Nonlinear Model Research Articles

Randomized greedy magic point selection schemes for nonlinear model reduction

An established way to tackle model nonlinearities in projection-based model reduction is via relying on partial information. This idea is shared by the methods of gappy proper orthogonal decomposition (POD), missing point estimation (MPE), masked projection, hyper reduction, and the (discrete) empirical interpolation method (DEIM). The selected indices of the partial information components are often referred to as “magic points.” The original contribution of the work at hand is a novel randomized greedy magic point selection. It is known that the greedy method is associated with minimizing the norm of an oblique projection operator, which, in turn, is associated with solving a sequence of rank-one SVD update problems. We propose simplification measures so that the resulting greedy point selection has the following main features: (1) The inherent rank-one SVD update problem is tackled in a way, such that its dimension does not grow with the number of selected magic points. (2) The approach is online efficient in the sense that the computational costs are independent from the dimension of the full-scale model. To the best of our knowledge, this is the first greedy magic point selection that features this property. We illustrate the findings by means of numerical examples. We find that the computational cost of the proposed method is orders of magnitude lower than that of its deterministic counterpart. Nevertheless, the prediction accuracy is just as good if not better. When compared to a state-of-the-art randomized method based on leverage scores, the randomized greedy method outperforms its competitor.

Numerical Procedure for the Solution of Non-Linear Pulp Washing Models

Numerical Procedure for the Solution of Non-Linear Pulp Washing Models

Optimized Discrete Nonlinear Control of Alternating Current Three-Phase Motors via an Industrial Variable Frequency Drive

This article presents a suboptimal nonlinear control strategy to improve the dynamics of a three-phase alternating current (AC) motor. Using dynamic programming, the calculation of the Bellman function is avoided by determining a suboptimal control sequence that locally minimizes a quadratic performance index at each step. The motor’s fixed-frame nonlinear mathematical model controls the stator currents, rotor magnetic fluxes, and rotor angular speed by applying voltages to the stator. Experimental tests are conducted using a Delta VFD007EL11A variable frequency drive (VFD), demonstrating improved motor state behavior and performance compared to an optimal proportional integral (PI) control and a fixed reference input in the VFD. The experiments include set point changes and a comparative analysis of the energy consumption between both controllers considering two cases: free and with load on the motor shaft.

Finite element analysis of a rubber bearing base isolator under vertical and horizontal loads using a nonlinear hyper-viscoelastic material model

This research is devoted to developing a finite element model using Abaqus code for the computer simulation of an in-house developed and manufactured rubber bearing subjected to static vertical and cyclic horizontal loads. A high-damping rubber compound was designed. The material behavior of the rubber was assumed to be described by the hyper-viscoelastic model. Both linear (Prony series) and nonlinear (strain hardening power law) viscoelastic relationships were used in conjunction with the Ogden-Roxburgh equation to take the addition of the stress softening phenomenon or Mullins effect into consideration. The parameters of the material model were determined using MCalibration code in which an optimization technique was used, and data obtained in experiments carried out on test specimens were fitted into the selected model. The results of the simulations were compared with their corresponding experimental data carried out on the rubber bearing. The force-displacement behavior, stress and strain fields, and computed energy were presented and discussed. It is shown that the nonlinear viscoelastic model accompanied by the Mullins effect gives the best results. Moreover, the model could accurately predict the energy variations during the earthquake loading.

MODELING THE EFFECTS OF PESTS AND PESTICIDE ON CROP YIELDS IN A MULTIPLE CROPPING SYSTEM

Pest infestation poses a significant threat to agricultural crop yields, and to control it, farmers spray chemical pesticides. The persistent use of these chemical agents not only leads to pesticide residues within crops but also exerts collateral damage on the beneficial pest population. In this research work, we formulate a nonlinear mathematical model to assess the impacts of pesticide on crop yields within a multiple cropping system. Model analysis illustrates that crop consumption rates destabilize, and the spraying rate of pesticide stabilizes the system. Furthermore, we determine conditions for the global stability of the coexisting equilibrium and conduct a global sensitivity analysis to identify model parameters that significantly influence pest population density. Our findings emphasize that, for effective pest population control and enhanced crop yields, farmers should choose either pesticides with a high pest abatement rate or those with a higher pesticide uptake rate. Considering the spraying rate of pesticide as time-dependent, we also suggest an optimal control strategy to minimize the pest population and associated costs. We provide analytical results backed by numerical simulations implemented through the non-standard finite difference scheme to support our findings.

In-house validation of a visible and near infrared spectroscopy non-targeted method to support panel test of virgin olive oils

In this study, an in-house validation of Visible and Near Infrared Spectroscopy was performed to distinguish between extra virgin olive oil (EVOO) and virgin olive oil (VOO). A total of 161 samples of olive oil of three different categories (EVOO, VOO and lampante (LOO)) were analysed by transflectance using a monochromator instrument. One-class models were initially developed using Partial Least Squares (PLS) Density Modelling to characterize EVOO and VOO category. Once the LOO samples were discriminated, linear and non-linear discriminant models were built to classify EVOO and VOO. Different data pre-treatments and variable selection algorithms were evaluated to establish the best models in terms of Correct Classification Rate (CCR). The best model, obtained after variable selection using PLS Discriminant Analysis, yielded CCR values of 82.35 % for EVOO and 66.67 % for VOO in external validation. These results confirmed that VIS + NIRS technology may be used to provide rapid, non-destructive preliminary screening of olive oil samples for categorization; suspect samples may then be analysed by official analytical methods.

Nonlinear effects of agricultural drought on vegetation productivity in the Yellow River Basin, China

Agricultural drought (AD) is the main environmental factor affecting vegetation productivity (VP) in the Yellow River Basin (YRB). In recent years, the nonlinear effects of AD on VP in the YRB have attracted much attention. However, it is still unclear whether fluctuating AD will have complex nonlinear effects on VP in the YRB, and there are scant previous studies at large scale on whether there is a threshold for nonlinear effects of AD on VP in the YRB. Therefore, this study used a newly developed agricultural drought index to explore nonlinear effects on VP revealing the nonlinear effects of AD on VP in the YRB. First, we developed a kernel temperature vegetation drought index (kTVDI) based on kernel normalized difference vegetation index (kNDVI) and land surface temperature data to study the spatiotemporal variation of AD in the YRB. Second, we used GPP data from solar-induced chlorophyll fluorescence inversion as an indicator to explore the spatiotemporal variation of VP in the YRB. Finally, we used several statistical indicators and a distributed lag nonlinear model (DLNM) to analyze the nonlinear effect of AD on VP in the YRB. The results showed that AD decreased significantly during 2000–2020, mainly in the southeast of the Loess Plateau, while GPP increased significantly in 80.93 % of the YRB. Meanwhile, moderate and severe AD stress limited VP growth, with the negative effects gradually decreasing, while mild AD had an increasingly positive promoting effect on VP. AD stress resulted in a VP decrease of 69.78 %, and severe AD stress resulted in a VP decrease of 65.52 %, mainly distributed in the northern Loess and Ordos Plateau. AD had significant nonlinear effects on VP. The effects of moderate and severe AD on the sustained nonlinear lag of vegetation were more obvious, and those of moderate and severe AD on the nonlinear lag of VP were the largest when the lag was approximately 1 month and 7 months. The effect of AD on the nonlinear hysteresis of VP in YRB was significantly different under different vegetation types, and forests were more able to withstand longer and more severe droughts than grasslands and croplands. The results of the study provide a theoretical basis for evaluating AD and analyzing the nonlinear impact of AD on VP. This will provide scientific basis for studying the mechanism of drought effect on vegetation in other regions.

Is There an Asymmetric Effect Due to Foreign Direct Investment on the Exports of the Manufacturing and Service Sectors of Central, Eastern, and South-Eastern European Countries?

ABSTRACT This study estimates the asymmetric effect of foreign direct investment on the exports of the manufacturing and service sectors of 11 Central, Eastern, and South-Eastern (CESEE) countries, using the nonlinear ARDL model, over the period of 1996–2022. The results show an asymmetric effect due to mergers & acquisitions (M&A) on the exports of 3 countries, while greenfield foreign direct investment (GFDI) has an impact on the exports of 4 of the 17 manufacturing sectors. There is also an asymmetric effect due to M&A on the exports of 5 out of the 6 service sectors.

Numerical threshold stability of an unconditionally positivity-preserving numerical method for a nonlinear age-structured reaction-diffusion brucellosis model

Numerical threshold stability of an unconditionally positivity-preserving numerical method for a nonlinear age-structured reaction-diffusion brucellosis model

Simulation-based inference on virtual brain models of disorders

Connectome-based models, also known as virtual brain models (VBMs), have been well established in network neuroscience to investigate pathophysiological causes underlying a large range of brain diseases. The integration of an individual’s brain imaging data in VBMs has improved patient-specific predictivity, although Bayesian estimation of spatially distributed parameters remains challenging even with state-of-the-art Monte Carlo sampling. VBMs imply latent nonlinear state space models driven by noise and network input, necessitating advanced probabilistic machine learning techniques for widely applicable Bayesian estimation. Here we present simulation-based inference on VBMs (SBI-VBMs), and demonstrate that training deep neural networks on both spatio-temporal and functional features allows for accurate estimation of generative parameters in brain disorders. The systematic use of brain stimulation provides an effective remedy for the non-identifiability issue in estimating the degradation limited to smaller subset of connections. By prioritizing model structure over data, we show that the hierarchical structure in SBI-VBMs renders the inference more effective, precise and biologically plausible. This approach could broadly advance precision medicine by enabling fast and reliable prediction of patient-specific brain disorders.

Effects of apparent temperature on hospitalization rates for cardiovascular diseases: a case study of different rural areas in Northwest China

ABSTRACT Apparent temperature (AT) is a composite index that combines ambient temperature, humidity, wind speed and other meteorological factors, and reflects heat perception more accurately than raw temperature. This is the first study to investigate the association between AT and CVD in rural areas of Jiuquan and Longnan, Gansu Province, China. In this study, the distributed lag nonlinear model (DLNM) was used to examine the exposure-response relationship between AT and the 21 days relative risk (RR) of CVD admission. The results showed that the exposure risk of the gender group in Jiuquan was opposite to that of Longnan under the influence of cold effect. Under the influence of heat effect, it has a protective effect on all groups in Jiuquan area, which is harmful to males and adults in Longnan area. The results of this study can help local governments to formulate public policies.

Increased e-cigarette use prevalence is associated with decreased smoking prevalence among US adults

BackgroundIf US adults who smoke cigarettes are switching to e-cigarettes, the effect may be observable at the population level: smoking prevalence should decline as e-cigarette prevalence increases, especially in sub-populations with highest e-cigarette use. This study aimed to assess such effects in recent nationally-representative data.MethodsWe updated a prior analysis with the latest available National Health Interview Survey data through 2022. Data were cross-sectional estimates of the yearly prevalence of smoking and e-cigarette use, respectively, among US adults and among specific age, race/ethnicity, and sex subpopulations. Non-linear models were fitted to observed smoking prevalence in the pre-e-cigarette era, with a range of ‘cut-off’ years explored (i.e., between when e-cigarettes were first introduced to when they became widely available). These trends were projected forward to predict what smoking prevalence would have been if pre-e-cigarette era trends had continued uninterrupted. The difference between actual and predicted smoking prevalence (‘discrepancy’) was compared to e-cigarette use prevalence in each year in the e-cigarette era to investigate whether the observed decline in smoking was statistically associated with e-cigarette use.ResultsObserved smoking prevalence in the e-cigarette era was significantly lower than expected based on pre-e-cigarette era trends; these discrepancies in smoking prevalence grew as e-cigarette use prevalence increased, and were larger in subpopulations with higher e-cigarette use, especially younger adults aged 18–34. Results were robust to sensitivity tests varying the analysis design.ConclusionsPopulation-level data continue to suggest that smoking prevalence has declined at an accelerated rate in the last decade in ways correlated with increased uptake of e-cigarette use.

Frailty Modeling using Machine Learning Methodologies: A Systematic Review with Discussions on Outstanding Questions.

Studying frailty is crucial for enhancing the health and quality of life among older adults, refining healthcare delivery methods, and tackling the obstacles linked to an aging demographic. Approaches to frailty modeling often utilise simple analytic techniques rather than available advanced machine learning methods, which may be sub-optimal. There is no large-scale systematic review on applications of machine learning methods on frailty modeling. In this study we explore the use of machine learning methods to predict or classify frailty in older persons in routinely collected data. We reviewed 181 research articles, and categorised analytic methods into three categories: generalised linear models, survival models, and non-linear models. These methods have a moderate agreement with existing frailty scores and predictive validity for adverse outcomes. Limited evidence suggests that non-linear methods outperform generalised linear methods. The top-three predictor/input variables are specific diagnosis or groups of diagnoses, functional performance (e.g., ADLs), and impaired cognition. Mortality, hospital admissions and prolonged hospital stay are the mainly predicted outcomes. Most studies utilise classical machine learning methods with cross-sectional data. Longitudinal data collected by wearable sensors have been used for frailty modeling. We also discuss the opportunities to use more advanced machine learning methods with high dimensional longitudinal data for more personalised and accessible frailty tools.

Assessment of coffee leaves nutritive value via portable X-ray fluorescence spectrometry and machine learning algorithms

Portable X-ray fluorescence (pXRF) spectrometry is a non-destructive technique that has been successfully used to analyze different matrices. Foliar analysis is challenging because some plant nutrients cannot be detected by pXRF. Even so, the uptake interactions among nutrients which reflect different concentrations of macro- and micronutrients can be accessed via pXRF, constituting a basis to obtain predictive models of plant nutrients. The objective of this work was to compare and assess the accuracy of linear regression and non-linear models (support vector machine – SVM; and random forest – RF) to predict the actual concentration of macro- (N, P, K, Ca, Mg, and S) and micronutrients (B, Cu, Fe, Zn, and Mn) in coffee leaves. A greenhouse experiment was conducted using Hoagland and Arnon solution to obtain leaves with contrasting elemental composition. Ground and oven-dried leaf samples were analyzed via pXRF using: i) a manufactured pXRF calibration developed for general earth-materials (Geoexploration mode); ii) the Spectrometer mode with varying voltage and current (15 kV and 25 μA; 10 kV and 10 μA). The same samples were also analyzed via conventional acid digestion and quantified via inductively coupled plasma-optical emission spectroscopy (ICP-OES). The best predictions were obtained using SVM and RF algorithms, with high R2 (0.82 to 0.99) and high residual prediction deviation (RPD) (2.35 to 9.34) values. However, some elements (e.g., K, Ca, Cu, Mn) were successfully predicted using linear models (LR and MLR). Even elements not detected (N and B) by pXRF were accurately predicted using the RF model. The pXRF operational conditions influenced the performance of the models. However, by parsimony, Geoexploration mode provided data for accurate prediction of macro- and micronutrients. This comprehensive study can potentially spark further investigations into examining coffee leaves from plants cultivated under various environmental and management conditions. Additionally, the methodological framework outlined here holds promise for ongoing experimentation across diverse crops, offering a streamlined, non-invasive, eco-friendly, and rapid approach for foliar analysis.

Longitudinal Nonlinear Equivalent Continuous Model for Shield Tunnel under Coupling of Longitudinal Axial Force and Bending Moment

Longitudinal Nonlinear Equivalent Continuous Model for Shield Tunnel under Coupling of Longitudinal Axial Force and Bending Moment

Nonlinear SIRS Fractional-Order Model: Analysing the Impact of Public Attitudes towards Vaccination, Government Actions, and Social Behavior on Disease Spread

This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the equilibrium points is analyzed. Sensitivity analysis is conducted to calculate and discuss the sensitivity index of various parameters. It has been established that the illness would spread across this system when the basic reproduction number is larger than 1, the system becomes infection-free when the reproduction number lies below its threshold value of 1. Numerical figures depict the effects of positive and negative attitudes towards vaccination to make the system disease-free sooner. A comprehensive study regarding various values of the order of fractional derivatives together with integer-order derivatives has been discussed in the numerical section to obtain some useful insights into the intricate dynamics of the proposed system. The Pontryagin principle is used in the formulation and subsequent discussion of an optimum control issue. The study also reveals the significant role of government actions in controlling the epidemic. A numerical analysis has been conducted to compare the system’s behavior under optimal control and without optimal control, aiming to discern their differences. The policies implemented by the government are regarded as the most adequate control strategy, and it is determined that the execution of control mechanisms considerably diminishes the ailment burden.

Individual Fertilization Response with Social Status and Crown Characteristics for Western Hemlock (Tsuga heterophylla)

Due to their high variability, the growth responses of western hemlock (Tsuga heterophylla (Raf.) Sarg.) stands to fertilization have been regarded as unresponsive or inconsistent. Tree-level fertilization response models for western hemlock were constructed to clarify the inconsistent stand-level responses, using extensive datasets from the United States and Canada. Tree growth in diameter and height, mortality, were assessed by fertilization, stand- and tree-level variables using generalized linear and non-linear mixed effects models. Western hemlock fertilization response was influenced not only by stand-level variables and application rates but also by tree social status and crown characteristics. Greater dominance and crown ratio in trees increased height growth responses but decreased diameter growth. The peak of fertilization effect on diameter growth was observed three years after application, while effect on height growth peaked at six years. Fertilization increased the overall mortality rate, but also ameliorated it for suppressed and steady-growing trees. These complicated fertilization responses of western hemlock may imply its tolerance and allocation strategy of resources at a given size and social status. The results highlight the importance of adopting a tree-level modelling approach to better understanding how western hemlock trees respond to fertilization, improving the accuracy of growth and yield prediction after fertilization.

Optimal designs for nonlinear mixed-effects models using competitive swarm optimizer with mutated agents

Optimal designs for nonlinear mixed-effects models using competitive swarm optimizer with mutated agents

Gas Free Dissipation Characteristics Analysis and Safety Repair Time Determination of Buried Pipeline Leakage Based on CFD

Buried pipelines, as the most common method of natural gas transportation, are prone to pipeline leakage accidents and are difficult to detect due to their harsh and concealed environment. This paper focused on the problem regarding the free dissipation of residual gas in buried gas pipelines and soil after closing the gas supply end valve after a period of leakage by numerical simulation. A multiple non-linear regression model was established based on the least squares method and multiple regression theory, and MATLAB 2016b mathematical calculation software was used to solve the problem. The research results indicated that compared to the gas leakage diffusion stage, the pressure and velocity distribution during the free dissipation stage were significantly reduced. The increase in leakage time, pipeline pressure, leakage size, and pipeline burial depth led to a large accumulation of natural gas, which increased the concentration and distribution range of gas on the same free dissipation stage monitoring line. A prediction model for natural gas concentration in the free dissipation stage was established with an average error of 7.88%. A calculation model for the safety repair time of buried gas pipeline leakage accidents was further derived to determine the safety repair time of leakage accidents.

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

In this study, we use analytical algorithms, specifically the auxiliary equation (AE) approach, the improved F-expansion method, and the modified Sardar sub-equation (MSSE) method to investigate complex wave structures for plentiful solutions associated with the fractional perturbed Gerdjikov-Ivanov (PGI) model with the M-fractional operator. The investigated model is a well-established mathematical model used to represent a variety of physical events in nonlinear dynamics and mathematical physics. By using the aforementioned techniques, we scrutinize some new optical wave solutions in the framework of dark, bright, periodic, combo, W-shaped, M-shape, V-shape, kink type, singular rational, exponential, trigonometric, and hyperbolic solutions. The acquired solutions address a wide range of optical solutions in the form of 3D plots, contour plots, and 2D plots, declaring the free parameters of such optical soliton solutions and comprehending their dynamic behavior. Also, the sensitive analysis of the selected model is analyzed. The main contribution of this study is to extract diverse solitary wave solutions of the adopted model. Some of the solutions are similar and some diverge from the previous solutions which justifies the novelty of the study. Finally, we discovered that the current technique provides a reliable instrument for investigating the analytic solutions of fractional differential equations. The proposed PGI model can be used to transmit ultra-fast pulses across optical fibers. This research goes beyond to the advancement of mathematical techniques for solving fractional differential equations and broadens their application to a wide range of real-world scientific and engineering problems.