Nonlinear Model Research Articles

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.

Waste consumption of bio-degradable products through a secondary supply chain

Food and agriculture organization estimates that 33% of the food is wasted in the world. It is essential to optimize the food supply chains to mitigate the economic and environmental impacts of this large amount of food waste. The targets of food waste reduction can be achieved by increasing lifetime and consuming the inevitably produced food waste for producing secondary products. This research proposes a primary and secondary supply chain model, where effective preservation policy increases lifetime of food items, and the yet produced food waste is converted into secondary products. This way, the waste from the system is removed and it is converted into a sustainable zero-waste system. A nonlinear mathematical model is proposed to set the objective function of the research, which best determines the production plan, inventory schedule and investment in preservation technology while maximizing profit. The model is solved using the Kuhn-Tucker method, and the model optimality is obtained by proposing an algorithm. Numerical analysis is carried out to validate the presented model, and sensitivity analysis is performed to demonstrate the effects of variation in cost parameters on the profit. The outcome of the analysis shows that the proposed secondary supply chain increases profit by 35% and the preservation policy increases the profit by 17.9%. Besides, the proposed policies minimize and remove the food waste from system. Managerial implications are provided for the practitioners to apply the proposed model in food supply chains.

Modeling of Cooperative Robotic Systems and Predictive Control Applied to Biped Robots and UAV-UGV Docking with Task Prioritization.

This paper studies a cooperative modeling framework to reduce the complexity in deriving the governing dynamical equations of complex systems composed of multiple bodies such as biped robots and unmanned aerial and ground vehicles. The approach also allows for an optimization-based trajectory generation for the complex system. This work also studies a fast-slow model predictive control strategy with task prioritization to perform docking maneuvers on cooperative systems. The method allows agents and a single agent to perform a docking maneuver. In addition, agents give different priorities to a specific subset of shared states. In this way, overall degrees of freedom to achieve the docking task are distributed among various subsets of the task space. The fast-slow model predictive control strategy uses non-linear and linear model predictive control formulations such that docking is handled as a non-linear problem until agents are close enough, where direct transcription is calculated using the Euler discretization method. During this phase, the trajectory generated is tracked with a linear model predictive controller and addresses the close proximity motion to complete docking. The trajectory generation and modeling is demonstrated on a biped robot, and the proposed MPC framework is illustrated in a case study, where a quadcopter docks on a non-holonomic rover using a leader-follower topology.

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.

Hammerstein-Wiener Motion Artifact Correction for Functional Near-Infrared Spectroscopy: A Novel Inertial Measurement Unit-Based Technique.

Participant movement is a major source of artifacts in functional near-infrared spectroscopy (fNIRS) experiments. Mitigating the impact of motion artifacts (MAs) is crucial to estimate brain activity robustly. Here, we suggest and evaluate a novel application of the nonlinear Hammerstein-Wiener model to estimate and mitigate MAs in fNIRS signals from direct-movement recordings through IMU sensors mounted on the participant's head (head-IMU) and the fNIRS probe (probe-IMU). To this end, we analyzed the hemodynamic responses of single-channel oxyhemoglobin (HbO) and deoxyhemoglobin (HbR) signals from 17 participants who performed a hand tapping task with different levels of concurrent head movement. Additionally, the tapping task was performed without head movements to estimate the ground-truth brain activation. We compared the performance of our novel approach with the probe-IMU and head-IMU to eight established methods (PCA, tPCA, spline, spline Savitzky-Golay, wavelet, CBSI, RLOESS, and WCBSI) on four quality metrics: SNR, △AUC, RMSE, and R. Our proposed nonlinear Hammerstein-Wiener method achieved the best SNR increase (p < 0.001) among all methods. Visual inspection revealed that our approach mitigated MA contaminations that other techniques could not remove effectively. MA correction quality was comparable with head- and probe-IMUs.

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.

Percolation transition for random forests in $d\geqslant 3$

AbstractThe arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor $\beta &gt;0$ β &gt; 0 per edge. It arises as the $q\to 0$ q → 0 limit of the $q$ q -state random cluster model with $p=\beta q$ p = β q . We prove that in dimensions $d\geqslant 3$ d ⩾ 3 the arboreal gas undergoes a percolation phase transition. This contrasts with the case of $d=2$ d = 2 where no percolation transition occurs.The starting point for our analysis is an exact relationship between the arboreal gas and a non-linear sigma model with target space the fermionic hyperbolic plane $\mathbb{H}^{0|2}$ H 0 | 2 . This latter model can be thought of as the 0-state Potts model, with the arboreal gas being its random cluster representation. Unlike the standard Potts models, the $\mathbb{H}^{0|2}$ H 0 | 2 model has continuous symmetries. By combining a renormalisation group analysis with Ward identities we prove that this symmetry is spontaneously broken at low temperatures. In terms of the arboreal gas, this symmetry breaking translates into the existence of infinite trees in the thermodynamic limit. Our analysis also establishes massless free field correlations at low temperatures and the existence of a macroscopic tree on finite tori.

A modified Manson-Halford model based on improved WOA for fatigue life prediction under multi-level loading

The Manson-Halford (M-H) nonlinear cumulative damage model is widely applied for fatigue life analysis problems under multi-level loading. In this model, the influence of loading sequence on the fatigue life can be better considerer, but the loading interaction effect is ignored. An improved whale optimization algorithm (IWOA) by integrating multiple strategies is proposed. The ability of global search and local exploitation is balanced and improved through nonlinear convergence factor, adaptive weighting factors and the Cauchy reverse learning strategies. In order to fully account for loading interaction effect, loading weighting factors are introduced to modify the M-H model, and the parameters are optimized through the global search properties of IWOA. The model is evaluated on multi-level loading fatigue experimental data from five metal materials and two aluminum alloy welded joints. The results suggest that the proposed IWOA has better optimization accuracy compared to the standard whale optimization algorithm (WOA). The proposed modified M-H model has better prediction performance compared to the four traditional cumulative damage models, which can be effectively applied to multi-level loading fatigue life analysis problems under actual working conditions. The proposed model is useful for the study of fatigue life evaluation methods.

Pinecone-Inspired Humidity-Responsive Paper Actuators with Bilayer Structure.

Many plant materials in nature have the ability to change their shape to respond to external stimuli, such as humidity or moisture, to ensure their survival or safe seed release. A well-known example for this phenomenon is the pinecone, which is able to open its scales at low humidity due to the specific bilayer structures of the scale. Inspired by this, we developed a novel humidity-driven actuator based on paper. This was realized by the lamination of untreated paper made from eucalyptus fibers to a paper-carboxymethyl cellulose (CMC) composite. As observed, the hygroexpansion of the composite can be easily controlled by the amount of CMC in the impregnated paper sheet, which, thus, controls the morphologic deformation of the paper bilayer. For a more detailed understanding of these novel paper soft robots, we also studied the dynamic water vapor adsorption, polymer distribution and hygroexpansion of the paper-polymer composites. Finally, we applied a geometrically nonlinear finite element model to predict the bending behavior of paper bilayers and compared the results to experimental data. From this, we conclude that due to the complexity of structure of the paper composite, a universal prediction of the hygromorphic behavior is not a trivial matter.

On the additive artificial intelligence-based discovery of nanoparticle neurodegenerative disease drug delivery systems.

Neurodegenerative diseases are characterized by slowly progressing neuronal cell death. Conventional drug treatment strategies often fail because of poor solubility, low bioavailability, and the inability of the drugs to effectively cross the blood-brain barrier. Therefore, the development of new neurodegenerative disease drugs (NDDs) requires immediate attention. Nanoparticle (NP) systems are of increasing interest for transporting NDDs to the central nervous system. However, discovering effective nanoparticle neuronal disease drug delivery systems (N2D3Ss) is challenging because of the vast number of combinations of NP and NDD compounds, as well as the various assays involved. Artificial intelligence/machine learning (AI/ML) algorithms have the potential to accelerate this process by predicting the most promising NDD and NP candidates for assaying. Nevertheless, the relatively limited amount of reported data on N2D3S activity compared to assayed NDDs makes AI/ML analysis challenging. In this work, the IFPTML technique, which combines information fusion (IF), perturbation theory (PT), and machine learning (ML), was employed to address this challenge. Initially, we conducted the fusion into a unified dataset comprising 4403 NDD assays from ChEMBL and 260 NP cytotoxicity assays from journal articles. Through a resampling process, three new working datasets were generated, each containing 500,000 cases. We utilized linear discriminant analysis (LDA) along with artificial neural network (ANN) algorithms, such as multilayer perceptron (MLP) and deep learning networks (DLN), to construct linear and non-linear IFPTML models. The IFPTML-LDA models exhibited sensitivity (Sn) and specificity (Sp) values in the range of 70% to 73% (>375,000 training cases) and 70% to 80% (>125,000 validation cases), respectively. In contrast, the IFPTML-MLP and IFPTML-DLN achieved Sn and Sp values in the range of 85% to 86% for both training and validation series. Additionally, IFPTML-ANN models showed an area under the receiver operating curve (AUROC) of approximately 0.93 to 0.95. These results indicate that the IFPTML models could serve as valuable tools in the design of drug delivery systems for neurosciences.