverse ANFIS controller.

AnFiS-MoH: Systematic exploration of hybrid ANFIS frameworks via metaheuristic optimization hybridization with evolutionary and swarm-based algorithms

The adaptive neuro-fuzzy inference system (ANFIS) has shown promising performance in modeling nonlinear problems, leveraging the strengths of both neural networks and fuzzy inference systems. However, as the problem scale increases, the growing number of tunable parameters in ANFIS can make it challenging to optimize via traditional gradient-based methods alone. This study introduces AnFiS-MoH, a novel framework that synergistically integrates ANFIS with metaheuristic optimization algorithms to address these challenges. By leveraging the global search capabilities of metaheuristics such as ant colony optimization (ACO), particle swarm optimization (PSO), genetic algorithm (GA), and simulated annealing (SA), ANFIS-MOH enhances the parameter tuning process of ANFIS models. We evaluate ANFIS-MOH on benchmark datasets including Boston Housing and Wine Quality, demonstrating significant improvements in prediction accuracy and generalization compared to traditional ANFIS and neural network approaches. The proposed framework achieves up to 20% reduction in Mean Squared Error and 15% increase in R2 scores, particularly excelling in handling high-dimensional, noisy data. This work contributes to the field of hybrid intelligent systems by introducing effective ways to combine the strengths of ANFIS with powerful metaheuristic optimization algorithms. The findings suggest that such hybrid approaches can be effective in tackling challenging nonlinear modeling problems. Our code is available at https://github.com/AmbitYuki/Metaheuristic-Adaptive-ANFIS.

Exact analytical investigation of Duffing oscillator vibration spectra under time-periodic oscillatory external force

This work introduces an analytical technique for determining solutions to a highly nonlinear Duffing-harmonic oscillator model problem. The parametric solutions of Duffing oscillator vibrations for an undamped case are achieved analytically in terms of Adomian polynomials by implementing the straightforward approach of the Laplace Transformation, known as the Laplace Decomposition Procedure (LDP). Possible plots of both numerical and analytical results sketched for various parameters are also presented to support our discussion. These graphs demonstrate variations of position-time, speed-time, and speed-position for an undamped Duffing oscillator case. When analyzed in general, they can provide vibration pattern descriptions for a variety of physical and engineering system configurations. We also examine their physical structures and behavioral characteristics within the conceptual framework of chaotic formalism.

A dual-energy CT reconstruction method based on anchor network from dual quarter scans.

Compared with conventional single-energy computed tomography (CT), dual-energy CT (DECT) provides better material differentiation but most DECT imaging systems require dual full-angle projection data at different X-ray spectra. Relaxing the requirement of data acquisition is an attractive research to promote the applications of DECT in wide range areas and reduce the radiation dose as low as reasonably achievable. In this work, we design a novel DECT imaging scheme with dual quarter scans and propose an efficient method to reconstruct the desired DECT images from the dual limited-angle projection data. We first study the characteristics of limited-angle artifacts under dual quarter scans scheme, and find that the negative and positive artifacts of DECT images are complementarily distributed in image domain because the corresponding X-rays of high- and low-energy scans are symmetric. Inspired by this finding, a fusion CT image is generated by integrating the limited-angle DECT images of dual quarter scans. This strategy enhances the true image information and suppresses the limited-angle artifacts, thereby restoring the image edges and inner structures. Utilizing the capability of neural network in the modeling of nonlinear problem, a novel Anchor network with single-entry double-out architecture is designed in this work to yield the desired DECT images from the generated fusion CT image. Experimental results on the simulated and real data verify the effectiveness of the proposed method. This work enables DECT on imaging configurations with half-scan and largely reduces scanning angles and radiation doses.

Robust generation expansion planning in power grids under renewable energy penetration via honey badger algorithm

Robust reliability Generation Expansion Planning (GEP) turns out to be a crucial step for an efficient energy management system in a modern power grid, especially under renewable energy employment. The integration of all such components in a GEP model makes it a large-scale, nonlinear, and mixed-variable mathematical modeling problem. In this paper, the presence of wind energy uncertainty is analyzed. Both long and short-term uncertainties are incorporated into the proposed GEP model. The first step concerns the impact of long-term wind uncertainties through the annual variations of the capacity credit of two real sites in Egypt at Zafaranh and Shark El-ouinate. The second step deals with the short-term uncertainties of each wind site. The wind speed uncertainty of each wind site is modeled by probability distribution function. Then, wind power is estimated from the wind power curve for each wind site and Monte-Carlo Simulation is performed. Fast Gas Turbine and/or Pump Hydro Storage are incorporated to cope with short-term uncertainties. Sensitivity analysis is implemented for 3, 6, and 12 stages as short and long planning horizons to minimize the total costs with wind energy penetration and emission reduction over planning horizons. Also, a novel Honey Badger Algorithm (HBA) with model modifications such as Virtual Mapping Procedure, Penalty Factor Approach, and the Modified of Intelligent Initial Population Generation is utilized for solving the proposed GEP problem. The obtained results are compared with other algorithms to ensure the superior performance of the proposed HBA. According to the results of the applicable test systems, the proposed HBA performs better than the others, with percentage reductions over CSA, AO, BES, and PSO ranging up to 4.2, 2.72, 2.7, and 3.4%, respectively.

Internal Temperature Estimation of Lithium-Ion Battery Based on Improved Electro-Thermal Coupling Model and ANFIS

Abstract Accurate estimation of the internal temperature of lithium-ion batteries plays an important role in the development of a suitable battery thermal management system, safeguarding the healthy and safe operation of batteries and improving battery performance. In order to accurately estimate the internal temperature of the battery, this paper proposes a method for estimating the internal temperature of lithium-ion batteries based on an improved electro-thermal coupling model and an Adaptive Network-Based Fuzzy Inference System (ANFIS). First, a parameterization method of the electrical model is proposed, and an electrical model whose parameters are affected by temperature and SOC is established. Second, to overcome the complex nonlinear modeling problem of lithium-ion batteries, the ANFIS thermal model is established. Then, an improved electro-thermal coupling model for lithium-ion batteries is established by combining the proposed electrical model and the ANFIS thermal model to improve the accuracy of estimating the internal temperature of the battery. Finally, the effectiveness of the proposed method is verified by simulation and experiment.

A coupling of Galerkin and mixed finite element methods for the quasi-static thermo-poroelasticity with nonlinear convective transport

In this paper, we propose a combined Galerkin and mixed finite element methods to analyze the fully coupled nonlinear thermo-poroelastic model problems. We design the Galerkin finite element method for the temperature, the mixed finite element method for the pressure, the Galerkin finite element method for the elastic displacement. We linearize the nonlinear convective transport term in the energy balance equation and establish the fully discrete finite element schemes. The stability and convergence of the coupled method are obtained. In particular, all previous works have required certain time step restrictions, but we unconditionally prove the optimal error estimates without certain extra restrictions on both time step and spatial meshes. Finally, some numerical examples are presented to illustrate the accuracy of the method and confirm the unconditional stability of the method.

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. We show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

A Semisupervised Soft-Sensor of Just-in-Time Learning With Structure Entropy Clustering and Applications for Industrial Processes Monitoring

To monitor industrial processes properly, soft-sensors are widely used to predict significant but difficult-to-measure quality variables. However, the prediction performances of traditional data-driven soft-sensors are usually unacceptable once suffering from high-nonlinear, high-dimension and imblance data issues. Therefore, a semi-supervised soft-sensor, which is learned by a just-in-time method with structure entropy clustering (SS-JITL-SEC), is proposed aiming to improve prediction performance with a simpler way. Inspired by a divide and conquer strategy, a novel SEC method is proposed to achieve several clusters and then to translate the highly complex and nonlinear modeling problems into simple and linear ones. Moreover, the training dataset is extended through a mixed semi-supervised (SS) labeling approach. Finally, dissimilarity-based just-in-time learning (JITL) works together with the resulting clustering sub-datasets to formulate a local adaptive prediction model. Two datasets from different types of wastewater treatment plants are used to verify the effectiveness of the proposed soft-sensor. The results show that the SS-JITL-SEC soft-sensor can achieve better prediction performance than other standard counterparts, and even for effective process monitoring with the resulted residuals.

Approximate solutions for a fractional thermostat model boundary value problem via Bernstein's collocation method with Legendre polynomials

Numerous classical models of thermostats have been analyzed in the literature, and while existence and uniqueness results have been established, the investigation of other properties, such as stability, can present significant challenges. Therefore, there is a need for fractional mathematical models that are nonlocal problems and allow for the straightforward study of the asymptotic behavior of their solutions. However, solving these problems is often exceedingly complex or even impossible, necessitating the use of numerical methods to obtain approximate solutions. The focus of this research is a generalized boundary value problem that is based on a classical thermostat model. Our initial step involves determining the associated integral equation for the problem at hand. The properties of existence and uniqueness are proved by exploiting the classical contraction principle of Banach together with another kind called ‐ ‐contraction. Afterwards, thanks to the Bernstein polynomials and fractional matrix of derivative, the approximate solutions of our nonlinear fractional thermostat model problem are obtained. This approach utilizes the Legendre operational matrix of fractional derivatives in combination with a truncated Legendre series for the numerical integration of fractional differential equations. By doing so, the problem can be reduced to solving a system of algebraic equations, resulting in significant simplification. This method has been successfully used to solve both linear and nonlinear fractional differential equations. Finally, an example on this type of problem have been studied and the approximate solution are plotted.

A New Class of Efficient Adaptive Filters for Online Nonlinear Modeling

Nonlinear models are known to provide excellent performance in real-world applications that often operate in non-ideal conditions. However, such applications often require online processing to be performed with limited computational resources. To address this problem, we propose a new class of efficient nonlinear models for online applications. The proposed algorithms are based on linear-in-the-parameters (LIP) nonlinear filters using functional link expansions. In order to make this class of functional link adaptive filters (FLAFs) efficient, we propose low-complexity expansions and frequency-domain adaptation of the parameters. Among this family of algorithms, we also define the partitioned-block frequency-domain FLAF, whose implementation is particularly suitable for online nonlinear modeling problems. We assess and compare frequency-domain FLAFs with different expansions providing the best possible tradeoff between performance and computational complexity. Experimental results prove that the proposed algorithms can be considered as an efficient and effective solution for online applications, such as the acoustic echo cancellation, even in the presence of adverse nonlinear conditions and with limited availability of computational resources.

CDBA: a novel multi-branch feature fusion model for EEG-based emotion recognition.

EEG-based emotion recognition through artificial intelligence is one of the major areas of biomedical and machine learning, which plays a key role in understanding brain activity and developing decision-making systems. However, the traditional EEG-based emotion recognition is a single feature input mode, which cannot obtain multiple feature information, and cannot meet the requirements of intelligent and high real-time brain computer interface. And because the EEG signal is nonlinear, the traditional methods of time domain or frequency domain are not suitable. In this paper, a CNN-DSC-Bi-LSTM-Attention (CDBA) model based on EEG signals for automatic emotion recognition is presented, which contains three feature-extracted channels. The normalized EEG signals are used as an input, the feature of which is extracted by multi-branching and then concatenated, and each channel feature weight is assigned through the attention mechanism layer. Finally, Softmax was used to classify EEG signals. To evaluate the performance of the proposed CDBA model, experiments were performed on SEED and DREAMER datasets, separately. The validation experimental results show that the proposed CDBA model is effective in classifying EEG emotions. For triple-category (positive, neutral and negative) and four-category (happiness, sadness, fear and neutrality), the classification accuracies were respectively 99.44% and 99.99% on SEED datasets. For five classification (Valence 1-Valence 5) on DREAMER datasets, the accuracy is 84.49%. To further verify and evaluate the model accuracy and credibility, the multi-classification experiments based on ten-fold cross-validation were conducted, the elevation indexes of which are all higher than other models. The results show that the multi-branch feature fusion deep learning model based on attention mechanism has strong fitting and generalization ability and can solve nonlinear modeling problems, so it is an effective emotion recognition method. Therefore, it is helpful to the diagnosis and treatment of nervous system diseases, and it is expected to be applied to emotion-based brain computer interface systems.

The Kernel Recursive Maximum Total Correntropy Algorithm

Focusing on the performance deterioration of nonlinear filtering algorithms in the error-in-variable (EIV) model, a nonlinear version of maximum total correntropy (MTC) algorithm called kernel recursive maximum total correntropy (KRMTC) is proposed in this brief, which constructs a nonlinear relationship based on MTC criterion between inputs and outputs in high-dimensional feature space. Compared with existing kernel adaptive filtering (KAF) algorithms based on traditional mean square error (MSE) and maximum correntropy criteria (MCC), the proposed algorithm can handle nonlinear modeling problems in the EIV model well. In addition, an approximate linear dependency (ALD) criterion is applied to reduce the computational complexity of KRMTC. To verify the feasibility of the proposed algorithm, firstly, the convergence of the KRMTC algorithm under some assumptions is discussed and its local convergence condition is given. Secondly, the proposed algorithm is applied to the Lorenz time-series prediction and wind prediction simulations. Simulation results display that the KRMTC algorithm has better performance than kernel recursive least squares (KRLS) and kernel recursive maximum correntropy (KRMC) algorithms in EIV case.

An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation

In this paper, we deal with the numerical solution of Sawada-Kotera (SK) equation classified as the type of fifth order Korteweg-de Veries (gfKdV) equations. In the first step of our study consisting of several steps, nonlinear model problem is split into the system with the coupled new equations by using the transformation w_xxx=v. In the second step, to get rid of the nonlinearity of the problem, Rubin-Graves type linearization are used. After these applications, the approximate solutions are obtained by using the trigonometric quintic B-Spline collocation method. The efficiency and accuracy of the present method is demonstrated with the tables and graphs. As it is seen in the tables given with the error norms L_2 and L_∞ for different time and space steps, the present method is more accurate for the larger element numbers and smaller time steps.

Research on aircraft servo system modeling method in hardware in the loop simulation

The performance of the servo system has a great influence on aircraft attitude control. In application, servo system has nonlinear characteristics such as friction, clearance, zero position and so on which make it difficult to precise modeling. In engineering application, we often use the approximately linearized modeling method. However, it has its localization and cannot accurately describe the real condition of the servo devices. To test the correctness of the control algorithm in ground test, the real aircraft servo devices are often added to the whole closed-loop test system in Hardware-In-Loop-Simulation (HILS). In this paper, we introduce the traditional linearized modeling method used in HILS. To deal with the problem of nonlinear modeling, we propose a modeling method using BP neural network. Utilizing the large amount of data produced in HILS, a relatively precise model is trained. Compared with the linear modeling method, the effectiveness of neural network for nonlinear system modeling is verified. The presented method has some engineering application values.

Model of transition zone evolution between coating and substrate under intense short thermal impulse

In the present work a model of the evolution of the composition of the transition zone between the material and the pre-applied coating under conditions of intense short-term thermal impulse is proposed. The pulse times are assumed to be comparable to the relaxation times of the heat and mass fluxes. This led to the need to account for finite rates of heat and mass propagation in the model, leading to hyperbolic transfer equations. The phenomena of thermodiffusion (Soret effect) and diffusive thermal conductivity (Dufour effect) and some possible chemical reactions leading to a change in the transition zone composition are also taken into account. This nonlinear model problem illustrates the necessity of the really coupled problem solution to reveal the feature of cross-effects in irreversible conditions. It was found that due to the wave heating and the wave nature of the movement of elements, chemical reactions can start during the action of a short pulse outside the heating zone expected only due to thermal conductivity.

On the Development and Performance Evaluation of Improved Radial Basis Function Neural Networks

This article deals with the development of four modified radial basis function neural network (RBFNN) models. The corresponding learning algorithms associated with the updating of internal parameters of the models are derived. The conventional inputs are used in the first and second modified RBFNN models (models 3 and 4) whereas exponential nonlinear inputs are used in the fifth and sixth RBFNN models to provide additional nonlinearity for achieving a better solution of nonlinear classification, and direct and inverse modeling problems. To assess and compare the performance potentiality of the proposed four new RBFNN models, one classification problem, one direct modeling problem, and one inverse modeling problem are solved through computer simulation-based experiments. For comparison and to assign the performance rank of each of the four modified RBFNN models, two conventional and commonly used RBFNN models (models 1 and 2) are also simulated. To access the performance of different models during the training phase of Examples 1 and 2, the root mean-square error (RMSE) value, mean absolute deviation (MAD), and the number of iterations required to achieve convergence are obtained. For the third example, only the first two performance measures are found. During the testing or validation phase, the output responses of the different models of Example 2 are compared with the desired response analysis. For Example 3, the bit-error rate (BER) plots are compared. The observation of all the results demonstrates consistent ranks of all models in the case of all three examples. It is, in general, found that the ranks of the models 1–6 are 6, 4, 3, 2, 5, and 1, respectively. In essence, in terms of all performance measures, model M-6 with an exponential version of inputs with weights on both layers occupies the first position whereas model M-4 with conventional inputs as the second position.

An explicit second order uniformly convergent difference algorithm for an initial value problem associated to second order differential equations

Abstract We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems. Our technique based on the method of finite difference approximations. We obtain a quadratic order accurate an explicit method using the set of initial conditions in a natural way and approximations for the approximate numerical solution after the discretization of the continuous problem under appropriate conditions. We discuss the development of the method and the periodic property of the solution of the problem. In the numerical experiment, we consider both linear and nonlinear model problems to test the efficiency and accuracy of the method. The tabulated numerical results in computational experiments approve the quadratic order accuracy and efficiency of the method.

Galerkin method for the fully coupled quasi-static thermo-poroelastic problem

In this paper, the standard Galerkin method for fully coupled nonlinear thermo-poroelastic model problems is studied. We establish the semi discrete and fully discrete finite element schemes and obtain the stability of this method. The error estimates for the displacement, pressure, temperature are derived. Finally, several numerical examples are given to illustrate the accuracy of the method.

Fractal-fractional SIRS epidemic model with temporary immunity using Atangana-Baleanu derivative

The basic SIRS deterministic model is one of the powerful and important compartmental modeling frameworks that serve as the foundation for a variety of epidemiological models and investigations. In this study, a nonlinear Atangana-Baleanu fractal-fractional SIRS epidemiological model is proposed and analysed. The model’s equilibrium points (disease-free and endemic) are studied for local asymptotic stability. The existence of the model’s solution and its uniqueness, as well as the Hyers-Ulam stability analysis, are established. Numerical solutions and phase portraits for the fractal-fractional model are generated using a recently constructed and effective Newton polynomial-based iterative scheme for nonlinear dynamical fractal-fractional model problems. Our numerical simulations demonstrate that fractal-fractional dynamic modeling is a very useful and appropriate mathematical modeling tool for developing and studying epidemiological models.