Nonlinear Model Research Articles

Bifurcation analysis and soliton solutions to the doubly dispersive equation in elastic inhomogeneous Murnaghan's rod.

The doubly dispersive (DD) equation finds extensive utility across scientific and engineering domains. It stands as a significant nonlinear physical model elucidating nonlinear wave propagation within the elastic inhomogeneous Murnaghan's rod (EIMR). With this in mind, we have focused on the integration of the DD model and the modified Khater (MK) method. Through the wave transformation, this model is effectively converted into an ordinary differential equation. In this paper, the goal of our work is to explore new wave solutions to the DD model by using the MK scheme. These solutions provide extremely helpful insights into the operation of the system. The three-dimensional (3D) plot and two-dimensional (2D) combined plot via the impacts of the parameters are provided for various parameters in this manuscript. We also discussed the dynamical properties of the model, which are accomplished through the bifurcation analysis, and also found the Hamiltonian function. This research makes a substantial contribution to the area by increasing our understanding of wave solutions in the DD, introducing novel investigation tools, and carrying out an in-depth investigation of the bifurcation and stability aspects of the system. As a direct result of this research, novel openings have been uncovered for further investigation and application in the various disciplines of science and engineering.

Optimal emergency hospitals construction in an unexpected epidemic with considering the interactive effect

AbstractConstructing emergency hospitals is one of the most critical measures to defeat an unexpected epidemic. However, existing operations research (OR) studies rarely consider the interactive effect between the construction of emergency hospitals and the dynamics of epidemic transmission. Inspired by this gap, we propose a new modeling framework for decision‐making in emergency hospital construction. In our optimization model, we address the pandemic evolution functions as constraints. We also consider the heterogeneity among infected individuals, distinguishing between those with mild and severe symptoms, each requiring treatment in different types of emergency hospitals. We formulate the problem as a mixed integer nonlinear programming model. Our model can envision the current and future evolution of the epidemic and the impact of different decisions regarding emergency hospital construction on epidemic development. Simultaneously, it provides the optimal strategy to build hospitals and minimize the total number of untreated patients due to the disease. The proposed model is tested using the Covid‐19 outbreak case in Wuhan. The results can provide precise guidelines for emergency hospitals construction, including timing and capacity, and offer decision boundaries for policymakers considering the uncertainty of disease transmission. Furthermore, our decision‐making framework is general and can be adapted to study other epidemics.

Graph-enhanced deep material network: multiscale materials modeling with microstructural informatics

AbstractThis study addresses the fundamental challenge of extending the deep material network (DMN) to accommodate multiple microstructures. DMN has gained significant attention due to its ability to be used for fast and accurate nonlinear multiscale modeling while being only trained on linear elastic data. Due to its limitation to a single microstructure, various works sought to generalize it based on the macroscopic description of microstructures. In this work, we utilize a mechanistic machine learning approach grounded instead in microstructural informatics, which can potentially be used for any family of microstructures. This is achieved by learning from the graph representation of microstructures through graph neural networks. Such an approach is a first in works related to DMN. We propose a mixed graph neural network (GNN)-DMN model that can single-handedly treat multiple microstructures and derive their DMN representations. Two examples are designed to demonstrate the validity and reliability of the approach, even when it comes to the prediction of nonlinear responses for microstructures unseen during training. Furthermore, the model trained on microstructures with complex topology accurately makes inferences on microstructures created under different and simpler assumptions. Our work opens the door for the possibility of unifying the multiscale modeling of many families of microstructures under a single model, as well as new possibilities in material design.

Wavelet Feature Screening

An initial screening of which covariates are relevant is a common practice in high-dimensional regression models. The classic feature screening selects only a subset of covariates correlated with the response variable. However, many important features might have a relevant albeit highly nonlinear relation with the response. One screening approach that handles nonlinearity is to compute the correlation between the response and nonparametric functions of each covariate. Wavelets are powerful tools for nonparametric and functional data analysis but are still seldom used in the feature screening literature. We propose a wavelet feature screening method that can be easily implemented, and we prove that, under suitable conditions, it captures the true covariates with high probability. Simulation results also show that our approach outperforms other screening methods in highly nonlinear models. We apply feature screening to two datasets about ozone concentration and epilepsy. In both applications, the proposed method selects features that match findings in the literature of their respective research fields, illustrating the applicability of feature screening. Supplementary material for this article is available online.

A Fast Feedforward Small-World Neural Network for Nonlinear System Modeling.

It is well-documented that cross-layer connections in feedforward small-world neural networks (FSWNNs) enhance the efficient transmission for gradients, thus improving its generalization ability with a fast learning. However, the merits of long-distance cross-layer connections are not fully utilized due to the random rewiring. In this study, aiming to further improve the learning efficiency, a fast FSWNN (FFSWNN) is proposed by taking into account the positive effects of long-distance cross-layer connections, and applied to nonlinear system modeling. First, a novel rewiring rule by giving priority to long-distance cross-layer connections is proposed to increase the gradient transmission efficiency when constructing FFSWNN. Second, an improved ridge regression method is put forward to determine the initial weights with high activation for the sigmoidal neurons in FFSWNN. Finally, to further improve the learning efficiency, an asynchronous learning algorithm is designed to train FFSWNN, with the weights connected to the output layer updated by the ridge regression method and other weights by the gradient descent method. Several experiments are conducted on four benchmark datasets from the University of California Irvine (UCI) machine learning repository and two datasets from real-life problems to evaluate the performance of FFSWNN on nonlinear system modeling. The results show that FFSWNN has significantly faster convergence speed and higher modeling accuracy than the comparative models, and the positive effects of the novel rewiring rule, the improved weight initialization, and the asynchronous learning algorithm on learning efficiency are demonstrated.

Non-Linear Creep-Relaxation Constitutive Damage Model for Aging Concrete

A thermodynamic constitutive damage model for plain concrete, and other quasi-brittle aging materials, under creep relaxation is developed. The model accounts for the anisotropic damage induced through a second-order tensor damage variable. The aging viscoelasticity of the material is considered through the theory of solidification for aging solidifying materials. The material is considered a viscoelastic-damageable material. The Helmholtz free energy, utilized in the formulation, is treated based on the representation theorem of coupled damage strain tensors and Volterra integral equations. The model can analyze time-dependent damage (tertiary creep) under constant loading and can account for damage due to cyclic creep. Theoretical case studies are considered to illustrate the applicability of the model. The determination of the functions and constants, representing the material behavior, as well as any experimental companion is proposed for further research.

Tenofovir, emtricitabine, lamivudine and dolutegravir concentrations in plasma and urine following drug intake cessation in a randomized controlled directly observed pharmacokinetic trial to aid point-of-care testing.

Poor adherence to ART and pre-exposure prophylaxis (PrEP) can impact patient and public health. Point-of-care testing (POCT) may aid monitoring and adherence interventions. We report the pharmacokinetics of tenofovir [dosed as tenofovir disoproxil (TDF) and tenofovir alafenamide (TAF)], emtricitabine (FTC), lamivudine (3TC) and dolutegravir (DTG) in plasma and urine following drug cessation to evaluate adherence targets in urine for POCT. Subjects were randomized (1:1) to receive DTG/FTC/TAF or DTG/3TC/TDF for 15 days. Plasma and spot urine were collected on Day 15 (0-336 h post final dose). Drug concentrations were quantified using LC-MS, and non-linear mixed-effects models applied to determine drug disposition between matrices and relationship with relevant plasma [dolutegravir protein-adjusted 90% inhibitory concentration (PA-IC90 = 64 ng/mL) and minimum effective concentration (MEC = 324 ng/mL)] and urinary thresholds [tenofovir disoproxil fumarate 1500 ng/mL]. Of 30 individuals enrolled, 29 were included (72% female at birth, 90% Caucasian). Median (range) predicted time to plasma dolutegravir PA-IC90 and MEC were 83.5 (41.0-152) and 49.0 h (23.7-78.9), corresponding to geometric mean (90%) urine concentrations of 5.42 (4.37-6.46) and 27.4 ng/mL (22.1-32.7). Tenofovir in urine reached 1500 ng/mL by 101 h (58.6-205) with an equivalent plasma concentration of 6.20 ng/mL (4.21-8.18). These data support use of a urinary tenofovir threshold of <1500 ng/mL (tenofovir disoproxil fumarate-based regimens) as a marker of three or more missed doses for a POCT platform. However, due to low dolutegravir concentrations in urine, POCT would be limited to a readout of recent dolutegravir intake (one missed dose).

Sum-rate maximization for a distributed space-time block code-aided cooperative NOMA with energy harvesting

AbstractIn this paper, we exploit the spatial and transmission diversities in cooperative non-orthogonal multiple access (C-NOMA) networks to improve the system sum-rate. To achieve this, we propose a user-pairing scheme where near-field user pairs serve as relays for user pairs in the far-field region. Based on this pairing scheme, we incorporate a space-time block code transmission technique at the near-field user pairs to maximize the transmission diversity in the cooperative phase. Moreover, we consider a non-linear energy harvesting model at the near-field user pair to alleviate the problem of energy consumption during the cooperative transmission phase. Further to this, we formulate a sum-rate maximization problem that is addressed from the viewpoint of joint power allocation factor and power splitting ratio optimization. We develop a low-computational iterative algorithm based on the concepts of the Stackelberg game and the Nash bargaining solution. We benchmark our findings with different scenarios, such as energy harvesting C-NOMA with a fixed power allocation factor and power splitting ratio, energy harvesting C-NOMA without STBC, non-cooperative NOMA, and orthogonal multiple access. The results obtained via simulations outperform the benchmark schemes.

Uncertain programming model for designing multi-objective reverse logistics networks

Given the contradiction between the rapid growth of products and the modest recovery rate of end-of-life products, there is a pressing need to understand the societal significance of establishing a reverse logistics network for end-of-life products. This research constructs an open-loop five-tier reverse logistic network model encompassing customers, centres for collection, disassembly and inspection, remanufacturing, and disposal. A multi-objective mixed-integer nonlinear programming model under uncertainty has been developed. Unlike previous research, this model accounts for surrounding residents' disutility of facilities while simultaneously minimising economic costs and environmental impact. Besides, uncertainty theory is introduced in solving the proposed model. More specifically, the formulated model converts all uncertain variables into uncertain distributions by implementing the uncertain multi-objective programming method. Furthermore, a customised non-dominated sorting genetic algorithm III (NSGA-III) is proposed and is employed for the first time to address facility selection and recycling volume distribution within the network. The model is then validated using a real-life case study focusing on end-of-life vehicles in Changchun, China. This research could assist decision-makers in both governmental and private sectors in achieving a balanced approach to the interests of the economy, environment, and local communities comprehensively when designing reverse supply chains.

Passivity-Based Control with Disturbance Observer of Electromagnetic Formation Flight Spacecraft in the Port-Hamiltonian Framework

Satellite formation flying technology currently represents a focal point in space mission research. Traditional spacecraft payload performance and lifespan are often constrained by propellant limitations. Electromagnetic Formation Flying (EMFF), a propellant-free formation flying technique, has garnered widespread attention. Its inherent strong nonlinearity and coupling present challenges for high-precision control within EMFF. This paper presents the relative motion dynamics of a two-satellite EMFF in the port-Hamiltonian framework and constructs an accurate nonlinear model of the dynamics. Utilizing the concept of Interconnection and Damping Assignment and nonlinear disturbance observer, a composite disturbance-rejection passivity-based controller is designed, offering a method for controlling the magnetic dipole strength of formation satellites. Finally, numerical simulations are conducted to demonstrate the viability of the proposed dynamics model and control strategy.

Regional Pulmonary Ventilation Assessment Method and System Based on Impedance Sensing Information from the Pentapulmonary Lobes

Regional lung ventilation assessment is a critical tool for the early detection of lung diseases and postoperative evaluation. Biosensor-based impedance measurements, known for their non-invasive nature, among other benefits, have garnered significant attention compared to traditional detection methods that utilize pressure sensors. However, solely utilizing overall thoracic impedance fails to accurately capture changes in regional lung air volume. This study introduces an assessment method for lung ventilation that utilizes impedance data from the five lobes, develops a nonlinear model correlating regional impedance with lung air volume, and formulates an approach to identify regional ventilation obstructions based on impedance variations in affected areas. The electrode configuration for the five lung lobes was established through numerical simulations, revealing a power–function nonlinear relationship between regional impedance and air volume changes. An analysis of 389 pulmonary function tests refined the equations for calculating pulmonary function parameters, taking into account individual differences. Validation tests on 30 cases indicated maximum relative errors of 0.82% for FVC and 0.98% for FEV1, all within the 95% confidence intervals. The index for assessing regional ventilation impairment was corroborated by CT scans in 50 critical care cases, with 10 validation trials showing agreement with CT lesion localization results.

The effects of meteorological factors and air pollutants on the incidence of tuberculosis in people living with HIV/AIDS in subtropical Guangxi, China.

Previous studies have shown the association between tuberculosis (TB) and meteorological factors/air pollutants. However, little information is available for people living with HIV/AIDS (PLWHA), who are highly susceptible to TB. Data regarding TB cases in PLWHA from 2014 to2020 were collected from the HIV antiviral therapy cohort in Guangxi, China. Meteorological and air pollutants data for the same period were obtained from the China Meteorological Science Data Sharing Service Network and Department of Ecology and Environment of Guangxi. A distribution lag non-linear model (DLNM) was used to evaluate the effects of meteorological factors and air pollutant exposure on the risk of TB in PLWHA. A total of 2087 new or re-active TB cases were collected, which had a significant seasonal and periodic distribution. Compared with the median values, the maximum cumulative relative risk (RR) for TB in PLWHA was 0.663 (95% confidence interval [CI]: 0.507-0.866, lag 4 weeks) for a 5-unit increase in temperature, and 1.478 (95% CI: 1.116-1.957, lag 4 weeks) for a 2-unit increase in precipitation. However, neither wind speed nor PM10 had a significant cumulative lag effect. Extreme analysis demonstrated that the hot effect (RR = 0.638, 95%CI: 0.425-0.958, lag 4 weeks), the rainy effect (RR = 0.285, 95%CI: 0.135-0.599, lag 4 weeks), and the rainless effect (RR = 0.552, 95%CI: 0.322-0.947, lag 4 weeks) reduced the risk of TB. Furthermore, in the CD4(+) T cells < 200 cells/µL subgroup, temperature, precipitation, and PM10 had a significant hysteretic effect on TB incidence, while temperature and precipitation had a significant cumulative lag effect. However, these effects were not observed in the CD4(+) T cells ≥ 200 cells/µL subgroup. For PLWHA in subtropical Guangxi, temperature and precipitation had a significant cumulative effect on TB incidence among PLWHA, while air pollutants had little effect. Moreover, the influence of meteorological factors on the incidence of TB also depends on the immune status of PLWHA.

High-Order Extended Kalman Filter for State Estimation of Nonlinear Systems

In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method.

Analysis of Equilibria and Connecting Orbits in a Nonlinear Viral Infection Model

Analysis of Equilibria and Connecting Orbits in a Nonlinear Viral Infection Model

Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise

In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s&gt;1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.

Incorporating Fine-Grained Linguistic Features and Explainable AI into Multi-Dimensional Automated Writing Assessment

With the flourishing development of corpus linguistics and technological revolutions in the AI-powered age, automated essay scoring (AES) models have been intensively developed. However, the intricate relationship between linguistic features and different constructs of writing quality has yet to be thoroughly investigated. The present study harnessed computational analytic tools and Principal Component Analysis (PCA) to distill and refine linguistic indicators for model construction. Findings revealed that both micro-features and their combination with aggregated features robustly described writing quality over aggregated features alone. Linear and non-linear models were thus developed to explore the associations between linguistic features and different constructs of writing quality. The non-linear AES model with Random Forest Regression demonstrated superior performance over other benchmark models. Furthermore, SHapley Additive exPlanations (SHAP) was employed to pinpoint the most powerful linguistic features for each rating trait, enhancing the model’s transparency through explainable AI (XAI). These insights hold the potential to substantially facilitate the advancement of multi-dimensional approaches toward writing assessment and instruction.

Viscoelastic Model of Fiber Concrete under Dynamic Loading Considering the Effect of Initial Stresses

Statement of the problem. The objective of the study was to identify the peculiarities of the stress-strain state of fiber concrete under two-stage static-dynamic loading and to develop a variant of a nonlinear viscoelastic model of concrete reinforced with steel fiber. Results. The paper presents the results of experimental tests of fiber-concrete prisms under quasi-static, dynamic and static-dynamic loading conditions. On the basis of the analysis of experimental data it is established that at dynamic loading there is an upward shift of the boundary of macrocrack formation. A nonlinear viscoelastic model of fiber concrete is proposed and compared with experimental data, taking into account the effect of the initial stress level caused by the service load. The parametric study performed using this model shows that as the loading rate increases, a more intensive dynamic hardening of concrete is observed. Conclusions. The proposed viscoelastic model of fiber concrete allows to estimate the ultimate strength and corresponding strain under static-dynamic mode of loading due to an accidental action caused by the collapse of one of the load-bearing members of the structural system of the building.

Optimized Design of a Soft Actuator Considering Force/Torque, Bendability, and Controllability via an Approximated Structure

Abstract This paper introduces a novel design method that enhances the force/torque, bendability, and controllability of soft pneumatic actuators (SPAs). The complex structure of the soft actuator is simplified by approximating it as a cantilever beam. This allows us to derive approximated nonlinear kinematic models and a dynamical model, which is explored to understand the correlation between natural frequency and dimensional parameters of SPA. The design problem is then transformed into an optimization problem, using kinematic equations as the objective function and the dynamical equation as a constraint. By solving this optimization problem, the optimal dimensional parameters are determined. Six prototypes are manufactured to validate the proposed approach. The optimal actuator successfully generates the desired force/torque and bending angle, while its natural frequency remains within the constrained range. This work highlights the potential of using optimization formulation and approximated nonlinear models to boost the performance and dynamical properties of soft pneumatic actuators.

Comparison of machine learning and deep learning models for the assessment of rondo wine grape quality with a hyperspectral camera

Hyperspectral images provide rich spectral/spatial data and have shown remarkable performance in precision viticulture. Standardized data-processing methods are necessary to reduce the dimensionality and to identify powerful wavelengths. Toward this goal, we evaluated and compared the performance and novel-wavelength-identification ability of five renowned machine learning models: the linear models Ridge and LASSO, a 1D + 2D convolutional neural network (1D +2D CNN) non-linear model, a gradient boosting decision tree (GBDT) using XGBoost as an ensemble model, and an explainable boosting machine (EBM) followed by support vector regression (SVR) as a hybrid model. The model evaluations were conducted using leave-one-out cross-validation (LOOCV) as we sought to clarify the best-fitted machine learning model. Our results demonstrated that Ridge, LASSO, showed better performance with relatively high accuracy but were weak as a wavelength identifier. GDBT-XGBoost showed considerable prediction power and wavelength identification. EBM-SVM emerged as the most powerful model, demonstrating exceptional stability and clear wavelength classification even for destructive measurements under varying environmental stresses across Rondo's growth stages. The combined approach of 1D + 2D CNN algorithms was advantageous to handle the dynamic shapes of spectral curve and horizontal shift of the wavelengths obtained from outdoor data acquisition, and notably, it showed the highest accuracy to predict the brix and pH of wine grapes for both indoor and outdoor sensings. But the combined effects of 1D and 2D CNN algorithms were difficult to clarify the importance of spectral features for the brix and pH prediction. The integrated machine learning models with dimensionality reduction, and proper image acquisition can increase the model's accuracy. The common absorption peaks were observed in the near-infrared region of 700 nm and 900 nm. Those wavelengths should be considered for the development of low-cost sensing platforms with fewer bands. Wavelengths over 900 nm are also important to develop outdoor sensing platforms.

An integrated vendor-buyer model with sustainability and remanufacturing of returned product

Carbon emission reduction is very crucial nowadays. A proper balance is required for carbon emission reduction and burning of fossils fuels because during fossil fuel burning carbon is emitted and it is essential for industrialization. This study presents an inventory model with green technology where production of new items and remanufacturing of returned items are allowed. Remembering the present global situation, the ordering cost is assumed as variable cost which contain order cancellation and reorder cost. Online order policy is considered with quality of product and a return rate. Keeping in mind the social, economic and environmental aspects, the demand function is considered as sustainability sensitive demand. A nonlinear model is designed based on the above concepts. The model is solved both theoretically and analytically. The main motives of the work are to find the effects of ordering cost, carbon emission cost and green technology investment on the inventory model for suggesting the best policy to the inventory manager. Sensitivity analysis is performed to validate the model. The numerical results prove that ignoring ordering cost, carbon emission cost and green technology investment can lead to a false optimal solution and this can be a huge economical loss for the inventory manager. The results also prove that a sustainable model with carbon emission and green technology investment is more realistic and profitable in compare with the other existing models.