Simple Nonlinear Model Research Articles

Detection and Correction of Likert Scale Multiplicative Response-Style Bias

Individuals may differ in their tendency to fully use the range of a Likert scale. Such individual response styles may have an effect on estimates of correlations. It is shown with simulated data that a relatively simple nonlinear latent model can be used to detect and correct (to some extent) for the bias introduced by differences in multiplicative response styles. A real-world dataset is examined to show that the effect may occur in reality and may lead to biased conclusions.

RBFNN based fixed time sliding mode control for PEMFC air supply system with input delay

Ensuring rapid regulation of the oxygen excess ratio (OER) in proton exchange membrane fuel cells (PEMFC) during load changes is an important challenge. In this paper, fixed time sliding mode control of a PEMFC with input delay has been investigated. First, a simplified fourth-order nonlinear dynamical model with input disturbance and input delay is considered and a cascade structure is selected for the control design. A radial basis function neural network (RBFNN) is designed to estimate the input disturbance. To achieve precise estimation, a Cuckoo Search Algorithm is utilized to calculate the parameters of the RBFNN. Then, a new sliding mode controller is proposed for trajectory tracking within a fixed time. To ensure the effectiveness of the proposed controller, the fixed time convergence of both sliding and reaching phases is investigated and proven. Finally, a robust prediction based sliding mode control is designed for the PEMFC system that by incorporating the disturbance estimation, can eliminate the effect of input delay. The effectiveness and robustness of the proposed controller are validated via comparative simulations. It is noteworthy that this is the first study to propose predictor based control for input delay PEMFCs.

Nonlinear model predictive control for maximum wind energy extraction of semi-submersible floating offshore wind turbine based on simplified dynamics model

The application of floating offshore wind turbines means better exploitation of offshore wind resources. However, the six-degree of freedom motion characteristics of floating platforms bring greater challenges to control system design. Based on the dynamic characteristics of semi-submersible floating offshore wind turbines, this paper establishes a simplified nonlinear dynamic model for control system design. On this basis, a complete framework for nonlinear model predictive control of maximum wind energy extraction for semi-submersible floating offshore wind turbines considering wind and wave disturbances is developed. Based on the previewed wind and wave, a dynamic optimization problem with both state and control constraints is constructed, considering maximum wind energy extraction and torque fluctuation. Then, an improved equilibrium optimizer is proposed to address the nonlinear non-convex dynamic optimization problems, which achieves a better trade-off between exploitation and exploration. Simulation results verify the superiority of the proposed nonlinear model predictive control framework via the improved equilibrium optimizer, and the influences of different control algorithms on the platform motion state, power coefficient, and equivalent wind speed are analyzed.

Numerical modeling of site response at large strains with simplified nonlinear models: Application to Lotung seismic array

Abstract Site response analyses at large strains are routinely carried out neglecting the shear strength of soil and the stiffness degradation due to the increase in pore pressures, leading to unrealistic predictions of the seismic response of soil deposits. The study investigates the performance of a simplified nonlinear (NL) approach, implemented in the Deepsoil code, constituted by coupling a hyperbolic model incorporating shear strength with a strain-based semi-empirical pore pressure generation model. The first part of the study, based on a large one-dimensional parametric study, shows that above a shear strain of 0.1%, it is necessary to include shear strength in the site response modelling to get more realistic results. Then, the approach has been evaluated with reference to the well-known downhole Large-Scale Seismic Test array located in Lotung (Taiwan): numerical results have been compared with recordings in terms of acceleration response spectra and pore water pressure time histories at different depths along the soil profiles. The comparison shows that the NL simplified model is characterized by an accuracy comparable with more sophisticated advanced elasto-plastic NL analyses adopting essentially the same input data of the traditional equivalent linear approaches(shear modulus and damping curves) and simple physical-mechanical properties routinely determined during geotechnical surveys (i.e., shear strength, relative density, fine content). This approach is therefore recommended for site response analyses reaching large strains (i.e., soft soil deposits and moderate-to-high input motions).

Decentralized control of nonlinear complex systems

Abstract In the paper, a novel approach to decentralized controller design for nonlinear systems is introduced. The proposed method is based on the relationship between the stability of complex nonlinear systems and the stability of their subsystems. The design procedure of the decentralized controller consists of three steps. In the first step, the stability of the complex nonlinear system is calculated. In the second step, stability conditions at the subsystem level are obtained such that guarantee the stability of the complex nonlinear system. Finally, in the third step, a controller design method is used to ensure that the subsystem stability conditions obtained in the second step are met. As an example, to better understanding the proposed method two simple nonlinear models are used to demonstrate the effectiveness of the proposed method.

Noise-induced transport in a periodic square-well potential

We investigate a thermal ratchet based on a Brownian particle in a spatially periodic square-well potential driven by a time-dependent square-wave signal. In this model, we rock the Brownian particle between two square-well potentials tilted in opposite directions to induce a net current. Employing the Stratonovich formula and an independent approach using suitable boundary conditions and a normalization condition, we obtain an exact expression for the current in the adiabatic limit, and we observe that there are optimal values of various parameters at which the current can be maximized. In several parameter regimes, our simple non-linear model displays a behavior distinct from some other models of a rocked ratchet. For example, a reversal in the current direction is observed as the square-wave signal’s amplitude or the thermal bath’s temperature is varied. However, under similar conditions, no such current reversal was seen in the case of a periodically rocked Brownian motor in a sawtooth or a smooth potential. Furthermore, unlike the latter type of rocked Brownian motors, the square-well model yields zero current in the deterministic limit, as thermal energy is indispensable for the functioning of the motor.

Non-Fourier heat and mass transport enhancement by hybrid nanofluid-flow over a non-linearly stretchable surface having variable thickness

This article uses non-classical Fick's law, non-Fourier's law, and conservation laws for mass and thermal transport. The hybrid nanoparticles Cu and Al2O3 are considered. The new correlations among the thermo-physical properties of base fluid, Cu and Al2O3 are coupled with simplified nonlinear mathematical models. The resulting models are solved numerically by the finite element method (FEM). The linear shape functions are chosen for the approximation of residual equations. This approximation leads to a nonlinear algebraic system that is linearized by the Picard scheme. The numerical results are ensured to be grid-independent, and convergence is analyzed. The results are validated, and an excellent agreement is obtained between available benchmarks and current outcomes. Thermal solutal relaxation phenomena are responsible for a significant reduction in the transport of heat and mass in Newtonian fluids. These non-Fourier's and non-classical Fick's laws are capable of capturing thermal and solutal elastic phenomena, respectively. Cu and Al2O3 simultaneously act as good conductors of heat, and their simultaneous dispersion in base fluid results in a significant rise in thermal conductivity. Numerical experiments have shown that the transport of heat can be optimized by simultaneous suspension of Cu and Al2O3.

Diagnosis of Voltage Losses of the Proton Exchange Membrane Water Electrolyzer with Nonlinear Frequency Response Method

Proton exchange membrane water electrolyzer (PEMWE) takes a central place in the hydrogen economy as a crucial technology for green hydrogen production. However, this technology still faces challenges, such as the cost of the materials, performance losses at high current densities, and durability. To overcome these obstacles, better comprehension of the phenomena occurring in the PEMWE is necessary. Typical electrochemical methods, such as polarization curves and high-frequency response measurements, lack detailed information about the individual contributions to the overall voltage losses and cannot point out the causes of the performance shortcomings. Therefore, the development of advanced diagnosis techniques for PEMWE is of importance both for the state of health analysis during the operation, as well as for the testing of new materials.In this work, a nonlinear frequency response (NFR) method was applied for the diagnosis of a lab-scale PEMWE. The NFR method represents an extension of the electrochemical impedance spectroscopy to the nonlinear domain by investigating the second-order frequency response function (FRF) in addition to the first-order FRF (equivalent to the impedance) [1]. Typical features corresponding to processes occurring in the PEMWE were observed in both the first- and the second-order FRFs. The experimental observations were interpreted based on a simple nonlinear model. The features observed at frequencies higher than 0.1 Hz were attributed to the electrochemical half-reactions, while a high current density feature observed at lower frequencies, could be attributed to the mass transport. During the analysis, the first-order FRF (impedance) was found not to be sensitive enough for the discrimination of the different sets of parameters and the second-order FRF had to be included for better parameter identification. The obtained parametrized model is dynamic and nonlinear and, thus, it can be utilized for model predictive control of the PEMWE and optimization of the overall green hydrogen production system.[1] Vidaković-Koch, T., Miličić, T., Živković, L.A., Chan, H.S., Krewer, U., Petkovska, M., Cur. Opin. Electrochem., 2021, 30, 100851

Optimal timing of invasive intervention for high-risk non-ST-segment-elevation myocardial infarction patients.

To compare the immediate, early, and delayed percutaneous coronary intervention (PCI) strategies in non-ST-segment-elevation myocardial infarction (NSTEMI) patients with high-risk. Medical records of patients treated at the Daping Hospital, Third Military Medical University, Chongqing, China between 2011 and 2021 were retrospectively reviewed. Only patients with complete available information were included. All patients assigned into three groups based on the timing of PCI including immediate (< 2 h), early (2-24 h) and delayed (≥ 24 h) intervention. Multivariable Cox hazards regression and simpler nonlinear models were performed. A total of 657 patients were included in the study. The median follow-up length was 3.29 (interquartile range: 1.45-4.85) years. Early PCI strategy improved the major adverse cardiac event (MACE) outcome compared to the immediate or delayed PCI strategy. Early PCI, diabetes mellitus, and left main or/and left anterior descending or/and left circumflex stenosis or/and right coronary artery ≥ 99% were predictors for MACE outcome. The optimal timing range for PCI to reduce MACE risk is 3-14 h post-admission. For high-risk NSTEMI patients, early PCI reduced primary clinical outcomes compared to immediate or delayed PCI, and the optimal timing range was 3-14 h post-admission. Delayed PCI was superior for NSTEMI with chronic kidney injury. Delayed invasive strategy was helpful to reduce the incidence of MACE for high-risk NSTEMI with chronic kidney injury. An immediate PCI strategy might increase the rate of MACE.

Validation and Parametric Study of a Soil–Structure Interaction Nonlinear Simplified Model

This paper established a numerical model for the structure system in a soil–structure interaction using MATLAB 23.2 and ANSYS 24.1 software and validated the effectiveness and accuracy of a simplified nonlinear calculation model for soil–structure interaction through the numerical simulation results. Meanwhile, a list of key parameters was identified according to their influence on the simplified model, including the free field area, site soil parameters, equivalent soil area, superstructure size and number of stories, and input seismic waves. On this basis, a series of parametric investigations were carried out with the validated simplified model, by varying the selected key parameters. The research findings demonstrated that the simplified calculation model exhibited excellent accuracy and efficiency, and was capable of reflecting the nonlinear response of the structural system. It is applicable to the field of dynamic response analysis of the superstructure, considering soil–structure interaction.

CGNSDE: Conditional Gaussian neural stochastic differential equation for modeling complex systems and data assimilation

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.

USING ECONOMETRIC MODELS FOR MANAGING DISTRIBUTION PROCESSES

Introduction. The constant increase in competition and rapid changes in market conditions compel various business entities to seek more efficient ways to manage the distribution of goods. In this context, econometric models become an indispensable tool for analysis and forecasting, enabling informed decision-making, optimization of logistics processes, and cost minimization. Objective. The aim of this article is to substantiate effective econometric models for managing the distribution of goods to optimize supply processes, sales, and maximize profits for manufacturers, retailers, and other participants in distribution channels. Methods. The theoretical and methodological basis of the research consists of works by domestic and foreign scientists on the implementation of econometric models for managing business processes, including distribution. The informational basis includes scientific, economic, and reference literature, works of leading domestic and foreign scientists, methodological materials, information portals, and periodicals of Ukraine. A set of methods and approaches were used: system analysis – for studying the role and significance of econometric models for goods distribution and identifying their features; methods of analysis and synthesis – for analyzing and systematizing econometric models and determining the advantages and limitations of their application for goods distribution. Results. The study investigates the role and significance of econometric models for goods distribution. It examines how these models can become a key tool in solving optimization tasks, adapting to changing market conditions, and ensuring competitiveness in a world where distribution strategies turn into strategic advantages. The advantages and limitations of applying such models are identified: simple linear or nonlinear demand models; time series autoregressive model ARIMA; exponentially smoothed model ETS; transportation problem model; Vehicle Routing Problem (VRP); Traveling Salesman Problem (TSP); orienteering problem; conjoint analysis. Conclusions. Based on a comparative analysis of the key aspects of using econometric models for goods distribution, their specific aspects depending on the implementation of particular tasks and needs of the business entity are detailed. The main advantages of applying econometric models in distribution are highlighted, primarily providing the ability to effectively consider a large number of factors affecting distribution processes, along with certain limitations of their use. Among the main benefits are more accurate demand forecasting, which allows for optimizing inventories and supply chain management costs, as well as strategies for warehouse placement, route selection for delivery, etc.

Hyper-Rayleigh Scattering and Third-Harmonic Scattering in Chiral Liquids: Basic Evidences and Differences with Linear Chiroptical Techniques.

Nonlinear chiroptical methods like hyper-Rayleigh optical activity (HROA) and third-harmonic optical activity (THOA) have a great potential in characterizing structure-chiroptical properties of molecular systems. Here, with these methods, we bring for the first time experimental and theoretical evidence of nonlinear chiroptical differences between enantiomers of simple chiral molecules, using exclusively linearly polarized incident light. The origin of these unexpected nonlinear chiroptical contributions comes from a new nonlinear source term of the form βOA(∇×μ(nω)), which is a bilinear coupling term including the linear chirality parameter, βOA, and the curl of the nonlinear induced electric dipole moment, μ(nω), both involving dipolar magnetic interactions. Through a simple nonlinear chiroptical model that we propose, we show that specific nonlinear chiroptical parameters can be quantified, thus bringing new insights into stereochemical and electronic structural features of molecular and supramolecular systems.

Enhanced nonlinear models for critical compressive stress-strain characteristics of rubberized concrete: Comprehensive experimental data and robust evaluation methodology

The integration of rubber aggregate (RA) into concrete presents a pivotal avenue for enhancing the material's sustainability and environmental impact. Despite its potential, a crucial gap persists in the field concerning the development of material models that accurately consider the influence of RA particle size on the stress-strain responses of Rubberized Concrete (RuC). To address this gap, this study explores the effects of incorporating RA into concrete on its ascending compressive stress-strain behavior. In this research, we have compiled a comprehensive database encompassing the compressive stress-strain characteristics of 80 distinct concrete mixes incorporating RA from varied sources, sizes, and attributes. The investigation also evaluated the effectiveness of recent models in predicting key parameters, including modulus of elasticity, peak stress, and strain at peak stress. We proposed more robust models to accurately capture essential features. Notably, the findings suggest that higher RA content leads to dispersed cracks and decreased stiffness, resulting in lower peak stress and strain. Moreover, compressive strength exhibits notable variations with RA content, with significant drops observed across both normal and high-strength concrete mixes. The performance evaluation of existing models underscores the superiority of Li et al.'s model for peak stress prediction and Abbara et al.'s model for elasticity modulus prediction. The proposed simplified nonlinear models in this research offer enhancements over existing ones, promising more accurate predictions. These findings have profound implications for the optimization of rubberized concrete mixes and pave the way for future research directions aimed at further refining predictive models and advancing the application of RA in concrete technology.

Simplified nonlinear model and 3D printing model experiment verification of longitudinal joints of shield tunnel segments

The segment joints represent vulnerable and core-bearing areas within shield tunnel structures. Their flexural stiffness, starting from the contact surface of longitudinal joints to the bolt hole, exhibits continuous changes under bending loads, typically demonstrating nonlinear mechanical characteristics. This study investigates the influence of joint contact surfaces on flexural stiffness, extending from the joint contact surface to damaged concrete in the compressed zone. A new simplified model for the variable nonlinear stiffness of longitudinal segment joints in shield tunnels is proposed, considering the flexural stiffness of the joint contact surface and the width of the damaged concrete zone in the segment ring while simulating the flexural stiffness decay induced by the opening of segment joints. Based on the minimum potential energy principle, a design calculation method for joint flexural stiffness is derived, establishing the nonlinear bending stiffness coupling relationship between the segment and the joint. Through similarity theory, 3D printing technology, and indoor loading tests, the theoretical model's accuracy regarding tunnel segment joints is verified. This theoretical model provides a basis for designing and assessing the performance of tunnel-segment joints.

A new simple masing-type soil nonlinear model considering modified damping and its application on KiK-net site response

In this paper, a series of simple Masing rules is first proposed for best fitting the shear modulus reduction and the damping ratio curves of soil based on the extended Masing rules and hysteretic damping formulation. A new masing-type nonlinear model is established and implemented in ABAQUS software based on the Matasovic back-bone curve and the new proposed Masing rules. To validate the practical applicability of the new model, the 1-Directional 3-Component nonlinear site response analysis for station KSRH10 (in Hamanaka, Hokkaido, Japan) is conducted. The numerically predicted results of the proposed nonlinear model are in excellent agreement with the recordings. The surface peak ground acceleration obtained by ABAQUS agrees well with the recording, which has a little difference of about 8.3% on average. The comparison between the proposed nonlinear model and the DEEPSOIL model indicate that the results of the former match better with recording to some extent, in term of acceleration time histories, spectral acceleration (SA) curves, and peak ground acceleration (PGA). The mean square error of acceleration time histories and SA curves obtained by the proposed model is smaller than the model in DEEPSOIL. The agreement with recording is improved by 10.8% compared with the DEEPSOIL model.

Structural condition assessment with structural health monitoring systems and nonlinear simplified models

Structural condition assessment with structural health monitoring systems and nonlinear simplified models

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

To better understand the mechanisms underlying the formation of blocking highs over the North Atlantic as a type of large-amplitude disturbance, this paper reports results from numerical experiments within the framework of local finite-amplitude wave activity (LWA). The numerical model employed in this study explicitly depicts two important atmospheric internal dynamic processes—nonlinear zonal eddy flux and Rossby wave packet propagation—which have been individually emphasized by different previous studies. The simulation results reveal that these two dynamic processes are the dominant contributors to the formation of Atlantic blocking cases. However, they exert different influences over different regions. The southern and northern parts of the primary LWA associated with the blocking cases are mainly induced by the nonlinear zonal eddy flux and Rossby wave packet propagation, respectively. Thus, this study reconciles and integrates insights from previous studies on Atlantic blocking events, providing a cohesive understanding of their formation.摘要为研究北大西洋阻高的形成机制, 本文在局部有限振幅波活动 (LWA) 框架下进行了一系列数值实验. 采用的数值模型能显式地描绘出两种重要的大气内部动力过程, 即非线性纬向位涡通量和Rossby波包传播. 模拟结果显示, 这两种动力学过程均是形成大西洋阻高的重要机理. 具体地, 非线性纬向位涡通量和Rossby波包传播, 分别是大西洋阻高南部和北部LWA形成的主导因子. 因此, 本研究综合了前人关于大西洋阻高的研究成果, 为其形成机理提供了新的认识.

A two-level MPC method for the operation of a gas pipeline system under demand variation

A gas pipeline system is in an almost continual state of transition due to changing gas demand. A control method is required to keep a gas pipeline operating in an energy-saving status and provide reliable transmission service for the customers. Model predictive control (MPC) predicts the future states of a system, making it suitable for following gas demand changes. However, to avoid computation time challenges associated with formulating the MPC problem as a large-scale MINLP, an online two-level MPC system is proposed, comprising an upper-level economic MPC (EMPC) and a lower-level tracking MPC (TMPC). EMPC adopts energy cost as the objective function and utilizes a simplified nonlinear model to address long-horizon optimization, while TMPC tracks the status optimized in EMPC, to find the optimal output pressure and the on-off status of the compressors and compressor stations. The performance of the method is demonstrated through application to case studies.

Simple Nonlinear Numerical Modeling for Unreinforced and FRP-Reinforced Masonry Domes

This paper presents a new method to model the nonlinear behavior of double-curvature masonry structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. The method is meant to be used in professional design, especially for assessment and retrofitting purposes, based on the exploitation of the simplest nonlinear finite elements available in commercial software, namely, trusses with elasto-fragile and elasto-ductile behavior (Cutoff Bars, according for instance to the definition provided by Strand7 R3.1.3a). Numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and by lumping nonlinearities on joints. These are assumed, in turn, to be elastic–brittle and elastic–plastic by using 1D elements, namely, Point Contacts, under the No-Tension Material hypothesis, and Cutoff Bars, respectively, assigning a small tensile resistance to the material. The reinforcement, realized with FRP hooping strips, is successfully modeled in a similar fashion, i.e., by applying perfectly bonded elastic–plastic Cutoff Bars at the extrados of the dome, where debonding is accounted for in a conventional way, limiting the tensile strength according to Italian Standards’ indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison. After an in-depth analysis of the obtained results, in terms of capacity curves, the robustness and accuracy of the proposed approach are assessed.