Nonlinear Behavior Research Articles

Enhancing prior-knowledge-based control with deep attention neural network for outlet moisture content of cut-tobacco

Monitoring and controlling the drying process is crucial, particularly for rotary dryers, to ensure optimal quality and efficiency. However, due to the process’s nonlinear behavior, delays, and input disturbances, achieving this can be quite challenging. Previous research has not adequately explored online forecasting for rotary dryer control in real production settings. To bridge this gap, our study focuses on tobacco drying in an actual plant and presents a novel online prediction model for moisture content. We conducted comparative experiments to validate the model’s practical application in production settings and demonstrate its effectiveness in enhancing drying control. Our approach, called MCTFormer, has proven to be scalable to high-dimensional problems. The results of our study indicate a 45% improvement in product quality through accurate prediction of outlet moisture content, better control over moisture levels, and reduced energy consumption.

Linear and Nonlinear Isotherm, Kinetic, and Thermodynamic Behavior of Safranine T Adsorption Using Porous Geopolymer Prepared from Coal Fly Ash Wastes

Linear and Nonlinear Isotherm, Kinetic, and Thermodynamic Behavior of Safranine T Adsorption Using Porous Geopolymer Prepared from Coal Fly Ash Wastes

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

Nonlinear Soil–Pile–Structure Interaction Behaviour of Marine Jetty Structures

Nonlinear soil–pile–structure interaction (SPSI) phenomena are known to play a vital role in the response of bottom-fixed marine structures. For such structures, these phenomena are commonly considered by the imposition of p-y, τ-z, and q-z springs, representing the lateral and axial shaft and axial base soil resistances, respectively. The importance of each resistance mechanism depends on the type of foundation system, with only very limited studies investigating their roles in the response of piled marine structures, such as jetties. Within this context, this study presents numerical three-dimensional pushover analysis results for two marine jetties, a smaller model with four piles and a larger model supported by twenty-four piles. SPSI effects are considered through p-y, τ-z, and q-z springs, the behaviours of which are determined by following commonly employed procedures. The structures’ responses are investigated under the influence of various assumptions regarding the behaviours of springs, as well as steel plasticity. The current investigation underscores the substantial influence of the axial soil–pile interaction on the response of the jetty, particularly in terms of its failure mode. Moreover, it demonstrates the importance of incorporating p-y springs, even though the choice between their linear or nonlinear constitutive behaviour is found to be less critical. Finally, the study concludes that the behaviours of the springs significantly affect the system’s ductility and the degree of steel yielding in the piles, while also highlighting the unconservative influence of neglecting SPSI phenomena.

Twinning quality sensors in wastewater treatment process via optimized echo state network-based soft sensors

The presence of a large amount of quality-related but hard-to-measure variables usually makes effective monitoring of industrial processes difficult, and even impossible. Soft computing techniques and digital twins can revolutionize standard approaches to solve this issue, even though industrial data are frustrated by nonlinearity, disturbances, and dynamic behaviors. In this light, this paper proposes a data-driven soft sensor with the help of the Fourier amplitude sensitivity test (FAST) and improved probabilistic regularized echo state network (IPRESN), then to twin the quality hardware sensors. Within this framework, the initial step is to rely on the FAST method to measure the collaborated importance of multiple process variables with respect to each quality variable. This quantification facilitates the selection of auxiliary variables for the training of IPRESN. Furthermore, a probabilistic regularization method is learned to improve the robust performance of the echo state network (ESN) by re-designing a new objective function to minimize the mean and variance of the modeling error. Additionally, the whale optimization algorithm (WOA) is improved and then used to optimize the critical hyper-parameters of ESN, thus mitigating the risks associated with suboptimal hyperparameter selection. The effectiveness of the proposed method is verified through a Benchmark Simulation Model 2 (BSM2) and a full-scale wastewater treatment plant data set. The findings show the potential of the proposed method in facilitating digital twin implementations for hardware sensors.

Multicomponent nonlinear fractional Schrödinger equation: On the study of optical wave propagation in the fiber optics

In this article, we investigate the soliton wave dynamics of the fractional three-component coupled nonlinear Schrödinger equation. This equation is considered as a fundamental tool for describing the behavior of optical pulses in optical fibers. There is increasing interest in studying these equations as they can be used to explain a wide range of complex physical phenomena in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. In order to obtain the required solutions, the first step is to apply the complex wave transformations with β-fractional derivative to obtain the nonlinear ordinary differential equations of the governing model. Furthermore, by applying the novel integration methods known as generalized Arnous method and multivariate generalized exponential rational integral function approach, different type of soliton solutions are extracted. Different sets and values of the physical parameters are used to study the optical soliton solutions of the studied system. Based on a comparative analysis of our results with existing techniques, this study concludes that our proposed solutions are novel. The results described in this work are able to enhance the nonlinear dynamical behavior of a given system and confirm the effectiveness of the methods used. Furthermore, the different graphs are sketched to visualize the solutions behavior with various parametric values. It is anticipated that obtained solutions will be significant in the study of wave propagation and other related fields.

Nonlocal strain gradient-based nonlinear vibration analysis of nonlinear FG three-phase HJCNT/MWCNT/epoxy composite microbeam resonators using a modified micromechanical model

This paper aims to study nonlinear dynamic behavior of functionally graded (FG) three-phase composite microbeam resonators made of an epoxy matrix and two reinforcements namely multi-walled carbon nanotubes (MWCNTs) and hetero-junction carbon nanotubes (HJCNTs). The effective mechanical properties of the composite microbeam are obtained using the modified Halpin-Tsai micromechanical model. The microbeam surrounding medium is simulated using a two-parameter elastic foundation. The von-Karman’s geometric nonlinearity relations are incorporated and the equations of motion are derived based on the nonlocal strain gradient Euler–Bernoulli beam model. A new closed-form analytical solution is obtained using the homotopy perturbation method. The effects of vibration amplitude, nanofiber volume fraction, nanofiber distribution pattern, small-scale parameters and the foundation parameters on the nonlinear frequency and deflection of the FG three-phase composite microbeams are studied in detail. The findings of the paper are valuable for researchers in the field of microbeam resonators.

Harvesting vibration energy by quad-stable piezoelectric cantilever beam: Modeling, fabrication and testing

The combination of beams with piezoelectric patches has become a prevalent energy harvesting tool due to its ease of use. Typical energy harvesting systems are usually linear, and their efficiency is not satisfying due to low-frequency bandwidth. In this paper, a quad-stable piezoelectric vibration energy harvester is analyzed both numerically and experimentally. The primary purpose of this investigation is to analyze the static and dynamic characteristics of a proposed quad-stable system to consider its potential for application in broadband energy harvesting comprehensively. The harvester system consists of a slotted cantilever beam, a piezoelectric patch, a pair of tip-mass blocks, and a double-sided clip. The cantilever beam is subjected to pre-displacement constraints made by a mutual self-constraint at the free end of it. The nonlinear behaviors of the harvester system, including snap-through and softening phenomena, are analyzed using the assumed modes and finite element method (FEM). The harvester's vibration equation is solved numerically and through an FE model which is made by an in-house finite element software. A prototype is designed and fabricated to validate the mathematical model and FE simulation. The experimental force-displacement diagram of the harvester displays distinct discontinuities, reflecting abrupt transitions occurring while switching its stable states. The prototype dynamics are analyzed by harmonic base excitation with different amplitude levels in two conditions, including the presence and absence of the piezoelectric patch. The results obtained from the mathematical and FEM model demonstrate a satisfactory correlation with the experimental data. Furthermore, the experimental data reveal the occurrence of the snap-through phenomenon, accompanied by a significant widening of the frequency bandwidth at relatively high amplitude levels. The system has the ability to provide an average output electrical power of 0.288 mW for an electrical resistance of 3.262 kΩ at the excitation frequency of 12.695 Hz and base acceleration amplitude of 3g.

Evaluation of the Influence of Bolt Fastener Spacing on the Elastic Critical Load from the Lateral-Torsional Buckling Condition of Built-Up Bending Members.

In an experimental study of two-branched beams bent transversely about the major stiffness axis, the elastic critical load from the lateral-torsional buckling condition was determined. The tests were conducted on simply supported two-branch beam models with a built-up section consisting of two cold-formed channel members (2C) bolted back-to-back. The bolts were located at the mid-height of the built-up cross-section. Five groups of members differing in longitudinal bolt spacing were examined. The models were gravitationally loaded (using ballast) at the centre of the beam span. This approach eliminated the undesirable effect of the lateral support of the beam, e.g., by the actuator head. The critical load, measured by the concentrated transverse force (Pz,cr), was determined using the modified Southwell method. It has been experimentally shown that, in built-up beams, there is an influence of bolt spacing on the elastic critical load from the lateral-torsional buckling condition. The lowest critical load capacity and the most non-linear behaviour of the built-up member were observed in beams bolted with only three bolts (at the supports and in the middle of the span). However, the experimental results obtained in this study show that increasing the number of bolts above a certain level (in the case of the tested models, it was seven bolts) does not result in a further increase in the critical load, which is a surprising result. The obtained values were 15 to 23% lower than the critical load determined numerically by the finite element method (LTBeamN) for an analogous element with a uniform I-section.

Revisiting Aerosol–Cloud Interactions From Weekly Cycles

AbstractWeekly cycles (WCs) in cloud properties have been reported and linked to aerosol effects. Yet the extent to which human activities contribute to their occurrence remains unclear. Here, we revisit aerosol–cloud interactions from the WCs over central Europe using long‐term satellite and reanalysis data. Significant WCs in aerosol and cloud droplet number concentration (Nd) are detected with minima/maxima on Monday/Friday, indicating a clear signal of the Twomey effect. Notably, Nd–to–aerosol sensitivity from WCs is found to decrease at larger aerosol concentrations, confirming the nonlinear behavior of the aerosol–Nd relation (in log–log space) reported previously, but from a distinct perspective. Nevertheless, no discernible WCs in liquid water path are found. The pronounced WCs in cloud cover are demonstrated to be driven by natural variability. Our results indicate that the WCs offer a useful pathway for investigating the Twomey effect, but are not as effective for detecting cloud adjustments.

Machine learning-based uncertainty analysis in power system planning: Insights and pathways for decarbonization

This study performs an extensive uncertainty analysis of decarbonization pathways for the Canadian power system. By leveraging machine learning (ML) techniques, we represent complexities and nonlinear behaviors of the power system, which are challenging to observe using traditional modeling methods due to computational limitations. We further utilize K-means clustering and statistical methods to identify correlations, investigate the effects of uncertainty in key parameters (capital costs, demand, and carbon tax), and identify opportunities for diversification of the power generation mix. Key findings include the increased flexibility of gas combined cycle (generation mean 4.8 TWh, installed capacity mean 4.8 GW) over gas simple cycle (generation mean 22.3 GWh, 0 installed capacity) in response to carbon tax, highlighting its role in a low-carbon future. Variations in solar and wind deployment rates, influenced by capacity factors and location-specific costs, underscore the necessity of a flexible grid system. This analysis reveals important correlations between renewable deployment, and transmission expansion and gas combined cycle reliance. The results also highlight minimal sensitivity of hydroelectric power generation (∼ 43 % of scenarios) to changes in input parameters. The novelty of our work lies in proposing a comprehensive approach which uses ML techniques to go beyond the capabilities of existing models, specifically by performing extensive uncertainty analysis and provides key insights into system behavior, causative factors, and an expanded breadth of potential pathways. Taken together, this proposed approach lays a foundation for strategic planning and policy formulation.

Nonlinear wave propagation in homogenized strain gradient 1D and 2D lattice materials: Applications to hexagonal and triangular networks

AbstractThis work aims to analyze the propagation of fully nonlinear waves, encompassing shear, extension, and bending deformation modes, within homogenized periodic nonlinear hexagonal and triangular networks, successively considering 1D and 2D situations. The wave analysis is conducted from the expression of the effective strain energy density of periodic hexagonal and triangular lattices in the nonlinear regime by a continualization of the discrete lattice equations, considering all forms of energy. We incorporate strain gradient effects into the continuous model to account for the wave‐dispersive nature. The resulting second‐gradient nonlinear continuum exhibits subsonic and supersonic propagation modes. We first examine in a 1D situation the dynamical response of the hexagonal and triangular lattices, considering varying levels of nonlinearity quantified by a single scalar valued parameter. We further evaluate the impact of a fully nonlinear analysis compared to an analysis solely based on the shear energy, regarding both supersonic and subsonic modes. The nonlinear wave propagation analysis is then extended to a 2D situation for the same two lattices. It is shown that the longitudinal mode exhibits a higher frequency at a low degree of nonlinearity; however, as the degree of nonlinearity increases, the shear mode surpasses the longitudinal mode in terms of frequency. As the wavenumber increases, the nonlinearity has a lesser impact on the frequency behavior, and the phase velocity is more influenced by other factors, such as the second gradient contributions of the effective constitutive law. Such a behavior indicates a transition from a highly nonlinear behavior at lower wave numbers to a more linear behavior at higher wave numbers.

Dynamics of novel soliton and periodic solutions to the coupled fractional nonlinear model

This study secures the soliton solutions of the (2+1)-dimensional Davey–Stewartson equation (DSE) incorporating the properties of the truncated M-fractional derivative. The DSE and its coupling with other systems have extensive applications in many fields, including physics, applied mathematics, engineering, hydrodynamics, plasma physics, and nonlinear optics. Various solutions, such as dark, singular, bright-dark, bright, complex, and combined solitons, are derived. In addition, exponential, periodic, and hyperbolic solutions are also generated. The newly designed integration method, known as the modified Sardar subequation method (MSSEM), has been applied in this study for extracting the solutions. The approach is efficient in explaining fractional nonlinear partial differential equations (FNLPDEs) by confirming pre-existing solutions and producing new ones. Furthermore, we plot the density, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The outcomes of this work indicate the effectiveness of the method utilized to improve nonlinear dynamical behavior. We anticipate that our work will be helpful for a large number of engineering models and other related problems.

Developing a scalable analytical framework for predicting the contact behavior of elastic rings against rigid surfaces

An elastic ring interacting with rigid surfaces is a fundamental engineering challenge with vast practical implications in various disciplines. However, the exploration of closed-form solutions for this issue has been limited, and existing studies often present complex, numerically unstable solution methods influenced by specific boundary conditions. Furthermore, the lack of scalable design principles for the ring-in-contact scenario has hindered its broader application across different geometries and materials. This study introduces a streamlined analytical and numerical approach to predict the contact behavior of orthotropic rings against centrosymmetric rigid surfaces, encompassing both flat and curved surfaces. Our approach, which simplifies the closed-form solution for extensible Timoshenko curved beams coupled with a contact algorithm that prevents penetration, yields robust and accurate predictions of nonlinear contact behaviors in elastic rings, including deformation patterns, contact angles, stresses, and stiffness. Additionally, we present a design map that serves as a scalable guideline for engineering elastic rings in contact, facilitating the choice of geometry and materials, such as ring radius, thickness, and elastic moduli. This research enhances the theoretical underpinnings of elasticity concerning ring contact and expands the engineering viewpoint on designing elastic rings in various contact scenarios.

Physics-based discrete models for magneto-mechanical metamaterials

Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials by combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implementing it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetically-driven smart structures, such as soft robots.

Characterization of pressure-dependent nonlinear bending behavior of yarns and its application in modeling the compression of 2D woven fabrics

This paper investigates the pressure-dependent nonlinear bending behavior of yarns, which is essential for the application of the virtual fiber modeling (VFM) method in the mechanical analyses of fabrics. An experimental method, along with a theoretical model based on classical beam theory, is presented to characterize the varying bending stiffness of yarns under different pressures. A tailored beam user element is then developed, incorporating the nonlinear bending behavior and combined with a truss element to create a physics-based virtual fiber formulation. Utilizing this formulation, the original kinematic VFM method is extended for modeling the mechanical response of 2D woven fabrics under compression. The predicted results of the proposed model closely match the reported experiment, demonstrating the significance of introducing the nonlinear bending behavior of yarns. This method can be a valuable tool for the fabric compression process and generating realistic mesoscale geometries for textile composites.

Nonlinear Static and Dynamic Responses of a Floating Rod Pendulum

Abstract A novel nonlinear dynamics model is developed in this paper to describe the static and dynamic nonlinear behaviors of a rod pendulum partially immersed in still water. The pendulum is hinged above the water level and subject to nonlinear gravity, hydrostatic, and hydrodynamic loads, all of which are incorporated into the system dynamics. The nonlinear static behavior and stability of the pendulum have been characterized by analyzing the fixed points. It is found that Pitchfork bifurcation governs the relationship between the rod density (the control parameter) and the static equilibrium angle. The pendulum's nonlinear response to external harmonic torque is obtained using Harmonic Balance Method (HBM). The influence of system parameters, including hinge height, rod diameter, and rod density, on the nonlinear frequency response is examined. Upon altering the system parameters, particularly the rod density, it is found that the system exhibits either a softening or a hardening effect.

A bi-fidelity DeepONet approach for modeling hysteretic systems under uncertainty

This study proposes a multi-fidelity paradigm for developing surrogates of degrading hysteretic systems under uncertainty through the use of deep operator networks (DeepONets). Instead of attempting to directly train a DeepONet on the original response, this study adopts a residual modeling approach wherein the DeepONet is trained on the discrepancy between the original (high-fidelity) data source and a relatively simpler (low-fidelity) representation of the system. Within these examples, a conventional Bouc-Wen model is treated as a “low-fidelity” representation given that it is free of any further assumptions about the nonlinear behavior, while the “high-fidelity” data is generated from different structures with various forms of complex hysteretic behavior. The results of this study show that the proposed multi-fidelity approach consistently outperforms standard surrogates trained on only the original datasets considering a variety of systems with unknown parameters. The results also show that the difference in performance grows as training data becomes more scarce, a critical consideration for many real-world engineering systems, and that the proposed multi-fidelity approach maintains its performance edge even when controlling for training time and noise in the training data.

Effect of temperature and pre-stretch on the dynamic performance of dielectric elastomer minimum energy structure

Dielectric Elastomer Minimum Energy Structures (DEMES) have the ability of actively adjusting their shape to accommodate complex scenarios, understanding the actuation mechanism of DEMES is essential for their effective design and control, which has rendered them a focus of research in the field of soft robotics. The actuation ability of DEMES is usually influenced by external conditions, among which the electromechanical properties of DE materials are highly sensitive to temperature changes, and the pre-stretch ratio of DE materials has a significant impact on the dynamic performance of DEMES. Therefore, it is necessary to study the effects of temperature and pre-stretch ratio on the nonlinear dynamic behavior of DEMES. In this paper, in response to the lack of research on the influence of DE pre-stretch ratio on the actuation characteristics of DEMES, this paper proposes a systematic modeling and analysis framework that comprehensively considers pre-stretch factors, temperature factors, and viscoelastic factors, and establishes the motion control equation of DEMES affected by the coupling effect of DE pre-stretch ratio and temperature. The proposed analytical framework is used to analyze the evolution of the electromechanical response of DEMES under voltage excitation under the coupling of DE pre-stretch ratio and temperature. The results indicate that the bending angle, inelastic deformation, resonant frequency, and dynamic stability of DEMES can be jointly adjusted by the DE pre-stretch ratio and ambient temperature. A low pre-stretch ratio of DE can lead to dynamic instability of DEMES, while appropriate temperature conditions and higher pre-stretch ratios can significantly improve the actuation ability of DEMES. This can provide theoretical guidance for the design and deformation control of DEMES.

Explainable artificial intelligence in breast cancer detection and risk prediction: A systematic scoping review.

With the advances in artificial intelligence (AI), data-driven algorithms are becoming increasingly popular in the medical domain. However, due to the nonlinear and complex behavior of many of these algorithms, decision-making by such algorithms is not trustworthy for clinicians and is considered a black-box process. Hence, the scientific community has introduced explainable artificial intelligence (XAI) to remedy the problem. This systematic scoping review investigates the application of XAI in breast cancer detection and risk prediction. We conducted a comprehensive search on Scopus, IEEE Explore, PubMed, and Google Scholar (first 50 citations) using a systematic search strategy. The search spanned from January 2017 to July 2023, focusing on peer-reviewed studies implementing XAI methods in breast cancer datasets. Thirty studies met our inclusion criteria and were included in the analysis. The results revealed that SHapley Additive exPlanations (SHAP) is the top model-agnostic XAI technique in breast cancer research in terms of usage, explaining the model prediction results, diagnosis and classification of biomarkers, and prognosis and survival analysis. Additionally, the SHAP model primarily explained tree-based ensemble machine learning models. The most common reason is that SHAP is model agnostic, which makes it both popular and useful for explaining any model prediction. Additionally, it is relatively easy to implement effectively and completely suits performant models, such as tree-based models. Explainable AI improves the transparency, interpretability, fairness, and trustworthiness of AI-enabled health systems and medical devices and, ultimately, the quality of care and outcomes.