Nonlinear Model Research Articles

The heat-mortality association in Jordan: Effect modification by greenness, population density and urbanization level

BackgroundThe Middle East is one of the most vulnerable regions to the impacts of climate change, yet evidence of the heat-related mortality remains limited in this area. Our present study investigated the heat-mortality association in Jordan and the potential modifying effect of greenness, population density and urbanization level on the association. MethodsFor each of the 42 included districts, daily meteorological and mortality data from 2000 to 2020 were obtained for the warmest months (May to September). First, a distributed lag non-linear model was applied to estimate the district level heat-mortality association, then the district specific estimates were pooled using multivariate meta-regression models to obtain an overall estimate. Last, the modifying effect of district level greenness, population density and urbanization level was examined through subgroup analysis. ResultsWhen compared to the minimum mortality temperature (MMT, percentile 0th, 22.20 °C), the 99th temperature percentile exhibited a relative risk (RR) of 1.34 (95 % CI 1.23, 1.45). Districts with low greenness had a higher heat-mortality risk (RR 1.39, 95 % CI 1.22, 1.58) when compared to the high greenness (RR 1.28, 95 % CI 1.13, 1.45). While heat-mortality risk did not significantly differ between population density subgroups, highly urbanized districts had a greater heat-mortality risk (RR 1.41, 95 % CI 1.23, 1.62) as compared to ones with low levels of urbanization (RR 1.32, 95 % CI 1.13, 1.55). Districts with high urbanization level had the highest heat-mortality risk if they were further categorized as having low greenness (RR 1.63, 95 % CI 1.30, 2.04). ConclusionExposure to heat was associated with increased mortality risk in Jordan. This risk was higher in districts with low greenness and high urbanization level. As climate change-related heat mortality will be on the rise, early warning systems in highly vulnerable communities in Jordan are required and greening initiatives should be pursued.

Optimization-based design of structure and operation parameters simultaneously for real-world distillation column based on rate-based model

Simultaneously optimizing the structure and operating parameters of distillation columns based on rigorous rate-based models is critical for various process intensification technologies to achieve their intended purpose in real-world distillation columns. However, efficiently optimizing a distillation column based on rate-based models while considering the column hydraulics is far from practical. The biggest obstacle in using rigorous models for distillation columns in an equation-oriented environment is ensuring a robust solution for large-scale, strongly coupled nonlinear models, along with the simultaneous optimization of integer and continuous variables. In this study, a new optimization framework was introduced. It incorporated a pseudo-transient simulation method to ensure convergence of the simulation in equation-oriented environment. Additionally, an efficient relaxation method transformed the mixed integer nonlinear programming problem into a nonlinear programming problem, facilitating simultaneous optimization of both the integer variable representing column structure and the continuous variables governing column operation. Three examples, including a complex intensified catalytic distillation column, were optimized to demonstrate the efficiency of the proposed framework. Specifically, its advantages in terms of mathematical optimality and industrial feasibility were illustrated.

Short-Term Effects of Lower Air Temperature and Cold Spells on Myocardial Infarction Hospitalizations in Sweden

BackgroundLower air temperature and cold spells have been associated with an increased risk of various diseases. However, the short-term effect of lower air temperature and cold spells on myocardial infarction (MI) remains incompletely understood. ObjectivesThe purpose of this study was to investigate the short-term effects of lower air temperature and cold spells on the risk of hospitalization for MI in Sweden. MethodsThis population-based nationwide study included 120,380 MI cases admitted to hospitals in Sweden during the cold season (October to March) from 2005 to 2019. Daily mean air temperature (1 km2 resolution) was estimated using machine learning, and percentiles of daily temperatures experienced by individuals in the same municipality were used as individual exposure indicators to account for potential geographic adaptation. Cold spells were defined as periods of at least 2 consecutive days with a daily mean temperature below the 10th percentile of the temperature distribution for each municipality. A time-stratified case-crossover design incorporating conditional logistic regression models with distributed lag nonlinear models using lag 0 to 1 (immediate) and 2 to 6 days (delayed) was used to evaluate the short-term effects of lower air temperature and cold spells on total MI, non–ST-segment elevation myocardial infarction (NSTEMI) and ST-segment elevation myocardial infarction (STEMI). ResultsA decrease of 1-U in percentile temperature at a lag of 2 to 6 days was significantly associated with increased risks of total MI, NSTEMI, and STEMI, with ORs of 1.099 (95% CI: 1.057-1.142), 1.110 (95% CI: 1.060-1.164), and 1.076 (95% CI: 1.004-1.153), respectively. Additionally, cold spells at a lag of 2 to 6 days were significantly associated with increased risks for total MI, NSTEMI, and STEMI, with ORs of 1.077 (95% CI: 1.037-1.120), 1.069 (95% CI: 1.020-1.119), and 1.095 (95% CI: 1.023-1.172), respectively. Conversely, lower air temperature and cold spells at a lag of 0 to 1 days were associated with decreased risks for MI. ConclusionsThis nationwide case-crossover study reveals that short-term exposures to lower air temperature and cold spells are associated with an increased risk of hospitalization for MI at lag 2 to 6 days.

A Reliable Bayesian Regularization Neural Network Approach to Solve the Global Stability of Infectious Disease Model

The purpose of this study is to perform the numerical results of the global stability of infectious disease mathematical model by using the stochastic computing scheme. The design of proposed solver is presented by one of the efficient and reliable schemes named as Bayesian regularization neural network (BRNN). The global stability of infectious disease mathematical nonlinear model is categorized into susceptible, infected, recovered and vaccinated. The construction of dataset is performed through the Runge-Kutta scheme in order to lessen the mean square error (MSE) by dividing the statics as training 74%, while 13% for both testing and endorsement. The proposed stochastic process contains log-sigmoid merit function, twenty neurons and optimization through RBNN for the numerical solutions of the global stability of infectious disease mathematical system. The best training values for each model's case are performed around 10-11. The scheme's correctness is performed by the matching of the results and the minor calculated absolute error performances. Moreover, the regression, state transmission, error histogram and MSE indicate the trustworthiness of the designed solver.

Signature of conservation laws and solitary wave solution with different dynamics in Thomas–Fermi plasma: Lie theory

We propose a Lie group method to discuss the modified KP equation appearing in Thomas–Fermi (TM) plasma, characterised by cold and hot electrons. The Lie method facilitates the identification of similarity reductions, infinitesimal symmetries, group-invariant solutions, and novel analytical solutions for nonlinear models. The similarity reduction method is carried out to transform the nonlinear partial differential equations (NLPDE) into the nonlinear ordinary differential equations (NLODE). This study focuses on solitary wave profiles due to their usefulness in various engineering applications, including monitoring public transportation systems, managing coastlines, and mitigating disaster risks. It also addresses the conservation laws associated with the modified KP equation. The generalised auxiliary equation (GAEM) scheme is used to compute the new solitary wave patterns of the modified KP equation, which explains the dynamics of nonlinear waves in Thomas–Fermi plasma. The idea of nonlinear self-adjointness is used to compute the conservation laws of the examined model. The graphical behaviour of some solutions is represented by adjusting the suitable value of the parameters involved.

Evaluation of forest ecosystem resilience to drought considering lagged effects of drought.

Drought can cause significant disruption to forest ecosystems and may have long-term impacts on the structure and function of ecosystems after the end of drought. This is the key to quantifying the ability of ecosystem to respond to disturbance events by comprehensively analyzing the impact of drought on vegetation, the lagged effect, and ecosystem resilience to drought. This article takes broad-leaved forests and coniferous forests in multiple temperature zones of China as the object of study, using distributed lagged nonlinear model (DLNM) to construct a systematic method. Our results show that the main sensitive lagged time for coniferous forests and broad-leaved forests is the first 3 months in various temperature zones, with the strongest lagged effect in the month when the drought incidents occur. Coping capacity represents ecosystems to remain stable during droughts, and we quantified the indicator by the ratio of the resistance (the difference between NDVI value before the drought and during the drought) to recovery (the difference between NDVI value after the drought and during the drought). When dealing with intensive drought events, the coping capacity of subtropical broad-leaved forests (-0.67) and tropical broad-leaved forests (-0.88) exhibit the strongest coping capacity (value tends to -1). Overall, vegetation growth in subtropical and tropical regions is less affected by drought compared to temperate and cold temperate zones. The research results help us understand the comprehensive impact of drought on vegetation and the strategies for different vegetation to cope with drought.

Adaptive Model Predictive Control of Yaw Rate and Lateral Acceleration for an Active Steering Vehicle Based on Tire Stiffness Estimation

Dynamic systems for vehicles are commonly established based on physical rules that are simplified and are not accurately reflective of their dynamic characteristics under certain operating conditions, affecting their accuracy and safety. This paper presents an adaptive model predictive controller (AMPC) with an estimator that controls the yaw rate and lateral acceleration of a realistic ground vehicle. A number of vehicle parameters are estimated using different advanced estimators, of which recursive least squares is one that is widely used. AMPCs and estimators are used to manage the driving process in order for vehicles to remain stable and controllable. In this research, experiments were conducted on a realistic vehicle based on a nonlinear brush tire model. In this estimator, lateral force measurements are analyzed to estimate the tire cornering stiffnesses that are used in the AMPC from a linear bicycle model (lateral force model), where each parameter describes the nonlinearity of the vehicle model. The results demonstrate that the controlled vehicle's performance is improved by combining a recursive least squares estimator with an AMPC in the simulation process. As tire stiffness estimates become more accurate, AMPC performance improves. Yet, AMPC controllers are described in terms of a table of design parameters. As different steering inputs are applied to different vehicles, the yaw rate and lateral acceleration are varied, while tire stiffness is determined. According to the results of this paper, the proposed method for estimating tire-cornering stiffness exhibits high estimation accuracy, robustness, computational efficiency, stability, comfort, and accuracy and reliability under a variety of steering input maneuvers using an AMPC controller.

Statistical and machine learning models for location-specific crop yield prediction using weather indices.

Crop yield prediction gains growing importance for all stakeholders in agriculture. Since the growth and development of crops are fully connected with many weather factors, it is inevitable to incorporate meteorological information into yield prediction mechanism. The changes in climate-yield relationship are more pronounced at a local level than across relatively large regions. Hence, district or sub-region-level modeling may be an appropriate approach. To obtain a location- and crop-specific model, different models with different functional forms have to be explored. This systematic review aims to discuss research papers related to statistical and machine-learning models commonly used to predict crop yield using weather factors. It was found that Artificial Neural Network (ANN) and Multiple Linear Regression were the most applied models. Support Vector Regression (SVR) model has a high success ratio as it performed well in most of the cases. The optimization options in ANN and SVR models allow us to tune models to specific patterns of association between weather conditions of a location and crop yield. ANN model can be trained using different activation functions with optimized learning rate and number of hidden layer neurons. Similarly, the SVR model can be trained with different kernel functions and various combinations of hyperparameters. Penalized regression models namely, LASSO and Elastic Net are better alternatives to simple linear regression. The nonlinear machine learning models namely, SVR and ANN were found to perform better in most of the cases which indicates there exists a nonlinear complex association between crop yield and weather factors.

Electromagnetic Fields Calculation and Optimization of Structural Parameters for Axial and Radial Helical Air-Core Inductors

To improve the current density distribution and electromagnetic performance of air-core inductors, a structural optimization method combining back-propagation(BP) neural network and genetic algorithm(GA) is proposed for the study of axial and radial spiral multi-winding inductors. The Monte Carlo method was used to extract the structural size samples of the inductors, and the training dataset was obtained through the finite element calculation of electromagnetic fields. Based on BP neural networks, nonlinear mapping models between the inductance value, volumetric inductance density, current distribution non-uniformity coefficient, and inductor structural parameters were constructed. A sensitivity analysis of the inductor inductance value affected by the structural parameters was conducted using the Sobol index calculation. Using the current distribution non-uniformity coefficient as the fitness function and the volumetric inductance density as the constraint condition, a genetic algorithm was applied to globally optimize the structural parameters of the inductor. The optimization results were verified through a finite element comparison. The results show that, under the requirement of satisfying the volumetric inductance density, the current distribution non-uniformity coefficient of the Axial Helical Inductor (AHI)-type inductor was reduced by 4.57% compared with the best sample in the sampling, while that of the Radial Helical Inductor (RHI)-type inductor was reduced by 5.33%, demonstrating the practicality of the BP-GA joint algorithm in the structural optimization design of inductors.

Effect of Temperature and Precipitation on Acute Appendicitis Incidence in Seoul: A Time Series Regression Analysis.

This study aimed to investigate the relationship between meteorological factors, specifically temperature and precipitation, and the incidence of appendicitis in Seoul, South Korea. Using data from the National Health Insurance Service spanning 2010-2020, the study analyzed 165,077 appendicitis cases in Seoul. Time series regression modeling with distributed-lag non-linear models was employed. Regarding acute appendicitis and daily average temperature, the incidence rate ratio (IRR) showed an increasing trend from approximately - 10°C to 10°C. At temperatures above 10°C, the increase was more gradual. The IRR approached a value close to 1 at temperatures below - 10°C and above 30°C. Both total and complicated appendicitis exhibited similar trends. Increased precipitation was negatively associated with the incidence of total acute appendicitis around the 50mm/day range, but not with complicated appendicitis. The findings suggest that environmental factors, especially temperature, may play a role in the occurrence of appendicitis. This research underscores the potential health implications of global climate change and the need for further studies to understand the broader impacts of environmental changes on various diseases.

VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D

AbstractWe present a Virtual Element MATLAB solver for elliptic and parabolic, linear and semilinear Partial Differential Equations (PDEs) in two and three space dimensions, which is coined VEMcomp. Such PDEs are widely applicable to describing problems in material sciences, engineering, cellular and developmental biology, among many other applications. The library covers linear and nonlinear models posed on different simple and complex geometries, involving time-dependent bulk, surface, and bulk-surface PDEs. The solver employs the Virtual Element Method (VEM) of lowest polynomial order $${k=1}$$ k = 1 on general polygonal and polyhedral meshes, including the Finite Element Method (FEM) of order $${k=1}$$ k = 1 as a special case when the considered mesh is simplicial. VEMcomp has three main purposes. First, VEMcomp generates polygonal and polyhedral meshes optimized for fast matrix assembly. Triangular and tetrahedral meshes are encompassed as special cases. For surface PDEs, VEMcomp is compatible with the well-known Matlab package DistMesh for mesh generation. Second, given a mesh for the considered geometry, possibly generated with an external package, VEMcomp computes all the matrices (mass and stiffness) required by the VEM or FEM method. Third, for multiple classes of stationary and time-dependent bulk, surface and bulk-surface PDEs, VEMcomp solves the considered PDE problem with the VEM or FEM in space and IMEX Euler in time, through a user-friendly interface. As an optional post-processing, VEMcomp comes with its own functions for plotting the numerical solutions and evaluating the error when possible. An extensive set of examples illustrates the usage of the library.

Integrability and renormalizability for the fully anisotropic SU(2) principal chiral field and its deformations

For the class of 1 + 1 dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on the example of the so-called fully anisotropic SU(2) Principal Chiral Field (PCF). Along the way, we discover a new classically integrable four parameter family of sigma models, which is obtained from the fully anisotropic SU(2) PCF by means of the Poisson-Lie deformation. The theory turns out to be one-loop renormalizable and the system of ODEs describing the flow of the four couplings is derived. Also provided are explicit analytical expressions for the full set of functionally independent first integrals (renormalization group invariants).

Maximizing the toughness of polymer nanocomposites based on the radial strength of carbon nanotubes

Similarity in the mechanical properties of a matrix and an inclusion is key to designing tough nanocomposites. Matching the matrix and inclusions with similar mechanical strengths prevents stress perturbation at the interface, enabling nanocomposites to withstand higher loads as a homogeneous material. We tabulate the chirality-dependent radial buckling properties of multi-walled carbon nanotubes (MWCNTs) and present a design methodology for providing optimal strengthening properties for poly(p-phenylene terephthalamide) matrices. The structural orientation effect of the aromatic rings of polymer chains surrounding MWCNTs provides a strong support against transverse loading. The effect of the interfacial area of different materials on the toughness of the entire continuum system is characterized through a nonlinear finite element model. MWCNT buckling and polymer yielding occur simultaneously under conditions selected by the proposed methodology, thereby maximizing the reinforcing effect of the nanocomposites by creating a continuous stress field at the interface.

Modeling nonlinear inactivation of hygiene indicator bacteria in pig carcasses during scalding at different pHs.

This study aimed to investigate the influence of adding an alkalizing agent to the scalding water of a slaughterhouse in Brazil to inactivate hygiene indicator bacteria in pig carcasses. Scalding is critical during carcass processing because slaughterhouses' scalding water is constantly renewed; therefore, it is usually contaminated with organic matter, such as faeces and dirt from the previous carcasses. The treatments evaluated consisted of counting Enterobacteriaceae and mesophilic bacteria in pork jowls at 62°C, 65°C, 68C, and 72°C after 0.0, 1.5, 3.0, 4.5, 6.0, and 7.5min of simulated scalding at the pHs of 7.0 (control) and 11.0 (after addition of alkalizing agent). Decimal reduction times of hygiene indicator bacteria for all treatments were estimated with different nonlinear bacterial inactivation models. As a result, adding the alkalizing agent did not significantly inactivate most of the bacteria in the studied samples. However, it contributed to the inactivation of some bacteria, mostly belonging to the mesophilic group, at some specific temperatures. The results obtained in the current study can provide useful insights into dealing with pig carcass contamination in a real-world scenario and applying the obtained information in the industrial environment.

Finite Element Modeling and Calibration of a Three-Span Continuous Suspension Bridge Based on Loop Adjustment and Temperature Correction.

Precise finite element modeling is critically important for the construction and maintenance of long-span suspension bridges. During the process of modeling, shape-finding and model calibration directly impact the accuracy and reliability. Scholars have provided numerous alternative proposals for the shape-finding of main cables in suspension bridges from both theoretical and finite element analysis perspectives. However, it is difficult to apply these solutions to suspension bridges with special components. Seeking a viable solution for such suspension bridges holds practical significance. The Nanjing Qixiashan Yangtze River Bridge is the first three-span suspension bridge in China. To maintain the configuration of the main cable, the suspension bridge is equipped with specialized suspenders near the anchors, referred to as displacement-limiting suspenders. It is the first suspension bridge in China to use displacement-limiting suspenders and their anchorage system. Taking the suspension bridge as a research background, this paper introduces a refined finite element modeling approach considering the effect of geometric nonlinearity. Firstly, based on the loop adjustment and temperature correction, the shape-finding and force assessment of the main cables are carried out. On this basis, a nonlinear finite element model of the bridge was established and calibrated, taking into account factors such as pylon settlement and cable saddle precession. Finally, the static and dynamic characteristics of the suspension bridge were thoroughly investigated. This study aims to provide a reference for the design, construction and operation of the three-span continuous suspension bridge.

Bayesian modeling of the Gompertz curve for meat quails growth data considering different error distributions

This study applied the Gompertz model to quail growth data, assuming symmetric and asymmetric homoscedastic and heteroscedastic error distributions (Normal, t-Student, Skew normal, and Skew t), undera Bayesian framework. Model selection criteria included the Bayesian Deviance Information Criterion (DIC) and the analysis of residual standard deviation (σ), as well as graphical assessment of the fit. For both homoscedastic error structures (males: DIC=7.186; σ=10.73) and (females: DIC=5.572; σ=11.88) as well as heteroscedastic structures (males: DIC=6.493; σ=0.795) and (females: DIC=4.405; σ=0.824), the best fits were obtained by considering the Skew t distribution for errors. In homoscedastic fits, significant residual asymmetry (λ) was observed only for female quails (CI(λ)=[-8.039;-0.340]), whereas in heteroscedastic fits, the parameter was not significant for both sexes. Additionally, heteroscedasticity (δ) captured in the fits was significant for both sexes (males: CI(δ)=[1.66;2.13] and females: CI(δ)=[1.80;2.26]). Understanding animal growth is crucial for optimizing management and feeding practices, reducing time and costs in production. In this case, the use of nonlinear models considering heteroscedastic and/or asymmetric residual structures contributes to greater accuracy in decision-making.

Immersion and Invariance-Based Linear Tracking and Regulation Controller for Depth Position of an AUV

This paper addresses the tracking control challenge in the diving motion system of a specific class of autonomous underwater vehicles (AUVs) characterized by a torpedo-like shape. A decoupled and reduced-order three degrees-of-freedom linearized diving motion model is employed for depth position control. A control law is synthesized using the immersion and invariance (I&I) technique to achieve the control objectives. The primary aim is to attain tracking by immersing a stable, lower-order target (second-order) dynamic system into a three-dimensional manifold, upon which the closed-loop system evolves. We address the regulation problem as a specialized instance of the tracking problem, with the reference input set as a predetermined known depth that requires regulation. The efficacy of the proposed control law is evaluated through simulation studies involving various scenarios. Robustness tests are conducted to assess the control law’s performance under modeling uncertainties and underwater disturbances. The computer simulation employs an AUV named MAYA, utilizing experimentally validated diving motion parameters. A comparative analysis is performed between the proposed control law and other benchmark controllers to gauge its performance. Additionally, the effectiveness of the proposed control law is confirmed by validating its application to the nonlinear model of the diving motion system.

Identification of nonlinear system model and inverse model based on conditional invertible neural network

In applications such as adaptive inverse control, internal model control, and active noise control, the identification accuracy of the system model and the inverse model directly affects the performance. However, it is not easy to identify inverse models for nonlinear systems. Moreover, existing methods require two identification calculations to obtain the system model and the inverse model. Therefore, an identification method of nonlinear system model and inverse model based on conditional invertible neural network (cINN) is proposed. The invertible structure of cINN enables simultaneous approximation of complex nonlinear functions and simultaneous acquisition of the corresponding inverse functions. Consequently, both the nonlinear system model and the inverse model can be identified concurrently through cINN. Moreover, the identification performance of the cINN-based method is validated and applied to disturbance cancellation in a classical nonlinear simulation system. Finally, the inverse model of the actuator is identified by cINN, and the inverse model is applied to the nonlinear compensation of the actuator.

Comparative analysis and optimization of nonlinear hysteresis models for a magnetorheological fluid dual-clutch of an electric vehicle transmission

Comparative analysis and optimization of nonlinear hysteresis models for a magnetorheological fluid dual-clutch of an electric vehicle transmission

Data-driven prediction of wind pressure on low-rise buildings in complex heterogeneous terrains

This study presents a data-driven methodology for predicting the pressure coefficient statistics on the windward wall, roof, and leeward wall of low-rise buildings situated downwind of complex heterogeneous terrains. Two types of artificial neural network models were developed: the empirical parameter-based ANN (PANN) and the morphology-based ANN (MANN). Pressure data from wind tunnel tests on the Wind Engineering Research Field Laboratory (WERFL) building model (building height H = 4 m) in complex heterogeneous terrain were used to develop the ANN models. These models were evaluated against a non-linear fitted model to assess their predictive performances. PANN and MANN demonstrated superior performance in capturing the effects of terrain complexity on the mean (Cp,mean) and the root-mean-square (Cp,RMS) wind pressure coefficients for the windward wall, roof, and leeward wall. Optimal prediction was achieved with a terrain patch size of W × L = 4 × 2, equating to a full-scale area of approximately 72 m × 23 m. This suggests that the morphology within approximately 100 m × 50 m (25H× 12.5H) in front of a low-rise building has the greatest correlation with the wind pressure coefficient. Despite lower R2 values for max Cp,RMS on the leeward wall across all models, both PANN and MANN showed promising accuracy for the six outputs studied. Moreover, a global sensitivity analysis confirmed the impact of terrain roughness and complexity on the prediction models particularly on max Cp,RMS, and underscored the dominance of effective roughness length z0,eff and the coefficient of variation of roughness length COVz0 in influencing model outcomes.