Nonlinear Model Research Articles

Rate expression model from thermodynamics application and optimal kinetic parameters determination for urea synthesis and production process

Urea, an essential organic fertilizer, enhances soil fertility by providing 0.466 nitrogen for maximum crop yield. In this study, urea is synthesized from NH3 and CO2 in an equilibrium reaction process adhering to Le Chatelier's principle, maintained under process conditions: flow rate of 63.5 kg/s, temperature of 184 °C, and pressure of 160 kg/cm2. A new rate expression model, formulated in terms of extent of reaction and mole fraction, was developed based on mass action relations and thermodynamic models. Two industrial reactors were considered: a plug flow reactor (PFR) at Notore and a continuous stirred tank reactor (CSTR) at Indorama plants. Transient reactor models, based on material and energy balance conservation principles, were numerically resolved using MATLAB version 2020 with specified input conditions. A non-linear regression statistical optimization model was employed to refine kinetic parameter values, ensuring optimal and high-quality urea yield. Model validations were conducted using literature data, revealing higher urea yields of 0.726 and 0.7032 for the CSTR and PFR, respectively. Deviations (0.134, 0.10 to 1.135 and 0.635, 0.326 to 0.850) and root mean square errors (RMSE) (0.043, 0.033 to 0.193 and 0.137, 0.087 to 0.162) were observed when validated against plant and literature values for the CSTR and PFR respectively. The refined kinetic parameters (activation energies, Arrhenius constants, and rate constants) exhibited negligible deviations (0.0004–0.0466 and 0.0004 to 0.0491) and RMSE (0.0228, 0.0055, and 0.0256 and 0.0241, 0.0096, and 0.0269) when validated against plant data, significantly enhancing urea yield in CSTR and PFR reactors respectively.

Modular stochastic configuration network with attention mechanism for soft measurement of water quality parameters in wastewater treatment processes

Due to the complex and multi-distributed nature of wastewater treatment process data, stochastic configuration networks (SCNs) face difficulties such as large network structure and complex construction process when dealing with data modeling tasks. To address these challenges, this paper proposes a modular stochastic configuration network with attention mechanism, which integrates the advantages of modular partitioning, attention mechanism, and SCN. The model employs a fuzzy mean clustering strategy to simplify and decompose the complex multi-case and multi-distribution nonlinear modeling task, thereby reducing the modeling complexity of a single model. Furthermore, the model utilizes a stochastic configuration algorithm to learn the subtasks and construct corresponding sub-networks. The output weights are then assigned to each sub-network based on the attention mechanism to obtain the model’s final output. The validity of the proposed method is validated through two benchmark experiments. Then the model is applied to measure effluent ammonia nitrogen. The results indicate that compared with the classical randomized and modularized network models, the proposed model exhibits certain advantages in terms of learning accuracy and generalization performance.

Dynamics of a nonlinear infection viral propagation model with one fixed boundary and one free boundary

In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always expands to the half line [0,∞), and that the virus and infected cells always die out when the Basic Reproduction NumberR0≤1, while the virus and infected cells have persistence properties when R0>1. To obtain the persistence properties of virus and infected cells when R0>1, the most work of this paper focuses on the existence and uniqueness of bounded positive equilibrium solutions for subsystems and the existence of positive equilibrium solutions for the entire system.

A theoretical model for the load-transfer analyses of load distributive compression anchor integrating DSC-based interface nonlinear model

An innovative anchorage technology named load distributive compression anchor (LDCA) has recently been employed in a multitude of geotechnical engineering. The anchoring structure comprises multiple anchor bodies, thereby overcoming the bearing defects associated with conventional load-concentrated anchors and providing superior bearing performance. The complex structural configuration of LDCA considerably complicates the process of load-transfer theoretical modeling. A lack of relevant studies from theoretical solution perspective is yet evident in previous works. In this paper, a theoretical model was proposed for the load-transfer analyses of LDCA, of which the soil-anchor interface mechanical behavior was specially characterized by a disturbed state concept (DSC)-based nonlinear model. The mechanical simulation for the connections in different anchor bodies was incorporated into the theoretical analysis framework through the utilization of finite difference method. Three groups of 3D finite element (FE) models were established to simulate the load-transfer behaviors of LDCAs with different numbers of anchor bodies. The theoretical calculations agree well with the FE numerical results and the in-situ pullout test data, thereby confirming the applicability of the load-transfer theoretical model. The axial force and interface shear stress distributions, as well as the bearing capacity for LDCAs, were discussed based on theoretical calculations and FE simulations. Sensitivity analysis of several key design parameters was conducted to investigate their effects on the bearing capacity of LDCAs. The findings achieved in this study can provide insights into the understanding of the load-transfer behaviors of LDCA, and contribute to the bearing performance evaluation.

Amplification factors of intensity measures for site-specific PSHA using spectrally equivalent pulse-like and non-pulse-like ground motion records

Proper representations of ground motion characteristics and prediction of rock-to-ground amplification factors (AFs) of intensity measures (IMs) are crucial in site-specific probabilistic seismic hazard analysis (PSHA). By using spectrally equivalent pulse-like and non-pulse-like ground motion suites within the convolution-based PSHA framework, this paper aims to (i) investigate the amplification patterns and AF prediction efficiency for 16 typical IMs; and (ii) evaluate the sensitivities of AF and PSHA to the pulse-characteristic, rock-IM type, and AF functional form. The results reveal that IMs are generally amplified, whereas de-amplification occurs at soft sites for IMs largely dominated by high-frequency content (e.g., Arias intensity). Specific rock-IMs for predicting AFs are recommended through efficiency criterion. The results for pulse-like and non-pulse-like suites are found to be not significantly different; hence, including pulse-like records is generally not essential in convolution-based PSHA as long as the bedrock spectra designed with pulse-type features have been matched. Meanwhile, the similar AF predictions from the linear and nonlinear models indicate that the choice of functional form is of secondary importance. Instead, the selection of rock-IM is of higher importance, especially for soft sites and high-frequency dominated IMs. This study could provide useful insights into ground motion selection and AF prediction for site-specific PSHA.

Application of the non-linear three-component model for simulating accelerated creep behavior of polymer-alloy geocell sheets

The polymer-alloy geocell sheets (PAGS) represent a novel geocell material developed to replace conventional geocell materials. Accelerated creep testing, a convenient and precise performance evaluation method, presents a viable alternative to traditional creep testing for obtaining long-term creep strains. Nonetheless, there is a lack of prediction and in-depth exploration of accelerated creep testing. This paper aims to assess the efficacy of using the non-linear three-component (NLTC) model to simulate the accelerated creep behavior of PAGS. The predictive accuracy of the NLTC model has undergone evaluation through a comparison between stepped isothermal method (SIM) accelerated creep experimental tests and numerical simulations. Subsequently, the validated NLTC model was employed to simulate the time-temperature superposition method (TTSM), time-stress superposition method (TSSM), and stepped isostress method (SSM) accelerated creep tests, thereby verifying its effectiveness in predicting all accelerated creep tests. The results indicate that the NLTC model can effectively simulate creep deformation induced by temperature increases, particularly the temperatures below 41 °C. Although some errors are observed at elevated temperatures, it is within the acceptable range of 17.4%. Numerical simulation results of TTSM, TSSM, and SSM tests also suggest the model's proficiency in simulating the accelerated creep behavior by temperature and creep load increasing.

Optimizing the polar phase transformation in PVDF-HFP/BaTiO3-activated carbon composite films with the mixture design of experiments

ABSTRACT A salient bottleneck to driving the wider use of polyvinylidene fluoride (PVDF) and its copolymers in smart applications is the requirement for a high-voltage poling process required to activate their β -phase crystal structure before the realisation of the piezoelectricity response. In pursuit of enhancing the β-phase content of PVDF-based films, various approaches have been employed in recent years. Yet, a perfect solution to the challenge remains elusive. Here, we report a preliminary investigation into the production of unpoled poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) films reinforced with barium titanate (BaTiO3) and activated carbon (AC) to improve the piezoelectric property. Employing the mixture design of experiments (MDOE) method, various formulations of the composite’s constituents weight fractions were determined. Afterwards, series of composite films were produced via a toxic-free solution casting method and characterised by Fourier Transform Infrared Spectrum (FTIR) to determine the β-phase content. A non-linear polynomial regression model was established from the experimental FTIR data, and the adequacy of the model was confirmed using ANOVA. Subsequently, an MDOE-enabled optimisation was undertaken, generating a formulation of the composite to obtain the highest β-phase content to be 15 wt.% BaTiO3 and 0.74 wt.% AC. This combination produces a theoretically predicted β-phase content of 72.7 %. A further experimental test employing the optimal formulation produced a β-phase content of 71.90 %, achieved with neither mechanical stretching, thermal annealing, nor electrical poling.

Population pharmacokinetic analysis of zastaprazan (JP-1366), a novel potassium-competitive acid blocker, in patients and healthy volunteers.

Zastaprazan (JP-1366) is a novel potassium-competitive acid blocker for the treatment of acid-related disorders. We aimed to establish a population pharmacokinetic (PK) model of zastaprazan, thereby characterizing the PK of zastaprazan in patients with gastroesophageal reflux disease (GERD) as well as evaluating the impact of various covariates, including CYP2C19 phenotypes, on zastaprazan PK. This population PK analysis included zastaprazan plasma concentration-time data from 92 patients with erosive GERD and 68 healthy volunteers without any gastrointestinal disorders and was performed using nonlinear mixed-effect modeling. Simulations were conducted to predict zastaprazan PK under various dosing regimens in patients with GERD. The plasma PK of zastaprazan was adequately described by a two-compartment model with Erlang-type absorption (six sequential compartments) and first-order elimination. CYP2C19 phenotypes had no significant effect on zastaprazan PK. The disease status was identified as a significant covariate on apparent clearance of zastaprazan, showing lower values in patients with GERD compared to healthy volunteers. However, the model-based simulation indicated that the impact of disease status on zastaprazan exposure was not clinically meaningful. Overall, the current population PK model successfully characterized the observed zastaprazan PK in both patients with GERD and healthy volunteers.

Hybrid nonlinear probabilistic model using Monte Carlo simulation and hybrid support vector regression for evaporation predictions

This study presents a hybrid model combining Support Vector Regression (SVR) with the Gray Wolf Optimizer (GWO) for evaluating evaporation dynamics. The model was tested using 50 years of meteorological data from Zabol and Chabahar stations in Iran, and compared against standard SVR. Results show that the SVR-GWO significantly outperforms SVR, reducing predictive errors by over 41% on average. For Zabol, the SVR-GWO markedly improved performance, particularly in July where R2 increased from 0.867 to 0.973. The model more closely matched observed statistics, especially for mean and standard deviation, though challenges remain in reproducing higher-order statistics. Interestingly, 5,000 functions evaluation proved nearly as effective as 500,000 suggesting computational efficiency. This integrated approach, incorporating Monte Carlo simulations and kernel density estimation, provides valuable probabilistic insights into evaporation dynamics, offering a promising tool for drought vulnerability assessment and water resources planning in regions with complex climatic patterns.

Nonlinear hydrodynamic assessment of a floating solar double-hull substructure using viscous numerical wave tank

This paper assesses a viscous numerical solver for hydrodynamic simulations of floating double-hull substructures supporting solar panels, critical for advancing floating solar technologies. Using the OpenFOAM repository, the study develops a model based on the Finite Volume method and Volume of Fluid approach, focusing on a range of wave frequencies, from weakly to strongly nonlinear, at intermediate depths. A free decay test calibrated the mesh morphology of the control volume, enabling comparative analysis of single and double-cylinder structures exposed to Stokes second-order nonlinear waves, alongside nonlinear potential models and experimental data. Spectral analysis of these solutions quantifies the nonlinearities' influence on structural responses and high-order dynamic prediction accuracy. The key findings demonstrate that the viscous model accurately predicted heave and surge responses, outperforming the potential model under steep waves. The gap distance between the cylinder in the double-cylinder platforms significantly affects fluid flow and stability, especially under shorter waves. Accurate wave-body simulations require appropriate mesh resolution and tailored wavemaker functions for nonlinear waves. These findings highlight the need to incorporate viscous effects in floating solar platform design to enhance stability and performance in real-world environments.

Mediators of racial/ethnic inequities in clinical trial participation among patients with cancer, 2011-2023.

While minoritized populations are less likely to participate in cancer trials, it is unknown whether social determinants of health (SDOH) explain these inequities. Here we identify SDOH factors that contribute to racial/ethnic inequities in clinical trial participation among patients with 22 common cancers. This retrospective cohort study used electronic health record data (2011-2023) linked to neighborhood (Census tract) data from multiple sources. Patients were followed from diagnosis to clinical study drug receipt (proxy for trial participation), death, or last recorded activity. Associations were assessed using Cox proportional hazards models adjusted for clinical factors (diagnosis year, age, sex, performance status, stage, cancer type). To elucidate which area-level SDOH underlie racial/ethnic inequities, mediation analysis was performed using nonlinear multiple additive regression tree models. This study included 250105 patients (64.7% non-Latinx White, 8.9% non-Latinx Black, 5.2% Latinx). Black and Latinx patients were more likely to live in economically/socially marginalized areas (eg, disproportionately minoritized [measure of segregation], limited English proficiency [LEP], low vehicle ownership) than White patients. Black (3.7%; HR = 0.55 [CI = 0.52-0.60]) and Latinx patients (4.4%; HR = 0.63 [CI = 0.58-0.69]) were less likely to participate in trials than White patients (6.3%). Fewer patients in economically/socially marginalized neighborhoods participated in trials. Mediators explained 62.2% (CI = 49.5%-74.8%) of participation inequities between Black and White patients; area-level SDOH-including segregation (29.9% [CI = 21.2%-38.6%]) and vehicle ownership (11.6% [CI = 7.0%-16.1%])-were the most important mediators. Similarly, Latinx-White participation inequities were mediated (65.1%, [CI = 49.8%-80.3%]) by area-level SDOH such as segregation (39.8% [CI = 28.3%-51.3%]), LEP (11.6%, [CI = 2.8%-20.4%]), and vehicle ownership (9.6% [CI = 5.8%-13.5%]). To improve racial/ethnic diversity in cancer trials, efforts to address barriers related to adverse neighborhood SDOH factors are necessary.

DNA breathing integration with deep learning foundational model advances genome-wide binding prediction of human transcription factors.

It was previously shown that DNA breathing, thermodynamic stability, as well as transcriptional activity and transcription factor (TF) bindings are functionally correlated. To ascertain the precise relationship between TF binding and DNA breathing, we developed the multi-modal deep learning model EPBDxDNABERT-2, which is based on the Extended Peyrard-Bishop-Dauxois (EPBD) nonlinear DNA dynamics model. To train our EPBDxDNABERT-2, we used chromatin immunoprecipitation sequencing (ChIP-Seq) data comprising 690 ChIP-seq experimental results encompassing 161 distinct TFs and 91 human cell types. EPBDxDNABERT-2 significantly improves the prediction of over 660 TF-DNA, with an increase in the area under the receiver operating characteristic (AUROC) metric of up to 9.6% when compared to the baseline model that does not leverage DNA biophysical properties. We expanded our analysis to in vitro high-throughput Systematic Evolution of Ligands by Exponential enrichment (HT-SELEX) dataset of 215 TFs from 27 families, comparing EPBD with established frameworks. The integration of the DNA breathing features with DNABERT-2 foundational model, greatly enhanced TF-binding predictions. Notably, EPBDxDNABERT-2, trained on a large-scale multi-species genomes, with a cross-attention mechanism, improved predictive power shedding light on the mechanisms underlying disease-related non-coding variants discovered in genome-wide association studies.

A dead-time compensation method for motor drive inverters based on nonlinear observer

Silicon carbide (SiC) inverters and interior permanent magnet synchronous motors (IPMSMs) are widely employed in electric vehicles (EVs) due to their superior efficiency and high power density. However, the harmonics generated by the high switching frequency and the dead-time effect in SiC inverters present a significant challenge. The time-varying nature of on–off delays and conduction voltage drops in power devices makes it difficult to establish a precise nonlinear model for inverters, thus limiting the effectiveness of traditional dead-time compensation methods. This paper introduces a dead-time compensation approach for voltage source inverters (VSIs) that leverages a nonlinear observer, thereby circumventing the need for a complex inverter model while enhancing compensation accuracy. The method determines the three-phase stator current polarity of the IPMSM by deriving the relationship between the current vector angle and the rotor position angle. Along with duty cycle variations computed by the PI controller, the inverter’s nonlinearity is adaptively compensated. Simulation and experimental results indicate that the proposed method outperforms the traditional method based on the error voltage model, effectively reducing the total harmonic distortion (THD) of the phase current.

Association between periodic variation of air temperature, humidity, atmospheric pressure and hospital admissions for acute occlusive mesenteric ischaemia

Referring to the intestinal ischemic injury caused by sudden interruption of the blood supply, acute mesenteric ischemia (AMI) is a highly fatal emergency with mortality rates varying from 58 to 80%. The aim of this study was to explore the effect of temperature on AMI admission. This was a retrospective, multicentric study. The medical records of 1477 patients with verified AMI who were consecutively admitted to 3 hospitals anytime between January 2010 and December 2020 were included in the study. Distributed lag non-linear model was applied, the model was adjusted for temperature, atmospheric pressure, relative humidity, year, holiday, day of the week, time and seasonality. AMI exhibited obvious sex preference, AMI patients tended to be male (M/F ratio = 2.3:1) and in their late 50 s. Hospital admissions of acute mesenteric arterial thromboembolism (AMAT) increased significantly with high temperatures on day of exposure and lag 0–14 day. The effect curve of daily average temperature on acute mesenteric venous thromboembolism (AMVT) admission was J-shaped, and the duration of cold effect was longer, while the duration of heat effect was shorter. An increase in hospital admissions of AMVT was found above 20 °C at lag 0–30. For the first time, our study indicated that temperature is significantly associated with the risk of AMI. Although it is not possible to always avoid exposure to extreme temperatures, one should be aware of dramatic temperature fluctuations and take appropriate precautions.

Forecasting of Turkey's Hazelnut Export Amounts According to Seasons with Dendritic Neuron Model Artificial Neural Network

It is seen that artificial neural networks have begun to be used extensively in the literature in solving the time series forecasting problem. In addition to artificial neural networks, classical forecasting methods can often be used to solve this problem. It is seen that classical forecasting methods give successful results for linear time series analysis. However, there is no linear relationship in many time series. Therefore, it can be thought that deep artificial neural networks, which contain more parameters but create more flexible non-linear model structures compared to classical time series forecasting methods, may enable the production of more successful forecasting methods. In this study, the problem of forecasting hazelnut export amounts according to seasons in Turkey with a dendritic neuron model artificial neural network is discussed. In this study, a training algorithm based on the particle swarm optimization algorithm is given for training the dendritic neuron model artificial neural network. The motivation of the study is to investigate Turkey's hazelnut export amounts according to seasons, using a dendritic neuron model artificial neural network. The performance of the proposed method has been compared with artificial neural networks used in the literature.

Association between ambient temperature and economic burden of unintentional injury in Tianjin: a case-crossover study

ObjectiveUnintentional injuries constitute a significant global public health issue with significant social and economic costs. Previous evidence suggests ambient temperatures are associated with unintentional injury occurrences. However, the impacts of...

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.

Advanced Non-linear Modeling and Explainable Artificial Intelligence Techniques for Predicting 30-Day Complications in Bariatric Surgery: A Single-Center Study.

Metabolic bariatric surgery (MBS) became integral to managing severe obesity. Understanding surgical risks associated with MBS is crucial. Different scores, such as the Metabolic and Bariatric Surgery Accreditation and Quality Improvement Program (MBSAQIP), aid in patient selection and outcome prediction. This study aims to evaluate machine learning (ML) models performance in predicting 30-day post-operative complications and compare them with the MBSAQIP risk score. We retrospectively evaluated 424 consecutive patients (2006-2020) who underwent MBS, analyzing 30-day surgical complications according to Clavien-Dindo Classification. ML models, including logistic regression, support vector machine, random forest, k-nearest neighbors, multi-layer perceptron, and extreme gradient boosting, were analyzed and compared to MBSAQIP risk score. Performance was measured by area under receiver operating characteristic curve (AUROC) analysis. Random forest showed the highest AUROC in the training (AUROC = 0.94) and the validation set (AUROC = 0.88). ML algorithms, particularly random forest, outperformed MBSAQIP in predicting negative 30-day outcomes in both the training and validation sets (AUROC = 0.64, DeLong's Test p < 0.001). The five features that were more relevant for the prediction of the random forest model were serum alkaline phosphatase, platelet count, triglycerides, glycated hemoglobin, and albumin. We developed several ML model that identifies patients at risk for 30-day complications after MBS. Among these, random forest is the most performing one and outperforms the already established MBSAQIP score. This model could increase the identification of high-risk patients before MBS.

A nonlinear phase-field model of corrosion with charging kinetics of electric double layer

Abstract A nonlinear phase-field model is developed to simulate corrosion damage. The motion of the electrode-electrolyte interface follows the usual kinetic rate theory for chemical reactions based on the Butler-Volmer equation. The model links the surface polarization variation associated with the charging kinetics of an electric double layer (EDL) to the mesoscale transport. The effects of the EDL are integrated as a boundary condition on the solution potential equation. The boundary condition controls the magnitude of the solution potential at the electrode$-$electrolyte interface. The ion concentration field outside the EDL is obtained by solving the electro$-$diffusion equation and Ohm's law for the solution potential. The model is validated against the classic benchmark pencil electrode test. The framework developed reproduces experimental measurements of both pit kinetics and transient current density response. The model enables more accurate information on corrosion damage, current density, and environmental response in terms of the distribution of electric potential and charged species. The sensitivity analysis for different properties of the EDL is performed to investigate their role in the electrochemical response of the system. Simulation results show that the properties of the EDL significantly influence the transport of ionic species in the electrolyte.