Nonlinear Model Research Articles

Nonlinear flow modeling of electro hydrostatic pump unit based on Gauss Newton iterative method for high performance control

For the electric hydrostatic pump unit (EPU), which is a crucial component in the electro hydraulic servo pump control system (EHSPCS), nonlinear flow modelling is a key challenge to achieve high performance operation, especially in position control. For the nonlinear flow of EPUs, simple linearization combined with compensation has become a popular control method recently. However, the control performance is constrained by the reliance on deviation correction. This paper proposes utilizing the Gauss Newton iterative method to investigate the nonlinear flow modeling in the EPU, aiming to obtain the mapping relationship between the load flow and operating parameters in the EPU, thereby directly improving the control performance. A nonlinear flow model is built by utilizing the Gauss Newton iterative method based on test data obtained from various operating conditions, and the mapping relationship is presented accordingly. Experimental studies show that compared to well-established methods, this model exhibits high accuracy and practicality in improving the control performance, particularly in position control of the EPU.

Programmable supratransmission in a mechanical chain with tri-stable oscillators

Abstract Supratransmission refers to a phenomenon that nonlinear medium allows large-amplitude waves to transmit energy through the band gap, which has been extensively studied in many nonlinear models. Recently, controlling supratransmission using bi-stable nonlinearities has gained growing attentions. Nevertheless, the general principles of controlling supratransmission using multi-stable nonlinearities have remained elusive. As a first step to address such challenge, this work presents programmable supratransmission using tri-stable nonlinearities. Through numerical simulations, we demonstrate that a mechanical chain consisting of tri-stable oscillators can achieve rich programmable features of supratransmission by simply tuning the tri-stable potential energy curve, providing new insights into how supratransmission can be controlled. The current work deepens the understanding of programmable supratransmission using multi-stable nonlinearities.

A Multi-Mechanism Fusion Method for Robust State of Charge Estimation via Bidirectional Long Short-Term Memory Model with Mixture Kernel Mean p-Power Error Loss Optimized by Golden Jackal Optimization Algorithm

Abstract Accurate state of charge (SOC) estimation is crucial for effective battery management in various applications. The bidirectional long short-term memory (BiLSTM) as an outstanding nonlinear regression model can be used for SOC estimation. This work develops a novel multi-mechanism fusion method based on BiLSTM to further enhance its estimation performance for SOC, in which the convolutional neural network (CNN), attention mechanism, and mixture kernel mean p-power error (MKMPE) loss are introduced into the BiLSTM framework for addressing different issues. First, the introduction of CNN components aims to extract essential features from battery data, enhancing the model's comprehension of complex information. Then, the attention mechanism is used to further refine the model's perceptual ability and a robust MKMPE loss is introduced into the BiLSTM framework to replace its original mean squared error loss, and a novel robust model is developed to suppress non-Gaussian noise interference. Finally, some key hyperparameters of the proposed model are fine-tuned using the golden jackal optimization algorithm, resulting in improved estimation performance. Comparative numerical experiments are meticulously conducted in various cases to evaluate the performance of the proposed method, and the experiment results demonstrate that it can perform outstanding effectiveness in handling non-Gaussian noise scenarios.

Non-linear biphasic mixture model: Existence and uniqueness results

Abstract This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumour. The classical mixture theory is adopted for mass and momentum balance equations for a two-phase system. A main contribution of this study is we treat the physiological transport parameter (i.e., hydraulic resistivity) as anisotropic and heterogeneous, thus the governing system is strongly coupled and non-linear. We derived a weak formulation and then formulated the equivalent fixed-point problem. This enabled us to use the Galerkin method, and the classical results on monotone operators combined with the well-known Schauder and Banach fixed-point theorems to prove the existence and uniqueness of results.

Numerical modeling of site response at large strains with simplified nonlinear models: Application to Lotung seismic array

Abstract Site response analyses at large strains are routinely carried out neglecting the shear strength of soil and the stiffness degradation due to the increase in pore pressures, leading to unrealistic predictions of the seismic response of soil deposits. The study investigates the performance of a simplified nonlinear (NL) approach, implemented in the Deepsoil code, constituted by coupling a hyperbolic model incorporating shear strength with a strain-based semi-empirical pore pressure generation model. The first part of the study, based on a large one-dimensional parametric study, shows that above a shear strain of 0.1%, it is necessary to include shear strength in the site response modelling to get more realistic results. Then, the approach has been evaluated with reference to the well-known downhole Large-Scale Seismic Test array located in Lotung (Taiwan): numerical results have been compared with recordings in terms of acceleration response spectra and pore water pressure time histories at different depths along the soil profiles. The comparison shows that the NL simplified model is characterized by an accuracy comparable with more sophisticated advanced elasto-plastic NL analyses adopting essentially the same input data of the traditional equivalent linear approaches(shear modulus and damping curves) and simple physical-mechanical properties routinely determined during geotechnical surveys (i.e., shear strength, relative density, fine content). This approach is therefore recommended for site response analyses reaching large strains (i.e., soft soil deposits and moderate-to-high input motions).

Some approximations to the path formula for some nonlinear models

AbstractIn linear least squares regression there exists a simple decomposition of the effect of an exposure on an outcome into two parts in the presence of an intermediate variable. This decomposition is described and then analogous decompositions for other models are examined, namely for logistic regression and proportional hazards models.

Predicting newborn birth outcomes with prenatal maternal health features and correlates in the United States: a machine learning approach using archival data

BackgroundNewborns are shaped by prenatal maternal experiences. These include a pregnant person’s physical health, prior pregnancy experiences, emotion regulation, and socially determined health markers. We used a series of machine learning models to predict markers of fetal growth and development—specifically, newborn birthweight and head circumference (HC).MethodsWe used a pre-registered archival data analytic approach. These data consisted of maternal and newborn characteristics of 594 maternal-infant dyads in the western U.S. Participants also completed a measure of emotion dysregulation. In total, there were 22 predictors of newborn HC and birthweight. We used regularized regression for predictor selection and linear prediction, followed by nonlinear models if linear models were overfit.ResultsHC was predicted best with a linear model (ridge regression). Newborn sex (male), number of living children, and maternal BMI predicted a larger HC, whereas maternal preeclampsia, number of prior preterm births, and race/ethnicity (Latina) predicted a smaller HC. Birthweight was predicted best with a nonlinear model (support vector machine). Occupational prestige (a marker similar to socioeconomic status) predicted higher birthweight, maternal race/ethnicity (non-White and non-Latina) predicted lower birthweight, and the number of living children, prior preterm births, and difficulty with emotional clarity had nonlinear effects.ConclusionsHC and birthweight were predicted by a variety of variables associated with prenatal stressful experiences, spanning medical, psychological, and social markers of health and stress. These findings may highlight the importance of viewing prenatal maternal health across multiple dimensions. Findings also suggest that assessing difficulties with emotional clarity during standard obstetric care (in the U.S.) may help identify risk for adverse newborn outcomes.

Prediction of thermal protection performance and empirical study of flame-retardant cotton based on a combined model

Thermal protection performance (TPP) is an important index to evaluate the performance of firefighting clothing. The purpose of this work is to build a model to predict the TPP values of fabrics with fewer variables. Two properties of flame-retardant cotton were tested with TPP values under different air gaps, and the correlations between these properties were also analyzed. A combined model was established by integrating multivariate nonlinear regression model and gradient boosting regression tree model. Then the combined model was compared with these two single models. The results showed that the correlation coefficients between gram weight and thickness of fabric and TPP value were 0.833 and 0.837, respectively, indicating a strong correlation. The correlation coefficient between air gap and TPP value was 0.304, indicating a weak correlation. In predicting the thermal protective performance of flame-retardant cotton, this study employed a multivariate nonlinear regression model, a Gradient Boosting Regression Tree (GBRT) model, and a combined model. After comparing various evaluation metrics, it was finally decided to adopt the combined model for predicting the thermal protective performance values of flame-retardant cotton. This method improved the prediction accuracy of thermal protective performance, facilitating the promotion and application of the combined model. Furthermore, when exploring the thermal protective performance of flame-retardant cotton, the use of fewer variables to establish the prediction model can not only significantly simplify the complex structure of the model but also greatly enhance the analysis efficiency, ensuring the efficiency and precision of the research process.

Nonlinear Modeling and Analysis of Vehicle Vibrations Crossing Over a Speed Bump

Nonlinear Modeling and Analysis of Vehicle Vibrations Crossing Over a Speed Bump

Nonlinear model predictive control of a conductance-based neuron model via data-driven forecasting

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control, which employs a dynamical model of the system to find optimal control inputs, has promise for dealing with the nonlinear dynamics, high levels of exogenous noise, and limited information about unmeasured states and parameters that are common in a wide range of neural systems. However, the challenge still remains of selecting the right model, constraining its parameters, and synchronizing to the neural system.Approach. As a proof of principle, we used recent advances in data-driven forecasting to construct a nonlinear machine-learning model of a Hodgkin-Huxley type neuron when only the membrane voltage is observable and there are an unknown number of intrinsic currents.Main Results. We show that this approach is able to learn the dynamics of different neuron types and can be used with model predictive control (MPC) to force the neuron to engage in arbitrary, researcher-defined spiking behaviors.Significance.To the best of our knowledge, this is the first application of nonlinear MPC of a conductance-based model where there is only realistically limited information about unobservable states and parameters.

Optimal control and cost-effectiveness analysis of nonlinear deterministic Zika virus model

Optimal control and cost-effectiveness analysis of nonlinear deterministic Zika virus model

Temperature‐Dependent Recombination Dynamics of Photocarriers in CsPbBr3 Microcrystals Revealed by Ultrafast Terahertz Spectroscopy

AbstractThe ultrafast dynamics of photoexcited charge carriers are studied in micron‐scale crystals composed of the inorganic perovskite CsPbBr3 with time‐resolved terahertz spectroscopy. Exciting with photon energy close to the band edge, it is found that a fast (<10 ps) decay emerges in the terahertz photoconductivity with increasing pump fluence and decreasing temperature, dominating the dynamics at 4 K. The fluence‐dependent dynamics can be globally fit by a nonlinear recombination model, which reveals that the influence of different nonlinear recombination mechanisms in the studied pump fluence range depends on temperature. Whereas the Auger scattering rate decreases with decreasing temperature from 77 to 4 K, the radiative recombination rate increases by three orders of magnitude. Spectroscopically, the terahertz photoconductivity resembles a Drude response at all delays, yet an additional Lorentz component due to an above‐bandwidth resonance is needed to fully reproduce the data.

On the instability of single-axis acoustic levitation under radial perturbations

Acoustic levitation is widely used in non-container measurement and non-contact manipulation. Particles in the single-axis acoustic levitation are easily unstable in the radial direction under external perturbations. In order to explore the instability in the acoustic levitation during radial perturbations, a nonlinear acoustic levitation model considering the coupling of radial and axial vibration is proposed to analyze the dominant factors influencing the levitation stability, an acoustic levitation system consisting of a transducer and a plane reflector is established, and high-speed photography is used to observe the vibration behavior of the particle with large radial vibration and the levitation stability. The simulation results are compared and verified with the experiments, which indicate that the reduction in axial trapping stiffness due to radial vibration plays a vital role in the levitation instability. The present model can characterize the radial anti-interference ability of different levitators as well as predict the movement trajectories of levitated particles after being disturbed, which is helpful to optimize the design of acoustic levitators and provide guidance for acoustic manipulation.

Research on Trajectory Planning and Tracking Algorithm of Crawler Paver

The implementation of unmanned intelligent construction on the concrete surfaces of an airport effectively improves construction accuracy and reduces personnel investment. On the basis of three known common tracked vehicle dynamics models, reference trajectory planning and trajectory tracking controller algorithms need to be designed. In this paper, based on the driving characteristics of the tracked vehicle and the requirements of the stepping trajectory, a quartic polynomial trajectory planning algorithm was selected with the stability of the curve as a whole and the end point as the optimization goal, combining the tracked vehicle dynamics model, collision constraints, start–stop constraints and other boundary conditions. The objective function of trajectory planning was designed to effectively plan the reference trajectory of the tracked vehicle’s step-by-step travel. In order to realize accurate trajectory tracking control, a nonlinear model predictive controller with transverse-longitudinal integrated control was designed. To improve the real-time performance of the controller, a linear model predictive controller with horizontal and longitudinal decoupling was designed. MATLAB 2023A and CoppeliaSim V4.5.1 were used to co-simulate the two controller models. The experimental results show that the advantages and disadvantages of the tracked vehicle dynamics model and controller design are verified.

Prevalence Characteristics of Osteoporosis Fractures in the Elderly in Two Regions of China and Analysis of the Lag Effect of Air Pollutants on them.

Air pollution is increasing and threatening human health. The objective of this study is to investigate the population distribution characteristics of elderly osteoporosis fractures in Hebei Province and Xinjiang Uygur Autonomous Region and to analyze the effects of air pollutants on the number of elderly osteoporosis fracture inpatients in the two regions. A retrospective collection of elderly osteoporosis fracture cases was conducted in selected hospitals in Hebei Province and Xinjiang Uygur Autonomous Region from January 1, 2018 to December 31, 2022. The chi-square test was used to compare the distributional characteristics of the population in the two regions. Additionally, we used a distributed lag nonlinear model (DLNM) in order to assess the effect of air pollutants on the number of daily hospital admissions of elderly osteoporosis fracture patients in different regions. A total of 19,203 elderly osteoporosis fracture patients were included in the study. The average age of these patients was 76.66 ± 7.55 years, and the majority of them were female (13,514 instances, 70.37%). The disparities in age distribution (χ2 = 133.9 p < 0.001), fracture site (χ2 = 62.0 p < 0.001), and hospitalization cost (Z = -15.635 p < 0.001) between the two regions were statistically significant. The lag effect curves of PM2.5, PM10, and NO2 on the number of elderly osteoporosis fracture hospitalizations in Xinjiang Uygur Autonomous Region exhibited a similar pattern resembling a "W"-shaped curve. All three pollutants reached their highest values after a lag time of 14 days (PM2.5: RR = 1.053, 95% CI: 1.031, 1.074; PM10: RR = 1.031, 95% CI: 1.018, 1.043; NO2: RR = 1.125, 95% CI: 1.070, 1.182). In Hebei Province, the largest impacts of PM2.5 and PM10 were observed after a lag of 14 days (PM2.5: RR = 1.022, 95% CI: 1.013, 1.028; PM10: RR = 1.013, 95% CI: 1.008, 1.018). Similarly, the maximum effect of NO2 was observed after a lag of 11 days (RR = 1.020, 95% CI: 1.010, 1.028). There were differences in the epidemiological characteristics of hospitalized patients with osteoporosis fractures between the two regions, PM2.5, PM10, and NO2 increased the number of hospitalizations for osteoporosis fractures. Exposure to air pollutants such as PM2.5 increases the risk of osteoporosis fractures in the elderly population.

Parameter tuning for active disturbance rejection control of fixed-wing UAV based on improved bald eagle search algorithm

Purpose This paper aims to develop a method for tuning the parameters of the active disturbance rejection controller (ADRC) for fixed-wing unmanned aerial vehicles (UAVs). The bald eagle search (BES) algorithm has been improved, and a cost function has been designed to enhance the optimization efficiency of ADRC parameters. Design/methodology/approach A six-degree-of-freedom nonlinear model for a fixed-wing UAV has been developed, and its attitude controller has been formulated using the active disturbance rejection control method. The parameters of the disturbance rejection controller have been fine-tuned using the collaborative mutual promotion bald eagle search (CMP-BES) algorithm. The pitch and roll controllers for the UAV have been individually optimized to obtain the most effective controller parameters. Findings Inspired by the salp swarm algorithm (SSA), the interaction among individual eagles has been incorporated into the CMP-BES algorithm, thereby enhancing the algorithm's exploration capability. The efficient and accurate optimization ability of the proposed algorithm has been demonstrated through comparative experiments with genetic algorithm, particle swarm optimization, Harris hawks optimization HHO, BES and modified bald eagle search algorithms. The algorithm's capability to solve complex optimization problems has been further proven by testing on the CEC2017 test function suite. A transitional function for fitness calculation has been introduced to accelerate the ability of the algorithm to find the optimal parameters for the ADRC controller. The tuned ADRC controller has been compared with the classical proportional-integral-derivative (PID) controller, with gust disturbances introduced to the UAV body axis. The results have shown that the tuned ADRC controller has faster response times and stronger disturbance rejection capabilities than the PID controller. Practical implications The proposed CMP-BES algorithm, combined with a fitness function composed of transition functions, can be used to optimize the ADRC controller parameters for fixed-wing UAVs more quickly and effectively. The tuned ADRC controller has exhibited excellent robustness and disturbance rejection capabilities. Originality/value The CMP-BES algorithm and transitional function have been proposed for the parameter optimization of the active disturbance rejection controller for fixed-wing UAVs.

Symmetric structures and dynamic analysis of a (2+1)-dimensional generalized Benny-Luke equation

We study the symmetric structures and dynamic analysis of a (2 + 1)-dimensional generalized Benny-Luke (GBL) equation based on the Lie symmetry method, the GBL equation is an important non-integrable model of water waves. Specifically, we construct multiple exact solutions of the GBL equation and obtain its nonlocally related systems. Firstly, the Lie point symmetries and conservation laws of the GBL equation are computed, and then we get the reduced ordinary differential equation from one of the conservation laws. Multiple methods, for example, the dynamical systems method, the power series method, the homogeneous balancing method and generalized variable separation method, are used to solve the ordinary differential equation and abundant exact solutions of the GBL equation are got. Finally, we extend these exact solutions by discrete symmetries, and give three-dimensional graphs of partial exact solutions. In addition, we construct the nonlocally related PDE systems, which contains the potential systems from the conservation laws and an inverse system from a Lie point symmetry of the GBL equation. These findings reveal the dynamical behavior behind the GBL equation and broaden the range of nonlinear water wave model solutions.

Optimizing ethephon application timing for ‘Meyer’ zoysiagrass seedhead suppression

AbstractZoysiagrass (Zoysia spp. Willd.) is a desirable, low‐input turfgrass species used on golf courses. However, prolific zoysiagrass seedhead production in the spring can increase golf course maintenance costs and reduce aesthetics. Previous research demonstrates that a single autumn ethephon application can suppress zoysiagrass seedhead production the following spring, but the optimum application timing is not well‐defined. The objective of this research was to determine the optimum window for an effective ethephon application for ‘Meyer’ zoysiagrass seedhead suppression. Small‐plot field research was conducted in Indiana, Kansas, Arkansas, and Tennessee. Seedheads were suppressed up to 99% depending on application timing. In Indiana, applications made on September 19 provided 99% seedhead suppression. In Kansas, applications between August 30 and September 18 yielded &gt;64% seedhead suppression. In Arkansas, applications between October 3 and October 17 yielded &gt;52% seedhead suppression. In Tennessee, applications between September 19 and October 23 provided &gt;78% seedhead suppression. Applications made outside these windows resulted in more seedhead production at each respective location. Interestingly, optimum application timing was approximately 2 weeks later in Arkansas and Tennessee compared to Indiana and Kansas. Using growing degree days, a nonlinear Gaussian model was fit to predict the optimum ethephon application timing. In addition to data from this research, the proposed model accurately predicted observed zoysiagrass seedhead suppression in previously published research. This research better characterizes the optimum autumn application timing for Meyer zoysiagrass seedhead suppression across the transition zone.

A statistical modelling approach to feedforward neural network model selection

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the approaches used within statistical modelling, the majority of neural network research has been conducted outside of the field of statistics. This has resulted in a lack of statistically based methodology, and, in particular, there has been little emphasis on model parsimony. Determining the input layer structure is analogous to variable selection, while the structure for the hidden layer relates to model complexity. In practice, neural network model selection is often carried out by comparing models using out-of-sample performance. However, in contrast, the construction of an associated likelihood function opens the door to information-criteria-based variable and architecture selection. A novel model selection method, which performs both input- and hidden-node selection, is proposed using the Bayesian information criterion (BIC) for FNNs. The choice of BIC over out-of-sample performance as the model selection objective function leads to an increased probability of recovering the true model, while parsimoniously achieving favourable out-of-sample performance. Simulation studies are used to evaluate and justify the proposed method, and applications on real data are investigated.

Alginate-Based Hydrogel Bead Reinforced with Montmorillonite Clay and Bacterial Cellulose-Activated Carbon as an Effective Adsorbent for Removing Dye from Aqueous Solution

According to environmental concerns related to water pollution, this study aims to develop a novel hydrogel bead as a biocompatible and efficient adsorbent by integrating bacterial cellulose-activated carbon (BCAC) and montmorillonite (MT) in alginate hydrogel (ALG). The ionotropic gelation method was applied to the fabrication of BCAC/MT/ALG hydrogel beads. The BCAC/MT/ALG hydrogel bead exhibited significantly higher tensile strength, Young’s modulus, and thermal stability, with ~1.4 times higher adsorption uptake of methylene blue (MB) from aqueous solution as compared to the pristine ALG bead. The textural properties, including specific surface area and porosity, were beneficial to accommodate the size of cationic MB as the target molecule. This resulted in a remarkable MB adsorption uptake of 678.2 mg/g at pH 7 and 30 °C. The adsorption isotherm showed the best fit for the nonlinear Redlich-Peterson isotherm model. Experimental adsorption data were well-described by the pseudo-second order kinetic model, with R2 values reaching 0.997. In addition, the adsorbent bead demonstrated easy regeneration with high reusability with approximately 75% of MB removal after being used for six cycles. Therefore, BCAC/MT/ALG bead represents an eco-friendly, cost-effective, and highly efficient adsorbent for MB removal from water and could potentially be used for removal of a wide range of cationic dye pollutants from wastewater.