Search Results (64)

We introduce and study a new class of nonlinear operators on metric spaces, called rational $(a,p)-$quasicontractions. Within this framework, we establish Greguš-type fixed-point theorems for closed, convex subsets of Banach spaces. The results establish the existence and uniqueness of fixed points, as well as the convergence of the Picard iteration for every initial guess. We show that rational $(a,p)-$quasicontractions strictly extend several classical contractive classes, including Hardy-Rogers, Kannan, Chatterjea, and rational contractions, and we provide explicit examples exhibiting the properness of these inclusions. As an application, we consider a nonlocal boundary value problem for a Caputo fractional differential equation of order $\alpha \in (1,2)$ with distributed delay and mixed nonlocal boundary conditions. By rewriting the problem as a Hammerstein-Volterra integral equation on a cone, and imposing natural growth and rational Lipschitz conditions on the delayed nonlinearity, we show that the associated Hammerstein operator is a rational $(a,p)-$quasicontraction. This yields the existence, uniqueness, and global attractivity of a positive solution. Two model fractional nonlinearities with delayed feedback are discussed in detail, along with a numerical scheme that illustrates the predicted geometric convergence of the discrete Picard iteration in the Caputo fractional setting. Full article

Accurate estimation of the state of charge (SOC) of lithium-ion batteries is critical for assessing the safety and remaining range of electric vehicles. However, due to the complex and variable operating environment of batteries and their highly nonlinear internal mechanisms, achieving high-precision SOC prediction remains a central challenge in current research. To this end, this paper proposes a nonlinear Hammerstein model based on the Hippopotamus Optimization Algorithm (HO) to optimize the backpropagation neural network, thereby enhancing the accuracy of SOC prediction. The HO-BP-Hammerstein model optimizes the BP neural network architecture using the Hippopotamus Algorithm and conducts SOC prediction accuracy tests on real-world data. Experimental results demonstrate the superiority of the proposed method through comparative accuracy analysis of various SOC prediction approaches under different operating conditions, confirming its significant engineering application value. Full article

Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid architecture brings difficulties in performance analysis and coefficient estimation. This paper focuses on the performance analysis and coefficient estimation of the PH model for nonlinear systems with memory effects, such as power amplifiers. By comparing the PH model with the memory polynomial (MP) model under identical basis functions, we analyze its performance across varying numbers of parallel branches, nonlinear orders, and memory depths. Using singular value decomposition (SVD), we derive a closed-form expression for the PH model’s performance under underdetermined conditions, establishing its relationship to the non-zero singular values of the MP model’s coefficient matrix. Based on this, we propose a coefficient generation method combining SVD and least squares (LS), which directly computes coefficients and assesses performance during execution. Simulations confirm the method’s effectiveness, showing that selecting branches associated with larger singular values achieves near-optimal performance with reduced complexity. Full article

This paper proposes a simplified adaptive filtering approach using a Hammerstein function and the spline interpolation based on a Fair cost function for denoising electrocardiogram (ECG) signals. The use of linear filters in real-world applications has many limitations. Adaptive nonlinear filtering is a key development in tackling the challenge of discovering the specific characteristics of biomimetic systems for each person in order to eliminate unwanted signals. A biomimetic system refers to a system that mimics certain biological processes or characteristics of the human body, in this case, the individual features of a person’s cardiac signals (ECG). Here, the adaptive nonlinear filter is designed to cope with ECG variations and remove unwanted noise more effectively. The objective of this paper is to explore an individual biomedical filter based on adaptive nonlinear filtering for denoising the corrupted ECG signal. The Hammerstein spline adaptive filter (HSAF) architecture consists of two structural blocks: a nonlinear block connected to a linear one. In order to make a smooth convergence, the Fair cost function is introduced for convergence enhancement. The affine projection algorithm (APA) based on the Fair cost function is used to denoise the contaminated ECG signals, and also provides fast convergence. The MIT-BIH 12-lead database is used as the source of ECG biomedical signals contaminated by random noises modelled by Cauchy distribution. Experimental results show that the estimation error of the proposed HSAF–APA–Fair algorithm, based on the Fair cost function, can be reduced when compared with the conventional least mean square-based algorithm for denoising ECG signals. Full article

The Bagley–Torvik equation (BTE) is an important model in mathematical physics and mechanics, but obtaining its analytical solution remains challenging. For its numerical treatment, the presence of composite functions in the generalized BTE poses additional difficulties, and efficient approaches for handling nonlinear terms are still lacking in the literature. This study proposes an improved numerical method for the fractional BTE with integral boundary conditions. By employing an integration technique, the original problem is transformed into a weakly singular Fredholm–Hammerstein (F–H) integral equation of the second kind. To address the nonlinear terms, an enhanced piecewise Taylor expansion scheme is developed to construct the discrete form, while the uniqueness of the solution is proven using the contraction mapping theorem in Banach spaces. The convergence and error analyses are rigorously carried out, and numerical experiments confirm the accuracy and efficiency of the proposed approach. Full article

To address the issue of hysteresis nonlinearity adversely affecting the tracking accuracy of piezoelectric actuators, an improved particle swarm optimization (PSO) algorithm is proposed to improve the accuracy of hysteresis model parameter identification. Additionally, a discrete-time linear quadratic optimal tracking (DLQT) control strategy incorporating hysteresis compensation is developed to improve tracking performance. This study employs the Hammerstein model to characterize the nonlinear hysteresis behavior of piezoelectric actuators. Regarding parameter identification, the conventional PSO algorithm tends to suffer from premature convergence and being trapped in local optima. To address this, a cross-variation mechanism is introduced to enhance population diversity and improve global search ability. Furthermore, adaptive and dynamically adjustable inertia weights are designed based on evolutionary factors to balance exploration and exploitation, thereby enhancing convergence and identification accuracy. The inertia weights and learning factors are adaptively adjusted based on the evolutionary factor to balance local and global search capabilities and accelerate convergence. Benchmark function tests and model identification experiments demonstrate the improved algorithm’s superior convergence speed and accuracy. In terms of control strategy, a hysteresis compensator based on an asymmetric hysteresis model is designed to improve system linearity. To address the issues of incomplete hysteresis compensation and low tracking accuracy, a DLQT controller is developed based on hysteresis compensation. Hardware-in-the-loop tracking control experiments using single and composite frequency reference signals show that the relative error is below 3.3% in the no-load case and below 4.5% in the loaded case. Compared with the baseline method, the proposed control strategy achieves lower root-mean-square error and maximum steady-state error, demonstrating its effectiveness. Full article

Hammerstein adaptive filters (HAFs) are widely used for nonlinear system identification due to their structural simplicity and modeling effectiveness. However, their performance can degrade significantly in the presence of impulsive disturbance or other more complex non-Gaussian noise, which are common in real-world scenarios. To address this limitation, this paper proposes a robust HAF algorithm based on the kernel mean p-power error (KMPE) criterion. By extending the p-power loss into the kernel space, KMPE preserves its symmetry while providing enhanced robustness against non-Gaussian noise in adaptive filter design. In addition, random Fourier features are employed to flexibly and efficiently model the nonlinear component of the system. A theoretical analysis of steady-state excess mean square error is presented, and our simulation results validate the superior robustness and accuracy of the proposed method over the classical HAF and its robust variants. Full article

This work presents the development of soft sensor models for monitoring the operation of online process analyzers used to measure the sulfur content in the product of the refinery hydrodesulfurization process. Since sulfur content often fluctuates over time, soft sensor models must account for these frequency fluctuations. We have therefore developed dynamic data-driven models based on linear and nonlinear system identification techniques (finite impulse response—FIR, autoregressive with exogenous inputs—ARX, output error—OE, nonlinear ARX—NARX, Hammerstein–Wiener—HW) and machine learning techniques, including models based on long short-term memory (LSTM) and gated recurrent unit (GRU) networks, as well as artificial neural networks (ANNs). The core steps in model development included the selection and preprocessing of continuously measured plant process data, collected from a full-scale industrial hydrodesulfurization unit under normal operating conditions. The developed soft sensor models are intended to support or replace process analyzers during maintenance periods or equipment failures. Moreover, these models enable the application of inferential control strategies, where unmeasured process variables—such as sulfur content—can be estimated in real time and used as feedback for advanced process control. Full article

Some chemical reactors exhibit coupled dynamics with multiple equilibrium points and strong nonlinearities. The accurate modeling of these dynamics is crucial to optimal control and increasing the reactor’s economic performance. While neural networks can effectively handle complex nonlinearities, they sacrifice interpretability. Alternatively, block-oriented Hammerstein–Wiener models and Koopman operator-based linear predictors combine nonlinear representation with linear dynamics, offering a gray-box identification approach. This paper comprehensively reviews recent advancements in both the Hammerstein–Wiener and Koopman operator methods and benchmarks their accuracy against neural network-based approaches to modeling a large-scale industrial Fluid Catalytic Cracking fractionator. Furthermore, Monte Carlo simulations are employed to validate performance under varying signal-to-noise ratios. The results demonstrate that the Koopman bilinear model significantly outperforms the other methods in terms of accuracy and robustness. Full article

Smart tools are limited by actuation–sensing integration and structural redundancy, making it difficult to achieve compactness, ultra-precision feed, and immediate feedback. This paper proposes a self-sensing giant magnetostrictive actuator-based turning tool (SSGMT), which enables simultaneous actuation and output sensing without external sensors. A multi-objective optimization model is first established to determine the key design parameters of the SSGMT to improve magnetic transfer efficiency, system compactness, and sensing signal quality. Then, a dynamic hysteresis model with a Hammerstein structure is developed to capture its nonlinear characteristics. To ensure accurate positioning and a robust response, a hybrid control strategy combining feedforward compensation and adaptive feedback is implemented. The SSGMT is experimentally validated through a series of tests including self-sensing displacement accuracy and trajectory tracking under various frequencies and temperatures. The prototype achieves nanometer-level resolution, stable output, and precise tracking across different operating conditions. These results confirm the feasibility and effectiveness of integrating actuation and sensing in one structure, providing a promising solution for the application of smart turning tools. Full article

Fast steering mirrors (FSMs), actuated by piezoelectric ceramics, play pivotal roles in satellite laser communication, distinguished by their high bandwidth and fast responsiveness, thereby facilitating the precise pointing and robust tracking of laser beams. However, the dynamic performance of FSMs is notably impaired by the hysteresis nonlinearity inherent in piezoelectric ceramics. Under dynamic conditions, rate-dependent hysteresis models and Hammerstein models are predominantly employed to characterize hysteresis nonlinearity. By combining the advantages of these two models, a hysteresis model termed modified Hammerstein-like (MHL) model is proposed. This model integrates an input time delay, a rate-dependent hysteresis term, and a linear dynamic term in a cascaded structure, effectively capturing the dynamic characteristics of hysteresis systems across a broad frequency range. Additionally, a composite control strategy is tailored for the MHL model which consists of a feedforward compensator based on a rate-dependent hysteresis inverse model and a proportional–integral (PI) controller for closed-loop regulation. Experimental results demonstrate the effectiveness of the proposed modeling and composite control methods. Full article

For the non-homogeneous fractional-order Hammerstein multiple input single output (MISO) system, a method for identifying system coefficients and fractional-order parameters in stages is proposed. The coefficients of the system include the coefficients of nonlinear terms and the coefficients of the transfer function. In order to estimate them, we derived the coupling auxiliary form between the original system coefficients, developed a multi-innovation principle combined with the LM (Levenberg–Marquardt) parameter identification method, and introduced a decoupling strategy for the coupling coefficients. The entire identification process of fractional orders is split into three stages. The division of stages is based on assuming that the system is of different fractional order types, including global homogeneous fractional-order systems, local homogeneous fractional-order systems, and non-homogeneous fractional-order systems. Except for the first stage, the estimated initial value of the fractional order in each stage is derived from the estimated value of the fractional order in the previous stage. The fractional order iteration will re-drive the iteration of the system coefficients to achieve the purpose of alternate estimation. To validate the proposed algorithm, we modeled the fractional-order system of heat flow density through a two-layer wall system, demonstrating the algorithm’s effectiveness and practical applicability. Full article

This review examines the integration of advanced ultrasonic techniques and artificial intelligence (AI) for monitoring and analyzing concrete structures, focusing on detecting and classifying internal defects. Concrete structures are subject to damage over time due to environmental factors and dynamic loads, compromising their integrity. Non-destructive techniques, such as ultrasonics, allow for identifying discontinuities and microcracks without altering structural functionality. This review addresses key scientific challenges, such as the complexity of managing the large volumes of data generated by high-resolution inspections and the importance of non-linear models, such as the Hammerstein model, for interpreting ultrasonic signals. Integrating AI with advanced analytical models enhances early defect diagnosis and enables the creation of detailed maps of internal discontinuities. Results reported in the literature show significant improvements in diagnostic sensitivity (up to 30% compared to traditional linear techniques), accuracy in defect localization (improvements of 25%), and reductions in predictive maintenance costs by 20–40%, thanks to advanced systems based on convolutional neural networks and fuzzy logic. These innovative approaches contribute to the sustainability and safety of infrastructure, with significant implications for monitoring and maintaining the built environment. The scientific significance of this review lies in offering a systematic overview of emerging technologies and their application to concrete structures, providing tools to address challenges related to infrastructure degradation and contributing to advancements in composite sciences. Full article

In this paper, the nonlinear identification of the lateral dynamics of a road vehicle and the velocity dependence of the dynamics are presented. One of the most useful methods to define the mathematical model is system identification based on measured data. A test vehicle for autonomous driving was constrained to move in a straight line while the vehicle’s steering servo was artificially excited. The input of the system is therefore the sum of the artificial excitation and the control signal of the autonomous function, and the output is the lateral acceleration of the vehicle. The measurements are used to identify Wiener and Hammerstein models of the lateral dynamics at different speeds using nonlinear methods. The aim is to investigate the velocity dependence of the dynamics. Full article

In this paper, the nonlinear identification (ID) of the lateral dynamics of a road vehicle is presented. The mathematical description of lateral dynamics is crucial for developing various self-driving functions. One method of describing dynamics is system identification from measured data. During the measurements, the steering servo of a test vehicle kept in straight-line motion by a self-driving function was artificially excited. A Hammerstein–Wiener model was successfully applied for the identification of these measurements. A nonlinear estimator was used during the fitting, which needed high computing power. For the Hammerstein–Wiener model, we used the two-stage algorithm (TSA) with a bilinear estimation method, which makes it possible to apply linear regression. We compared these methods during simulations and real data. Full article