Nonlinear Modeling Method Research Articles

Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters

Higher-order asymptotic methods for nonlinear models with nuisance parameters are developed. We allow for both one-step estimators, in which the nuisance and parameters of interest are jointly estimated; and also two-step (or iterated) estimators, in which the nuisance parameters are first estimated. The properties of the former, although in principle simpler to conceptualize, are more difficult to establish explicitly. The iterated estimators allow for a variety of scenarios. The results indicate when second-order considerations should be taken into account when conducting inferences with two-step estimators. The results in the paper accomplish three objectives: (i) provide simpler methods for deriving higher-order moments when nuisance parameters are present; (ii) indicate more explicitly the sources of deviations of estimators’ sampling distributions from that given by standard first-order asymptotic theory; and, in turn, (iii) indicate in which situations the corrections (either analytically or by a resampling method such as bootstrap or jackknife) should be made when making inferences. We illustrate using several popular examples in econometrics. We also provide a numerical example which highlights how a simple analytical bias correction can improve inferences.

Research on correlation analysis and multivariate nonlinear regression modeling method for the tensile properties of mugwort petiole

The defoliation quality of mugwort defoliation equipment is an important factor to measure the defoliation efficiency, and the tensile properties of mugwort petiole will have an impact on the defoliation quality, such as the crushing rate and the abscission rate. In order to reduce the crushing rate and improve the abscission rate during mechanical harvesting of mugwort leaves, the tensile properties of mugwort petiole need to be studied. The tensile properties of mugwort petiole are closely related to its macroscopic and microscopic physicochemical parameters. Therefore, this paper takes Qichun mugwort as the research object, carries out the research on correlation analysis and multivariate nonlinear regression modeling of the tensile properties of mugwort petiole. First, the macroscopic physical parameters of mugwort, the microstructural parameters and the chemical components of mugwort were tested, and the tensile force of mugwort petiole was measured. Then, through the grey correlation and the Pearson correlation analysis, the weight values were determined with tensile properties of the mugwort petiole and each influential factors, and the multivariate nonlinear regression model of the tensile properties of mugwort petiole and its influencing factors was established by the weight values of each influencing factors. Finally, the regression model was verified. The results showed that the model had a goodness of fit of 0.725 to the experimental data, with an average absolute percentage error of 1.9%, a root mean square error of 16.3% and an average absolute error of 13.4%. The accuracy of the tensile properties model is high, which can provide data reference and theoretical basis for the design of mugwort defoliation equipment.

Dynamics Model and Its Verification of Aerospace Three-Ring Gear Reducer

This paper proposes a nonlinear dynamic modeling method based on the lumped mass approach to address the challenge of modeling the vibrations of the output external gear and internal gear plate in an aerospace three-ring gear reducer. A vibration model of bending–torsion coupling with 12 degrees of freedom was established by comprehensively considering factors such as the time-varying meshing stiffness, gear transmission error, tooth side clearance, bearing support stiffness, and damping. Finite element modal analysis and vibration test results verified the vibration model’s accuracy and applicability, indicating that the model is both precise and valid. The vibration model was solved using the fourth-order, five-level Runge–Kutta method. The results show that the symmetrical arrangement design of the internal gear plate cancels the vibrations in all directions and suppresses the vibration displacement response on the output shaft.

Degenerate phase-matching for multi-wavelength nonlinear mixing in aperiodic lattice lasers

Holographically designed aperiodic lattices (ALs) have proven to be an exciting engineering technique for achieving electrically switchable single- or multi-frequency emissions in terahertz (THz) semiconductor lasers. Here, we employ the nonlinear transfer matrix modeling method to investigate multi-wavelength nonlinear (sum- or difference-) frequency generation within an integrated THz (idler) laser cavity that also supports optical (pump and signal) waves. The laser cavity includes an aperiodic lattice, which engineers the idler photon lifetimes and effective refractive indices. The key findings are the following: (i) the nonlinear conversion efficiency reveals resonant enhancement at those idler frequencies where the photon lifetime is high; (ii) the resonant phase-matching (PM) process between the pump and idler waves has a one-to-one link with the engineered effective index dispersion; and (iii) in the absence of any other dispersion, the lowest threshold, multi-wavelength defect modes of the aperiodic lattice laser have degenerate phase-matched pump frequencies. This set of results will potentially have a significant impact on the wavelength multiplexing in electronically switchable THz-over-fiber communication systems [U.S. patent application 20,150,248,047A1 (3 September 2015)].

Cluster adsorption of L-histidine on carbon nanotubes at different temperatures

Cluster adsorption of L-histidine on carbon nanotubes at different temperatures

Supervised kernel principal component analysis-polynomial chaos-Kriging for high-dimensional surrogate modelling and optimization

Supervised kernel principal component analysis-polynomial chaos-Kriging for high-dimensional surrogate modelling and optimization

Identification of nonlinear system model and inverse model based on conditional invertible neural network

In applications such as adaptive inverse control, internal model control, and active noise control, the identification accuracy of the system model and the inverse model directly affects the performance. However, it is not easy to identify inverse models for nonlinear systems. Moreover, existing methods require two identification calculations to obtain the system model and the inverse model. Therefore, an identification method of nonlinear system model and inverse model based on conditional invertible neural network (cINN) is proposed. The invertible structure of cINN enables simultaneous approximation of complex nonlinear functions and simultaneous acquisition of the corresponding inverse functions. Consequently, both the nonlinear system model and the inverse model can be identified concurrently through cINN. Moreover, the identification performance of the cINN-based method is validated and applied to disturbance cancellation in a classical nonlinear simulation system. Finally, the inverse model of the actuator is identified by cINN, and the inverse model is applied to the nonlinear compensation of the actuator.

A combined active control method of restricted nonlinear model and machine learning technology for drag reduction in turbulent channel flow

A combined active control method of restricted nonlinear model and machine learning technology for drag reduction in turbulent channel flow

Accounting for dependencies among performance shaping factors in SPAR-H using a regularized autoencoder and WINGS-AISM

Accounting for dependencies among performance shaping factors in SPAR-H using a regularized autoencoder and WINGS-AISM

A Nonlinear Hybrid Modeling Method for Pump Turbines by Integrating Delaunay Triangulation Interpolation and an Improved BP Neural Network

In order to solve the problem that the data processing accuracy of the characteristic curves is not high, which affects the accuracy of the simulation of variable-speed pumped storage units, this paper proposes a nonlinear hybrid modeling method for pump turbines by integrating Delaunay triangulation interpolation and an improved back-propagation neural network. Firstly, the improved Sutter transform is used to preprocess the original curve, and the convex hull of the transformed curve is calculated. With the unknown point inside the convex hull, Delaunay triangulation interpolation is used to model the transformed curve. With the unknown point outside the convex hull, the back-propagation neural network is first established based on the input and output, and then the initial weights and thresholds of the network are determined using the mind evolution algorithm to complete the modeling and simulation of the curve. Simulation results show that the proposed method fully integrates the high-precision features of interpolation and the powerful nonlinear fitting ability of the neural network, which greatly improves the efficiency and accuracy of pump turbine modeling.

Synergistic activation of peroxymonosulfate by 3D CoNiO2/Co core-shell structure biochar catalyst for sulfamethoxazole degradation

In this study, a 3D CoNiO2/Co core-shell structure biochar catalyst derived from walnut shell was synthesized by hydrothermal and ion etching methods. The prepared BC@CoNi-600 catalyst exhibited exceptional peroxymonosulfate (PMS) activation. The system achieved 100% degradation of sulfamethoxazole (SMX). The reactive oxygen species in the BC@CoNi-600/PMS system included SO4-, OH, and O2-. Density functional theory calculations explored the synergistic effects between nickel-cobalt bimetallic and carbon matrix during PMS activation. The unique 3D core-shell structure of BC@CoNi-600 features an outer nickel-cobalt bimetallic layer with exceptional PMS adsorption capacity, while protecting the zero-valence Co of the inner layer from oxidation. Based on the experimental-data, machine learning modeling mechanism, and information theory, a nonlinear modeling method was proposed. This study utilizes a machine learning approach to investigate the degradation of SMX in complex aquatic environments. This study synthesized a novel biochar-based catalyst for activated PMS and provided unique insights into its environmental applications.

Early Warning for Continuous Rigid Frame Bridges Based on Nonlinear Modeling for Temperature-Induced Deflection.

Bridge early warning based on structural health monitoring (SHM) system is of significant importance for ensuring bridge safe operation. The temperature-induced deflection (TID) is a sensitive indicator for performance degradation of continuous rigid frame bridges, but the time-lag effect makes it challenging to predict the TID accurately. A bridge early warning method based on nonlinear modeling for the TID is proposed in this article. Firstly, the SHM data of temperature and deflection of a continuous rigid frame bridge are analyzed to examine the temperature gradient variation patterns. Kernel principal component analysis (KPCA) is used to extract principal temperature components. Then, the TID is extracted through wavelet transform, and a nonlinear modeling method for the TID considering the temperature gradient is proposed using the support vector machine (SVM). Finally, the prediction errors of the KPCA-SVM algorithm are analyzed, and the early warning thresholds are determined based on the statistical patterns of the errors. The results show that the KPCA-SVM algorithm achieves high-precision nonlinear modeling for the TID while significantly reducing the computational load. The prediction results have coefficients of determination above 0.98 and fluctuate within a small range with clear statistical patterns. Setting the early warning thresholds based on the statistical patterns of errors enables dynamic and multi-level warnings for bridge structures.

Linear and Non-Linear Modelling Methods for a Gas Sensor Array Developed for Process Control Applications.

New process developments linked to Power to X (energy storage or energy conversion to another form of energy) require tools to perform process monitoring. The main gases involved in these types of processes are H2, CO, CH4, and CO2. Because of the non-selectivity of the sensors, a multi-sensor matrix has been built in this work based on commercial sensors having very different transduction principles, and, therefore, providing richer information. To treat the data provided by the sensor array and extract gas mixture composition (nature and concentration), linear (Multi Linear Regression-Ordinary Least Square "MLR-OLS" and Multi Linear Regression-Partial Least Square "MLR-PLS") and non-linear (Artificial Neural Network "ANN") models have been built. The MLR-OLS model was disqualified during the training phase since it did not show good results even in the training phase, which could not lead to effective predictions during the validation phase. Then, the performances of MLR-PLS and ANN were evaluated with validation data. Good concentration predictions were obtained in both cases for all the involved analytes. However, in the case of methane, better prediction performances were obtained with ANN, which is consistent with the fact that the MOX sensor's response to CH4 is logarithmic, whereas only linear sensor responses were obtained for the other analytes. Finally, prediction tests performed on one-year aged sensor platforms revealed that PLS model predictions on aged platforms mainly suffered from concentration offsets and that ANN predictions mainly suffered from a drop of sensitivity.

Wind-Induced Dynamic Response of Inter-Story Isolated Tall Buildings with Friction Pendulum Bearing Based on an Enhanced Simplified Model

Isolation technology, especially for base isolation, is increasingly being applied in earthquake-prone areas. To satisfy some special demands (such as prevention from seawater erosion of an isolation layer, story-adding retrofit of existing buildings, avoidance of collision between base-isolated tall buildings, and so on), the isolation layer sometimes has to be set in the middle of a building to constitute inter-story isolated buildings. This special structural form inevitably encounters strong wind loads during service life, and its wind-resistant performance deserves to be investigated. This study conducts the wind-induced vibration analysis of inter-story isolated tall buildings with friction pendulum bearing (FPB). The nonlinear time domain analysis model and statistical linearization method to compute the wind-induced response of FPB inter-story isolated tall buildings are addressed based on an enhanced simplified model. Considering the independence of the upper and lower structures, two structural design schemes for inter-story isolated tall buildings are provided. Their dynamic characteristics are analyzed, and wind-induced responses are compared. Finally, the accuracy of the statistical linearization method is verified. This study provides an important theoretical basis for the structural design and wind resistance of inter-story isolated tall buildings.

Nonlinear Fast Modeling Method of Flux Linkage and Torque for a 12/8 Switched Reluctance Motors

Nonlinear Fast Modeling Method of Flux Linkage and Torque for a 12/8 Switched Reluctance Motors

ДВА СПОСОБА МОДЕЛИРОВАНИЯ РИСКА ПРОГРЕССИРУЮЩЕГО АТЕРОСКЛЕРОЗА

Background. Relevance Progressive atherosclerosis has attracted researchers for the last decade due to the fact that it is associated with unfavorable clinical outcomes. Application of modern methods of mathematical modeling will allow to identify patients with such extreme risk of cardiovascular events and optimize their management. Purpose of the study. To develop a mathematical model of the risk of progressive atherosclerosis using the free cross-platform visual programming system Orange and to compare it with the method of nonlinear regression model of logistic type implemented in C++ programming language. Materials and Methods. Female and male patients diagnosed with coronary heart disease (CHD) were included in the study, 100 of them had signs of progressive course of atherosclerosis, 102 - its spontaneous course. Risk models were built using the free cross-platform visual programming system Orange, SPSS 22.0 package, and C++ console. Results and conclusion. The author's proposed approaches to assess the risk of progressive atherosclerosis using regression analysis and machine learning have good prognostic accuracy; both methods are recommended by the authors for application in practice.

Comparison of nonlinear modeling methods for the composite rubber clamp

Comparison of nonlinear modeling methods for the composite rubber clamp

Research Progress on Nonlinear Modeling of Electro-Hydraulic Servo Systems and Innovative Applications of Control Strategies

Abstract: In various specific application domains, electro-hydraulic servo systems are widely adopted due to their high power-to-volume ratio, superior dynamic response performance, and extremely high control accuracy. However, the inevitable presence of nonlinear factors in the system poses a series of challenges for precise mathematical modeling and the design and application of different forms of control strategies. This article aims to explore how various control strategies are specifically implemented to address the nonlinear characteristics of electro-hydraulic servo systems, building upon the research progress in modeling these systems considering nonlinear factors. Subsequently, the article summarizes their innovative applications in electro-hydraulic servo systems. Simultaneously, relevant patents and technologies were reviewed and summarized. The paper provides a detailed comparison and analysis of various nonlinear modeling methods, with a particular focus on the significance of neural networks and fuzzy logic control in enhancing the performance of electro-hydraulic servo systems. The article reveals significant advancements in modern control strategies in dealing with uncertainties and disturbances within the system, offering new perspectives and ideas for improving system efficiency and achieving energy resource conservation with technological progress. The review provides a series of practical recommendations aimed at optimizing the performance of electro-hydraulic servo systems. Despite progress in multiple research endeavors, future research should focus on further enhancing system performance and applying these strategies to a broader range of scenarios.

A-stable spectral deferred correction method for nonlinear Allen-Cahn model

A-stable spectral deferred correction method for nonlinear Allen-Cahn model

Image Semantic Segmentation Approach for Studying Human Behavior on Image Data

Image semantic segmentation is an essential technique for studying human behavior through image data. This paper proposes an image semantic segmentation method for human behavior research. Firstly, an end-to-end convolutional neural network architecture is proposed, which consists of a depth-separable jump-connected fully convolutional network and a conditional random field network; then jump-connected convolution is used to classify each pixel in the image, and an image semantic segmentation method based on convolutional neural network is proposed; and then a conditional random field network is used to improve the effect of image segmentation of human behavior and a linear modeling and nonlinear modeling method based on the semantic segmentation of conditional random field image is proposed. Finally, using the proposed image segmentation network, the input entrepreneurial image data is semantically segmented to obtain the contour features of the person; and the segmentation of the images in the medical field. The experimental results show that the image semantic segmentation method is effective. It is a new way to use image data to study human behavior and can be extended to other research areas.