Parameters Of Nonlinear Model Research Articles

Smooth Sigmoid Surrogate (SSS): An Alternative to Greedy Search in Decision Trees

Greedy search (GS) or exhaustive search plays a crucial role in decision trees and their various extensions. We introduce an alternative splitting method called smooth sigmoid surrogate (SSS) in which the indicator threshold function used in GS is approximated by a smooth sigmoid function. This approach allows for parametric smoothing or regularization of the erratic and discrete GS process, making it more effective in identifying the true cutoff point, particularly in the presence of weak signals, as well as less prone to the inherent end-cut preference problem. Additionally, SSS provides a convenient means of evaluating the best split by referencing a parametric nonlinear model. Moreover, in many variants of recursive partitioning, SSS can be reformulated as a one-dimensional smooth optimization problem, rendering it computationally more efficient than GS. Extensive simulation studies and real data examples are provided to evaluate and demonstrate its effectiveness.

Seismic response of deep soft soil sites with varying shear wave velocities

The variations in seismic response between deep soft soil sites with different shear wave velocities were not fully understood. This study focuses on the seismic response of deep soft soil sites in the lower reaches of the Yangtze River, China. A nonlinear dynamic finite element model was developed for two representative deep soft soil sites with borehole profiles and the shear wave velocity tested by the single borehole method. Two nonlinear cyclic constitutive models are used and thus compared through the site seismic response. To accurately calibrate the nonlinear cyclic model parameters, resonant column tests were conducted on 21 soil samples collected from the two boreholes. The results show that the peak ground acceleration (PGA) under low-frequency (Liuan) input motion was higher for soft soil sites compared to that under medium- and high-frequency (Kobe and Nahanni) input motions. The PGA amplification factor for deep soft soil sites under different input motions can be approximated by an exponential function. The peak ground acceleration tends to be lower as the equivalent shear wave velocity (Vse) decreases. The shapes of the spectral acceleration were similar for the two sites, despite a substantial difference in the Vse between them. Additionally, a crossover point was observed in the spectral acceleration for the two sites. The period corresponding to this crossover point increased with increasing intensity of input motions, indicating that the sites became softer with higher intensity and thus generally exhibited a longer characteristic period of the spectral acceleration. This paper also highlights the significance of selecting nonlinear constitutive models and the precise calibration of model parameters in the seismic response analysis of deep soft soil sites, providing a scientific basis for future similar site analyses.

Mathematical modeling and model predictive control research on coal powder burners for aggregate dryers

Aggregate drying is a crucial step in asphalt mixture production. Enhancing the model accuracy and controller performance of aggregate dryer burners is essential for consistent flame characteristics, reducing NOx emissions, and minimizing fuel consumption. This paper introduces a second-order nonlinear parametric model for coal powder burners that includes delay and noise. Model parameters were determined through experimental data using the Salp Swarm Algorithm, showing higher accuracy than models based on the least square method. A dual-layer model predictive control (MPC) based on this mathematical model was developed to improve the economic efficiency of the aggregate drying process. Simulation results showed that the dual-layer MPC saves 1.08 tons of coal every 10 h compared to a standard MPC. A full-scale prototype demonstrated average flame length, flame temperature, and NOx emissions of 4242.6 mm, 1729.4 °C, and 460.2 mg/m³, respectively, validating the accuracy of the proposed mathematical model and controller.

A novel iterative model updating for jointed structures using nonlinear FRFs

A novel iterative model updating method is developed to identify the local nonlinear joint properties using the frequency response functions (FRFs) of assembled structures. In this paper, the least-squares fitting method was used to transform the sensitivity matrix into a square iteration matrix to match the dimensions of the objective functions and nonlinear joint model parameters. Leveraging the Newton’s iteration, the adaptive successive over-relaxation (A-SOR) was used to ensure iteration convergence while the multi-scale parameter adjusting (MPA) strategy was developed to degrade the ill-condition of the iteration matrix. Two updating examples of phenomenological equivalence models were applied to demonstrate the effectiveness of the proposed method. The nonlinear FRFs of a lap-type bolted joint beam system with Iwan model were simulated as the objective functions to identify the local nonlinear joint properties, as well as experimental investigations of a metal rubber isolation system with a high-order polynomial model. The proposed method was validated by the good agreement of the comparison results, and it indicated a better model updating performance with a much smaller condition number of the iteration matrix.

Bayesian structural model updating with multimodal variational autoencoder

A novel framework for Bayesian structural model updating is presented in this study. The proposed method utilizes the surrogate unimodal encoders of a multimodal variational autoencoder (VAE). The method facilitates an approximation of the likelihood when dealing with a small number of observations. It is particularly suitable for high-dimensional correlated simultaneous observations applicable to various dynamic analysis models. The proposed approach was benchmarked using a numerical model of a single-story frame building with acceleration and dynamic strain measurements. Additionally, an example involving a Bayesian update of nonlinear model parameters for a three-degree-of-freedom lumped mass model demonstrates computational efficiency when compared to using the original VAE, while maintaining adequate accuracy for practical applications.

GeTeSEPdb: A comprehensive database and online tool for the identification and analysis of gene profiles with temporal-specific expression patterns

Gene expression is dynamic and varies at different stages of processes. The identification of gene profiles with temporal-specific expression patterns can provide valuable insights into ongoing biological processes, such as the cell cycle, cell development, circadian rhythms, or responses to external stimuli such as drug treatments or viral infections. However, currently, no database defines, identifies or archives gene profiles with temporal-specific expression patterns. Here, using a high-throughput regression analysis approach, eight linear and nonlinear parametric models were fitted to gene expression profiles from time-series experiments to identify eight types of gene profiles with temporal-specific expression patterns. We curated 2684 time-series transcriptome datasets and identified 2644,370 gene profiles exhibiting temporal-specific expression patterns. The results were stored in the database GeTeSEPdb (gene profiles with temporal-specific expression patterns database, http://www.inbirg.com/GeTeSEPdb/). Moreover, we implemented an online tool to identify gene profiles with temporal-specific expression patterns from user-submitted data. In summary, GeTeSEPdb is a comprehensive web service that can be used to identify and analyse gene profiles with temporal-specific expression patterns. This approach facilitates the exploration of transcriptional changes and temporal patterns of responses. We firmly believe that GeTeSEPdb will become a valuable resource for biologists and bioinformaticians.

Bayesian fractional polynomial approach to quantile regression and variable selection with application in the analysis of blood pressure among US adults

Although the fractional polynomials (FPs) can act as a concise and accurate formula for examining smooth relationships between response and predictors, modelling conditional mean functions observes the partial view of a distribution of response variable, as distributions of many response variables such as blood pressure (BP) measures are typically skew. Conditional quantile functions with FPs provide a comprehensive relationship between the response variable and its predictors, such as median and extremely high-BP measures that may be often required in practical data analysis generally. To the best of our knowledge, this is new in the literature. Therefore, in this article, we develop and employ Bayesian variable selection with quantile-dependent prior for the FP model to propose a Bayesian variable selection with parametric non-linear quantile regression model. The objective is to examine a non-linear relationship between BP measures and their risk factors across median and upper quantile levels using data extracted from the 2007 to 2008 National Health and Nutrition Examination Survey (NHANES). The variable selection in the model analysis identified that the non-linear terms of continuous variables (body mass index, age), and categorical variables (ethnicity, gender, and marital status) were selected as important predictors in the model across all quantile levels.

Parametric Nonlinear Model Reduction Using Machine Learning on Grassmann Manifold with an Application on a Flow Simulation

Parametric Nonlinear Model Reduction Using Machine Learning on Grassmann Manifold with an Application on a Flow Simulation

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers.

Bubble growth processes are highly complex processes, which are not only dependent on the foaming process parameters (temperature, pressure and blowing agent concentration) but also on the type and structure of the polymer used. Since the elongational viscosity at the bubble wall during bubble growth also depends on these influencing factors, the so-called transient elongational viscosity plays a key role in describing the gas bubble growth behavior in polymer melts. The model-based description of the transient elongational viscosity function is difficult due to its dependence on time, Hencky strain and strain rate. Therefore, representative viscosities or shear viscosity models are usually used in the literature to predict the bubble growth behavior. In this work, the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth is described holistically for the first time. This is achieved by extending the so-called molecular stress function (MSF) model by superposition principles (temperature, pressure and blowing agent concentration) and by using the elongational deformation behavior (Hencky strain and strain rate) at the bubble wall during the initial, and thus viscosity-driven, bubble growth process. Therefore, transient uniaxial elongational viscosity measurements are performed and the non-linear MSF model parameters of the two investigated polymers PS (linear polymer chains) and PLA (long-chain branched polymer chains) are determined. By applying the superposition principles and by changing the strain mode parameter to the equibiaxial case in the MSF model, the transient equibiaxial viscosity master curve is obtained and used to describe the bubble growth process. The results show that the extended MSF model can fully predict the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth processes. The bubble growth behavior over time can then be realistically described using the defined transient equibiaxial elongational viscosity function at the bubble wall. This is not possible, for example, with a representative viscosity and therefore clearly demonstrates the influence and importance of knowing the transient deformation behavior that prevails at the bubble wall during bubble growth processes.

The Improved Method for Identifying Parameters of Interval Nonlinear Models of Static Systems

The article discusses the method of identifying parameters for interval nonlinear models of static systems. The method is based on solving an optimization problem with a smooth objective function. Additional coefficients are added to the objective function's variables to solve the optimization problem, complicating the computational procedures. The computational complexity of quasi-Newton methods used to solve the optimization problem is analyzed. Excessive computational complexity is caused by many iterations when transforming the value of the objective function to zero. To address this, the article proposes using the optimization stop criterion based on the determination of the model's adequacy at the current iteration of the computational optimization procedure. Numerical experiments were conducted to identify nonlinear models of depending the pH of the environment in the fermenter of the biogas plant on influencing factors. It was established that the proposed criterion reduced the number of iterations by 4.5 times, which is proportional to the same reduction in the number of calculations of the objective function. Gotten results are also important for reducing the computational complexity of algorithms of structural identification of these models.

CONTROL AND IDENTIFICATION OF CONTROLLED AUTO-REGRESSIVE MOVING AVERAGE (CARMA) FORM OF AN INTRODUCED SINGLE-INPUT SINGLE-OUTPUT TUMOR MODEL

The article investigates the parameter estimation for controlled auto-regressive moving average models with gradient based iterative approach and two-stage gradient based iterative approach. Since deriving a new model for tumor model is substantial, introduced system identification algorithms are used in order to estimate parameters of a specific nonlinear tumor model. Besides, in order to estimate tumor model a collection of output and input data is taken from the nonlinear system. Apart from that, effectiveness of the identification algorithms such as convergence rate and estimation error is depicted through various tables and figures. Finally, it is shown that the two stage approach has higher identification efficacy.

An adaptive internal model control approach for unmanned surface vehicle based on bidirectional long short-term memory neural network: Implementation and field testing

This paper investigates a practical adaptive internal model control (IMC) for an unmanned surface vehicle (USV) with unknown time-varying nonlinear model parameters and environmental disturbances. Firstly, an internal model of the USV is presented using the Bidirectional Long Short-Term Memory (BiLSTM) neural network. Then, an adaptive neural IMC controller is designed for the trajectory tracking of USV by using the IMC method. The internal model and the controller are updated by an error threshold algorithm. The proposed control scheme comprises of a trajectory guidance module via the Line-of-Sight (LOS) guidance method and a tracking control module designed by IMC theory. Under the proposed control scheme, the development processes of the vehicle platform and the control algorithms are described, and accurate tracking control can be achieved. Finally, the results of simulation and field experiments are presented and discussed to validate the effectiveness of the proposed control scheme.

Effect of Increasing Sample Size on Multi-Collinearity in Multilevel Non-Linear Model

A multilevel logistic regression model demonstrating high correlations among predictor variables is susceptible to multi-collinearity. Multi-collinearity significantly impacts the robustness and interpretability of multilevel non-linear models. In multilevel non-linear models, the effects of multi-collinearity can be amplified, leading to distorted parameter estimates and inflated standard errors. This phenomenon contributes to an escalation in the variances of parameter estimates, thereby resulting in inaccurate inferences regarding the relationships between the response and explanatory factors. The primary objective of this study is to investigate the impact of multi-collinearity on multilevel non-linear models. The research aims to assess whether the quantity of independent variables influences the Multilevel Variance Inflation Factor and to explore the effect of altering the correlation degree at one level on multi-collinearity within a multilevel non-linear model. Additionally, the research seeks to determine how multi-collinearity affects the standard errors of parameters in a multilevel non-linear model. In a 2-level logistic regression, a binary variable was the dependent variable, while pre-established standard variables functioned as regressors. The Monte Carlo analysis incorporated three distinct correlation strengths (0.2, 0.5, and 0.9) and sample sizes (500, 100, and 30). The Multilevel Variance Inflation Factor was employed for multi-collinearity diagnosis. The outcomes revealed that, within the logistic multilevel regression model, an increase in sample size correlated with a reduction in multi-collinearity. Notably, the influence of multi-collinearity on standard errors in a multilevel non-linear model was more pronounced. It was observed that increasing the sample size remains an effective strategy to mitigate multi-collinearity errors in a multilevel non-linear model. This approach is particularly crucial due to the reliance on maximum likelihood estimation in logistic regression, as opposed to ordinary least squares (OLS) regression, which contrasts with the methodology of OLS regression.

Machine learning tools to improve nonlinear modeling parameters of RC columns

Modeling parameters are essential to the fidelity of nonlinear models of concrete structures subjected to earthquake ground motions, especially when simulating seismic events strong enough to cause collapse. This paper addresses two of the most significant barriers to improving nonlinear modeling provisions in seismic evaluation standards using experimental data sets: identifying the most likely mode of failure of structural components, and implementing data fitting techniques capable of recognizing interdependencies between input parameters and nonlinear relationships between input parameters and model outputs. Machine learning tools in the Scikit-learn and Pytorch libraries were used to calibrate equations and black-box numerical models for nonlinear modeling parameters (MP) a and b of reinforced concrete columns defined in the ASCE 41 and ACI 369.1 standards, and to estimate their most likely mode of failure. It was found that machine learning regression models and machine learning black-boxes were more accurate than current provisions in the ACI 369.1/ASCE 41 Standards. Among the regression models, Regularized Linear Regression was the most accurate for estimating MP a, and Polynomial Regression was the most accurate for estimating MP b. The two black-box models evaluated, namely the Gaussian Process Regression and the Neural Network (NN), provided the most accurate estimates of MPs a and b. The NN model was the most accurate machine learning tool of all evaluated. A multi-class classification tool from the Scikit-learn machine learning library correctly identified column mode of failure with 79 % accuracy for rectangular columns and with 81 % accuracy for circular columns, a substantial improvement over the classification rules in ASCE 41-13.

Dynamic behaviors of delaminated nanofilms partly bonded on substrates with sub-nanoscale van der Waals dynamic boundaries

Abstract Dynamic buckling-induced delamination of nanofilms on substrates is a universal and essential phenomenon in nanoelectromechanical systems (NEMS). Van der Waals (vdWs) interactions play an important role in the dynamic buckling-induced delamination of nanofilms on substrates due to the interaction distances at nanoscale or even sub-nanoscale in NEMS. Therefore, it is interesting yet challenging to reveal the effect of intermolecular vdWs interactions on dynamic buckling-induced delamination of nanofilms on substrates. By considering sub-nanoscale dynamic boundary effects induced by intermolecular vdWs interactions, a parametric excitation nonlinear vibration model for dynamic buckling-induced delamination of nanofilms partly bonded on substrates is established. Effects of sub-nanoscale vdWs dynamic boundaries on transient and steady-state responses of dynamically delaminated nanofilms on substrates are analyzed. The sub-nanoscale vdWs dynamic boundaries lead the dynamic responses of delaminated-nanofilm/substrate systems very sensitive to initial conditions. The bending and shifting frequency response results demonstrated that the system nonlinearities can be greatly amplified by the sub-nanoscale vdWs dynamic boundary effect. Moreover, the spontaneous symmetry breaking and violent interfacial tearing/healing phenomena can be also triggered in the systems. Based on spontaneous symmetry breaking, a trans-scale relationship between nanofilm equilibrium positions and intermolecular vdWs interactions is established, which can provide a promising route for trans-scale measurements of molecular scale interfacial interactions. The work can also be helpful for the dynamic design of resonant NEMS devices based on nanofilm/substrate systems.

Entropy-metric estimation of the small data models with stochastic parameters

The formalization of dependencies between datasets, taking into account specific hypotheses about data properties, is a constantly relevant task, which is especially acute when it comes to small data. The aim of the study is to formalize the procedure for calculating optimal estimates of probability density functions of parameters of linear and nonlinear dynamic and static small data models, created taking into account specific hypotheses regarding the properties of the studied object. The research methodology includes probability theory and mathematical statistics, information theory, evaluation theory, and stochastic mathematical programming methods. The mathematical apparatus presented in the article is based on the principle of maximization of information entropy on sets determined as a result of a small number of censored measurements of “input" and “output" entities in the presence of noise. These data structures became the basis for the formalization of linear and nonlinear dynamic and static models of small data with stochastic parameters, which include both controlled and noise-oriented input and output measurement entities. For all variants of the above-mentioned small data models, the tasks of determining the optimal estimates of the probability density functions of the parameters were carried out. Formulated optimization problems are reduced to the forms canonical for the stochastic linear programming problem with probabilistic constraints.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia.

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

A comparison between static and dynamic load tests of Tapered steel jacking piles in Baskarp sand

In this study, four full scale static compression tests were performed on a tapered steel jacking pile with diameters 76 mm and 89 mm in both dry and saturated soil conditions. Each test consists of multiple sub-tests with respect to determination of in-situ Baskarp Sand No.15 conditions and bearing capacities of the piles. Further, a finite element methodology has been developed to predict the load-displacement response of tapered piles installed in sand, incorporating the effects of jacking installation. The methodology is based on the identification of the failure mechanism and shear strain formation at failure around the pile as well as adoption of soil-soil interface elements. The nonlinear soil model parameters for a fully wished-in-place (fully-WIP) condition were obtained through piezocone penetration tests where various methods were applied to obtain the relative density, among which those providing best fit according to Jamiolokowski et al., (2003) were selected for further assessment. Finally, the hammer tests were performed from which the dynamic bearing capacities and the relation between static and dynamic bearing capacities were obtained.

Gaussian process metamodel and Markov chain Monte Carlo-based Bayesian inference framework for stochastic nonlinear model updating with uncertainties

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties; thus, a novel Bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the Bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffré–Menegotto–Pinto modeled steel-frame structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the Bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based Bayesian method effectively estimates the posterior PDF of unknown parameters and is appropriate for stochastic nonlinear model updating even with multisource uncertainties.

Regulatory provisions for determining parameters of nonlinear mechanical behavior in hardening soil models

Presently, nonlinear mechanical soil models are widely used in the geotechnical practice. They are implemented in geotechnical finite-element software PLAXIS, MIDAS GTS NX, Z-Soil, Optum, etc. Notwithstanding the fact that International regulatory documents mainly recommend nonlinear models for calculating foundations, they do not specify methods for defining their parameters because nonlinear models are actually commercial products of various software manufactures and cannot be normalized in any country. For this very reason, specialists of Gersevanov Research Institute of Bases and Underground Structures (department of JSC "Research center of Construction") developed Standard of Organization STO 36554501-067-2021. The Standard is based on the world experience in assessing nonlinear model parameters defined with using advanced laboratory equipment. The article describes the most significant provisions of this Standard. Thus, depending on the problem to be solved, four groups of models are introduced: I - a model includes volumetric isotropic hardening (Soft Soil); II - a model includes volumetric isotropic hardening and rheological properties of the soil (Soft Soil Creep); III - a model includes double isotropic hardening (Hardening Soil) and IV - a model includes double isotropic hardening and stiffness at small strain (Hardening soil with small strain). Requirements to the necessary and sufficient types and scope of tests, which define model parameters, are reported. Taking into account that only laboratory tests define model parameters, Standard provides requirements for specimens' quality evaluation performed basing on measurements of the volumetric strain under effective natural stress. Specimens of poor and very poor quality cannot be considered. It is shown that power-law coefficient m , which indicates the relationship between soil stiffness and stress-strain-state in the models of III and IV groups can be received from triaxial compression and oedometer tests and shall be prescribed depending on prevailing deformation (shear or compression). Stiffness parameters at small strains can be defined wit in-situ tests (seismoacoustic profiling) or with laboratory tests (resonant column test, seismoacoustic profiling of specimens in triaxial cell equipped with bender element and strain gauges on the local base). The developed Standard specifies requirements for laboratory definition of stiffness at small strains.