Nonlinear Model Research Articles

Experimental and Numerical Study on Nonlinear Shear Behavior and Constitutive Model of Deep Shale Laminae Planes

The direct shear tests showed that the degradation of unevenness and waviness of the laminae plane is the primary reason for the dynamic decrease in shear strength. A shear constitutive model was proposed which considers the scale effect and the asperity geometry of the unevenness and waviness of the laminar plane. The evolution of the shear strength and stiffness with a normal stress and scale effect during the shearing of shale laminae planes was explored. The results show that high normal stress aggravates the stiffness hardening of laminae planes and forms larger peak shear stress and peak shear displacement. At the lab scale, the increase in the unevenness wavelength has a hardening effect on the shear stiffness and strength. The small-scale unevenness contributes most to the shear strength of shale laminae planes at the lab scale. At the field scale, the increase in the waviness wavelength has a softening effect on the shear stiffness and strength.

Impact of Non-Linear Contact Models on DEM Simulations of Cemented Angular Limestone Behavior

Impact of Non-Linear Contact Models on DEM Simulations of Cemented Angular Limestone Behavior

Reliability Analysis of Complex Structures Under Multi-Failure Mode Utilizing an Adaptive AdaBoost Algorithm

A reliability analysis can become intricate when addressing issues related to nonlinear implicit models of complex structures. To improve the accuracy and efficiency of such reliability analyses, this paper presents a surrogate model based on an adaptive AdaBoost algorithm. This model employs an adaptive method to determine the optimal training sample set, ensuring it is as evenly distributed as possible on both sides of the failure curve and fully contains the information it represents. Subsequently, with the integration and iterative characteristics of the AdaBoost algorithm, a simple binary classifier is iteratively applied to build a high-precision alternative model for complex structural fault diagnosis to cope with multiple failure modes. Then, the Monte Carlo simulation technique is employed to meticulously assess the failure probability. The accuracy and stability of the proposed method’s iterative convergence process are validated through three numerical examples. The findings of the study illuminate that the proposed method is not only remarkably precise but also exceptionally efficient, capable of addressing the challenges related to the reliability evaluation of complex structures under multi-failure mode. The method proposed in this paper enhances the application of mechanical structures and facilitates the utilization of complex mechanical designs.

Leveraging mathematical modeling framework to guide regimen strategy for phage therapy

Bacteriophage (phage) cocktail therapy has been relied upon more and more to treat antibiotic-resistant infections. Understanding of the complex kinetics between phages, target bacteria, and the emergence of phage resistance remain hurdles to successful clinical outcomes. Building upon previous mathematical concepts, we develop biologically-motivated nonlinear ordinary differential equation models to explore single, cocktail, and sequential phage treatment modalities. While the optimal pairwise phage treatment strategy was the double simultaneous administration of two highly potent and asymmetrically binding phage strains, it appears unable to prevent the evolution of resistance. This treatment regimen did have a greater lysis efficiency, promoted higher phage population sizes, reduced bacterial density the most, and suppressed the evolution of resistance the longest compared to all other treatments strategies tested. Conversely, the combination of phages with polar potencies allows the more efficiently replicating phages to monopolize susceptible host cells, thereby quickly negating the intended compounding effect of cocktails. Together, we demonstrate that a biologically-motivated modeling-based framework can be leveraged to quantify the effects of each phage’s properties to more precisely predict treatment responses.

Application of Machine Learning for Predictive Analysis and Management of Mediterranean-Farmed Fish Mortalities: A Risk Management Case Study Using Apache Spark

The current study evaluates the performance of three machine learning models—Decision Trees, Random Forest, and Linear Regression—applied to aquaculture data to mitigate risks in aquaculture management. The performances of these models are analyzed and properly demonstrated using metrics including the Mean Squared Error (MSE), R-squared (R2), Root Mean Squared Error (RMSE), and Concordance Index (C-index). The Random Forest model achieved the highest prediction accuracy among all machine learning models, followed by Linear Regression and the Decision Trees. The scatter plot for Linear Regression demonstrates good predictive accuracy for mid-range values. However, it shows significant deviations at the extremes, indicating that the model struggles to capture the full range of variability in the data. The bar chart of coefficients pinpoints the variables with the greatest impact on the predictions, providing suggestions for potential areas that can be improved and providing model interpretability. Future work could incorporate more predictive statistics models focusing on improving the models for extreme values by assessing non-linear models, feature engineering methods, and expanding research into less influential variables. The results greatly impact several sections, including aquaculture management, policy-making, and operational strategies, providing valuable insights for stakeholders and decision-makers. Apache Spark was used for data processing and machine learning model implementation; Apache Cassandra was also used for data storage, ensuring efficient large dataset management and SQL tools for structured data handling; Oracle VM VirtualBox for cross-platform virtualization; and Spark Connector was also used.

A NEW HYBRID OPTIMIZATION METHOD USED IN PREDICTIVE CONTROL OF A NONLINEAR FRACTIONAL MODEL BASED ON FRACTIONAL HAMMERSTEIN STRUCTURE

Fractional Hammerstein models represent various nonlinear processes, such as thermal and mechanical. Their major drawback is the non-convex optimization problem in a nonlinear model predictive control scheme due to its static nonlinearity. Indeed, an efficient optimization algorithm is needed. This work proposes a hybrid optimization algorithm combining the Nelder Mead optimization method and the Honey Badger one to synthesize a predictive control algorithm based on fractional Hammerstein models. As illustrated through simulation results, the proposed method offers clear improvements in convergence and tracking performances.

Attitude Control System for Quadrotor Using Robust Monte Carlo Model Predictive Control

Monte Carlo Model Predictive Control (MCMPC) is a kind of non-linear Model Predictive Control (MPC) that determines control inputs using the Monte Carlo method. The Monte Carlo method used in MCMPC can handle discontinuous phenomena, and there have been reports of its application in control systems for quadrotors, where the objective is to maintain the stability of the attitude during collisions. However, as with conventional MPC, concerns remain about control performance degradation due to modeling errors and external disturbances such as unexpected wind gusts. In this study, we propose a novel Robust Monte Carlo Model Predictive Control (RMCMPC), which improves the robustness of MCMPC by considering the hypersurface known from the Sliding Mode Control (SMC) theory. The proposed RMCMPC is applied to a quadrotor attitude control system, and its effectiveness is validated through numerical simulations.

Impact of Heat on Respiratory Hospitalizations among Older Adults in 120 Large US Urban Areas.

Extreme heat exposure is a well-known cause of mortality among older adults. However, the impacts of exposure on respiratory morbidity across US cities and population subgroups is not well understood. A nationwide study to determine the impact of high heat on respiratory disease hospitalizations among older adults (65+) living in the 120 largest US cities between 2000-2017. Daily rates of inpatient respiratory hospitalizations were examined with respect to variations in ZIP-code-level daily mean temperature and heat index. For each city, we estimated cumulative associations (lag-days 0-6) between warm-season heat (June-September) and cause-specific respiratory hospitalizations using time-stratified conditional quasi-Poisson regression with distributed lag non-linear models. We estimated nationwide associations using multivariate meta-regression and updated city-specific associations via best linear unbiased prediction. With stratified models, we explored effect modification by age, sex, and race (Black/white). Results were reported as percent change in hospitalizations at high temperatures (95th percentile) compared to median temperatures for each outcome, demographic group, and metropolitan area. We identified 3,275,033 respiratory hospitalizations among Medicare beneficiaries across 120 large US cites between 2000 and 2017. Nationwide, 7-day cumulative associations at high temperatures, resulted in a 1.2% (0.4%, 2.0%) increase in hospitalizations for primary diagnoses of all-cause respiratory disease, primarily driven by increases in respiratory tract infections [1.8% (0.6%, 3.0%)], and chronic respiratory diseases/respiratory failure [1.2% (0.0%, 2.4%)]. Stronger associations were observed when exposure was defined using the heat index instead of temperature. Across the 120 cities, we observed considerable geographic variation in the relative risk of heat-related respiratory hospitalizations, and we observed disproportionate burdens of heat-related respiratory hospitalizations among the oldest beneficiaries (85+ years), and among Black beneficiaries living in South Atlantic cities. During the 18-year study period, there were an estimated 11,710 excess respiratory hospitalizations due to heat exposure. Results suggest that high temperature and humidity contribute to exacerbation of respiratory tract infections and chronic lung diseases among older adults. Geographic variation in heat-related hospitalization rates suggests that contextual factors largely account for disproportionate burdens, and area-level influences should be further investigated in multi-city studies.

Forecasting techniques based on the use of time series models for forecasting expenditures on social protection and social security

In the context of a military conflict, it is growing the number of people who are in difficult life circumstances and need state assistance. Therefore, the issue of forecasting spending on social protection and social security is becoming increasingly relevant. The aim of the paper is to consider modern methods of analyzing and forecasting time series and propose their application to determine the need for spending on social protection and social security. The article provides a brief overview of regression models, their advantages and features of use for analyzing and predicting nonlinear and linear processes described by time series of statistical indicators used in the population social protection system. The paper offers a combination of predictions that can be made based on locally linear and nonlinear models, such as threshold autoregression (TAR) and exponential autoregression (ExAR), which have known quality characteristics. This approach primarily concerns time series that contain data on structural changes in the analyzed processes. Using combined predictions, it is possible to estimate the contribution of each component for both different and selected time points using variable weights. To build forecasts, depending on the scenario of distribution of social protection and social security expenditures, it is proposed to use Bayes networks. Their advantages are flexibility, high quality of results, the possibility of structural and parametric optimization and adaptation to new data and conditions, support for quality assessment by appropriate sets of statistical criteria, which makes it possible to analyze thoroughly intermediate and final results. It helps to increase the adequacy of models and the high quality of the final result of their application.

Multiplicity of solutions for a nonhomogeneous quasilinear elliptic equation with concave-convex nonlinearities

Abstract We investigate the multiplicity of solutions for a quasilinear scalar field equation with a nonhomogeneous differential operator defined by S u ≔ − div ϕ u 2 + ∣ ∇ u ∣ 2 2 ∇ u + ϕ u 2 + ∣ ∇ u ∣ 2 2 u , Su:= -\hspace{0.1em}\text{div}\hspace{0.1em}\left\{\phi \left(\frac{{u}^{2}+{| \nabla u| }^{2}}{2}\right)\nabla u\right\}+\phi \left(\frac{{u}^{2}+{| \nabla u| }^{2}}{2}\right)u, where ϕ : [ 0 , + ∞ ) → R \phi :\left[0,+\infty )\to {\mathbb{R}} is a positive continuous function. This operator is introduced by Stuart [Two positive solutions of a quasilinear elliptic Dirichlet problem, Milan J. Math. 79 (2011), 327–341] and depends on not only ∇ u \nabla u but also u u . This particular quasilinear term generally appears in the study of nonlinear optics model, which describes the propagation of self-trapped beam in a cylindrical optical fiber made from a self-focusing dielectric material. When the reaction term is concave-convex nonlinearities, by using the Nehari manifold and doing a fine analysis associated on the fibering map, we obtain that the equation admits at least one positive energy solution and negative energy solution, which is also the ground state solution of the equation. We overcome two main difficulties which are caused by the nonhomogeneity of the differential operator S S : (i) the almost everywhere convergence of the gradient for the minimizing sequence { u n } \left\{{u}_{n}\right\} ; (ii) seeking the reasonable restrictions about S S .

Action potential threshold variability for different electrostimulation models and its potential impact on occupational exposure limit values.

Occupational exposure limit values (ELVs) for body internal electric fields can be derived from thresholds for action potential generation. These thresholds can be calculated with electrostimulation models. The spatially extended nonlinear node model (SENN) is often used to determine such thresholds. Important parameters of these models are the membrane channel dynamics describing the ionic transmembrane currents as well as the temperature at which the models operate. This work compares action potential thresholds for five different membrane channel dynamics used with the SENN model. Furthermore, two more detailed double-cable models by Gaines et al. (MRG-Sensory and MRG-Motor) are also considered in this work. Thresholds calculated with the SENN model and the MRG models are compared for frequencies between 1 Hz and 100 kHz and temperatures at 22°C and 37°C. Results show that MRG thresholds are lower than SENN thresholds. Deriving alternative ELVs from these thresholds shows that the alternative ELVs can change significantly with different ion channel dynamics (up to a factor of 22). Using the double cable model could lead to approximately ten times lower alternative exposure limit values. On the contrary, using the SENN model with different membrane channel dynamics could also lead to higher alternative exposure limit values. Therefore, future exposure guidelines should take the influence of different electrostimulation models into account when deriving ELVs.

Population pharmacokinetic modeling of zavegepant, a calcitonin gene-related peptide receptor antagonist, in healthy adults and patients with migraine.

Zavegepant (ZAVZPRET™) is a high-affinity, selective, small-molecule calcitonin gene-related peptide receptor antagonist available for acute treatment of migraine in adults. A population pharmacokinetic analysis was performed to describe zavegepant plasma concentration-time course, characterize bioavailability, and identify covariates affecting zavegepant exposure. The model was developed and validated using data from 10 phase I clinical studies, wherein zavegepant was administered intravenously, intranasally, or orally to healthy adults and patients with migraine. Plasma concentration-time data were analyzed using nonlinear mixed-effects modeling. A three-compartment model with first-order elimination from the central compartment, and sequential zero- and first-order absorption best described the observed plasma concentration-time course of zavegepant. Bioavailability was 5.1% and 0.65% for intranasal and oral treatment, respectively; absorption rate constants were 5.8 and 0.8 h-1, respectively. Body weight-based empirical allometric scaling was applied using standard exponents (0.75 for clearance and 1 for volume of distribution). Age (range 18-71 years), race, ethnicity, sex, renal function, and co-administration of oral contraceptives or sumatriptan did not significantly change zavegepant pharmacokinetics. Moderate hepatic impairment (Child-Pugh score 7-9) or co-administration of rifampin decreased elimination clearance of oral zavegepant by ~40%. The zavegepant population pharmacokinetic model adequately characterized zavegepant concentration-time profiles, the bioavailability of intranasal and oral zavegepant, as well as the effect of intrinsic and extrinsic factors on zavegepant pharmacokinetics.

Chemically reactive stagnated third‐grade magnetized nanomaterial considering modern diffusion approaches

AbstractAn incompressible boundary‐layer third‐grade nanomaterial stagnated flow confined by stretchy regime is formulated. The laminar magnetized thermal and solutal flow features the aspects of Brownian diffusion, generalized thermal‐flux, thermophoresis, and generalized solutal‐flux. The dimensionalized third‐grade steady‐state model is obtained by implementing appropriate variables. The subsequent nonlinear mathematical model is analytically computed by utilizing homotopy algorithm. The graphics demonstration of nondimensional fields (i.e., velocity, concentration, and temperature) for distinct physical variables is exhibited. The outcomes for the skin‐friction coefficient are calculated and confirmed to be precise. The analysis reveals that augmented values of material parameters escalate nanomaterial velocity while the Hartman number exhibits lower velocity. The temperature field displays a decaying trend for Prandtl number and thermal relaxation variable while contrary effects for nanoscale parameters (i.e., thermophoresis diffusive and Brownian diffusive) are reported. Besides, the nanomaterial concentration shows a decreasing trend with respect to the Schmidt number, Brownian motion, and solutal‐relaxation variable while thermophoresis parameter exhibits opposite effects. Furthermore, this study could be valuable for the design of various lab‐on‐a‐chip and thermal microfluidic devices in the field of biomedicine. Besides contributing to the creation of new devices, they may also be advantageous for performing genetic testing and developing innovative tools.

Nonlinear second order plus time delay model identification and nonlinear PID controller tuning based on extended linearization method

PID control systems based on the first order plus time delay model (FOPTD), which approximate the full system dynamics, are well-accepted for a wide range of linear processes. While such controllers can be applied to overdamped nonlinear processes, they often experience excessive overshoots and oscillations for general nonlinear processes. To overcome this limitation, we propose a novel method to design a nonlinear PID controller based on the second order plus time delay (SOPTD) model. The system nonlinearity requires parameter adjustments of the linearized model across operational ranges. Hence, in this work, it is handled by the extended linearization method (ELM), ensuring local stability under the assumptions of slow and small changes in operating points. Importantly, the model achieves global input-to-output stability even without the above constraints, provided there are no structural and parametric errors. The resulting nonlinear SOPTD model can describe changes in process gain and two time constants as the operation point varies. We demonstrate the applicability of our approach with a polymerization reactor simulation and liquid-level control experiments.

Hyperspectral Inversion of Soil Cu Content in Agricultural Land Based on Continuous Wavelet Transform and Stacking Ensemble Learning

Heavy metal pollution in agricultural land poses significant threats to both the ecological environment and human health. Therefore, the rapid and accurate prediction of heavy metal content in agricultural soil is crucial for environmental protection and soil remediation. Acknowledging the limitations of traditional single linear or nonlinear machine learning models in terms of prediction accuracy, this study developed an ensemble learning model that integrates multiple linear or nonlinear learning models with a random forest (RF) model to improve both the prediction accuracy and reliability. In this study, we selected a typical copper (Cu) polluted area in the Pearl River Delta of Guangdong Province as the research site and collected Cu content data and indoor soil reflectance spectral data from 269 surface soil samples. First, the soil spectral data were preprocessed using Savitzky–Golay (SG) smoothing, multiplicative scattering correction (MSC), and continuous wavelet transform (CWT) to reduce noise interference. Next, principal components analysis (PCA) was employed to reduce the dimensionality of the preprocessed spectral data, eliminating redundant features and lowering the computational complexity. Finally, based on the dimensionality-reduced data and Cu content, we established a stacked ensemble learning model, where the base models included SVR, PLSR, BPNN, and XGBoost, with RF serving as the meta-model to estimate the soil heavy metal content. To evaluate the performance of the stacking model, we compared its prediction accuracy with that of individual models. The results indicate that, compared to the traditional machine learning models, the prediction accuracy of the stacking model was superior (R2 = 0.77; RMSE = 7.65 mg/kg; RPD = 2.29). This suggests that the integrated algorithm demonstrates a greater robustness and generalization capability. This study presents a method to improve soil heavy metal content estimation using hyperspectral technology, ensuring a robust model that supports policymakers in making informed decisions about land use, agriculture, and environmental protection.

Creep behavior of BFRP-confined coal gangue concrete under sulfate and high stress conditions

To recycle the coal gangue more economically and effectively, the basalt fiber reinforced polymer (BFRP) and coal gangue concrete (CGC) are combined to form a novel supporting structure in the underground mines, BFRP-confined CGC (FCGC). However, the underground mine environment is rich in sulfate corrosive ions, and meanwhile, the structure is subjected to a high sustained load. Thus, this paper presents an experimental and theoretical investigation on the long-term deformation properties of FCGC under sulfate and high stress conditions. The effects of inner concrete, FRP layer, stress-to-strength ratio, sulfate concentration and load duration time on the shrinkage and creep behavior were clarified in detail. The findings indicate that the shrinkage of FCGC is relatively lower as the BFRP confinement weakens the moisture exchange between inner CGC and external environment. In addition, under sulfate and high stress conditions, the creep strain and specific creep increase continuously in the early stage, while the growth rate gradually slows down in the later stage, where the high stress-to-strength ratio is the key factor. Moreover, when compared with a single high stress condition, the creep strain of FCGC is relatively larger under sulfate and high stress coupling conditions, attributed to the sulfate corrosion on the BFRP wraps. Theoretically, the ACI 209 was modified to predict the nonlinear creep of CGC, by introducing the coal gangue influence coefficient and the increasing coefficient of nonlinear creep. Furthermore, based on the creep model of CGC and BFRP, the nonlinear calculation model of FCGC was developed considering the creep of CGC under a triaxial-stress state and the interaction between inner CGC and BFRP confinement. Validations against the experimental results show that the nonlinear creep model of FCGC works well.

Optimized Kalman filtering in dynamical environments for thumb robot motion estimation

<span>Stroke, a prevalent nerve disorder in Indonesia, necessitates post-stroke rehabilitation like physical and occupational therapy. Hand and finger muscle training, crucial for restoring movement, often involves innovative solutions like finger prosthetic robotics arms. In particular, the advancement in thumb robotics emphasizes the estimation of thumb motion, where the ensemble Kalman filter square root (EnKF-SR) and H-infinity methods are deemed dependable for both linear and nonlinear models. Simulation results, using 400 ensembles, demonstrated nearly identical accuracy between the methods, exceeding 99%, with a 6-7% increase in accuracy compared to 200 ensembles. These advancements offer promising prospects for effective post-stroke rehabilitation and improved thumb movement restoration.</span>

Suspicious of Acute Kidney Graft Rejection: Tacrolimus Pharmacokinetics Under Methylprednisolone Therapy.

Acute rejection remains one of the main complications in the first months after transplantation and may influence long-term outcomes. Tacrolimus has proven its usefulness in solid organ transplants and its monitoring through the application of pharmacokinetic concepts to optimize individual drug therapy. This research proposes to evaluate the tacrolimus pharmacokinetic parameters in patients suspected of acute kidney graft rejection under methylprednisolone pulse therapy. Eleven adult tacrolimus-treated renal recipients were selected from a prospective, single-arm, single-center cohort study, with suspicion of acute rejection although in use of methylprednisolone pulses therapy. They were followed up for three months posttransplantation, being tacrolimus trough serum concentrations determined using a chemiluminescent magnetic immunoassay, and pharmacokinetic parameters were estimated by using a nonlinear mixed-effects model implemented by Monolix 2020R1. A tacrolimus trough serum concentration range of 8 to 12 ng.mL-1 was considered therapeutic. Six patients showed acute cellular rejection, and two of them in addition had an antibody- mediated rejection. Tacrolimus trough serum concentration was below the reference range in eight patients. Most patients showed a high tacrolimus concentration intrapatient and pharmacokinetic parameters variability. The obtained pharmacokinetics parameters helped in understanding the kidney recipient patients' tacrolimus behavior, assisting in the improvement of individual drug therapy and reducing the risk of acute rejection episodes.

A Review of Particle Packing Models and Their Applications to Characterize Properties of Sand-Silt Mixtures

This paper reviews particle packing models and explores their application in geotechnical engineering, specifically for sand-silt mixtures. The review covers key models, including limiting case, linear, and non-linear packing models, focusing on their mathematical structures, physical principles, assumptions, and limitations through the concept of excess free volume. The application of particle packing models in geotechnical engineering is explored in characterizing the properties of sand-silt mixtures, offering insights into maximum, minimum, and critical void ratios and inter-granular void ratio, and the prediction of mechanical properties.

Dosing strategy of tacrolimus when co-administered with Wuzhi tablet in renal transplant recipients.

Tacrolimus (TAC) is a first-line immunosuppressant to prevent allograft rejection. Wuzhi tablet is widely used as a TAC-sparing agent in China that could significantly elevate TAC exposure. However, insufficient data support the dose recommendation of TAC when co-administered with Wuzhi. A total of 305 adult renal transplant patients with 2,541 TAC trough concentrations (C0) were enrolled for population pharmacokinetic (PPK) modeling. CYP3A5 polymorphism was genotyped, and corresponding clinical factors were recorded. Nonlinear mixed-effects modeling and Monte Carlo simulation were used for dose recommendation. PK parameters were calculated based on one-compartment model with first-order absorption and elimination. The estimated total clearance (CL/F) and volume of distribution (Vd/F) of TAC were 23.84 L/h and 1,075.96 L, respectively. Wuzhi, CYP3A5 genotype, hematocrit (HCT), and weight were found to have a significant influence on CL/F. CL/F was significantly lower in the individuals who were CYP3A5 non-expressers and received TAC together with Wuzhi. CYP3A5 genotype (expressers or non-expressers), body weight (40-80 kg), and hematocrit (20 - 40%) were selected as the specific clinical scenarios, and the starting dose of TAC ranged from 1.5 to 4.5 mg when co-administered with Wuzhi. We establish a TAC PPK model comprising Wuzhi as a covariate in renal transplant recipients and recommend an initial dose of TAC when co-administered with Wuzhi, which could provide reference for the individualized regimens of TAC.