Nonlinear Method Research Articles

Nonlinear seismic analysis of city gate architectural heritages using a sensitive-based model updating method

Due to the unknown accumulation of internal damage and severe degradation of structural mechanisms, updating numerical model related to current damage using Operational Modal Analysis and performing nonlinear seismic analysis pose significant challenges. In this paper, a nonlinear seismic analysis method is proposed involving a three-stage finite element model updating process. This method not only updates the global parameters and local parameters of substructure, but also updates the FEM to true current damage state based on elastic-plastic constitutive model considering current damage. First, on-site vibration and material performance tests were conducted to obtain modal data and material properties of the structure. Second, each component in the model was updated to detect damage, employing a sensitivity-based approach in Stage 1. Then, each element within the severely damaged components obtained from Stage 1 was updated for damage detection, again using a sensitivity-based approach in Stage 2. Finally, the current damage state was updated based on elastoplastic constitutive model considering the current damage and a seismic analysis was performed in Stage 3. The results indicate that, in Stage 1, updating the global parameters of the model aligns the calculated data with the measured data. In Stage 2, updating the local parameters to accurately identify the location and severity of damage within the heavily affected components is demonstrated by a simple example. These results can establish a scientific foundation for the nonlinear seismic analysis of city gate architectural heritages.

Dynamic Modeling and Improved Nonlinear Model Predictive Control of a Free-Floating Dual-Arm Space Robot

With the increasing demand for space missions, space robots have become the focus of research and attention. As a typical representative, the free-floating dual-arm space robot has the characteristics of multiple degrees of freedom, a floating base, and dynamic coupling between the manipulator and the base, so its modeling and control are very challenging. To address these challenges, a novel dynamic modeling and control method is proposed for a free-floating dual-arm space robot. First, an explicit dynamic model of a free-floating dual-arm space robot is established based on the explicit canonical multi-rigid-body dynamic modeling theory and combined with the concept of a dynamic equivalent manipulator. The establishment process of this model is not only simple and canonical to avoid the definition and calculation of many intermediate variables, but the symbolic result expression of the model also has the characteristics of iteration, which is convenient for computer automatic modeling. Next, aiming at addressing the problem of trajectory tracking and the base attitude stability of a free-floating dual-arm space robot with parameter perturbation and external disturbance, an improved nonlinear model predictive control method introducing the idea of sliding mode variable structure is proposed. Theoretical analysis shows that the proposed controller has better robustness than the traditional nonlinear model predictive controller. Then, an in-orbit service task is designed to verify the effectiveness of the proposed dynamic modeling and control strategy of the free-floating dual-arm space robot. Finally, the dynamic modeling and control methods proposed are discussed and summarized. The proposed methods can not only realize the tracking of the desired trajectory of the arms of the free-floating space robot, but can also realize the stable control of the base of the free-floating space robot. This paper provides new insights into the difficult problems regarding the dynamics and control of free-floating dual-arm space robots.

Non-linear behavior of functionally graded elastoplastic beam under torsion

The torsional behavior of beams graded in one and two directions under large displacements and angular deformations was analyzed using the power law and sinusoidal functions. Functionally graded material is elastoplastic, consisting of ceramic and metal. A nonlinear finite element method with isoparametric hexahedral elements was used. The finite element formulation was made using the updated Lagrangian formulation based on the virtual displacement principle. An iterative solution using Newton-Raphson and updated Newton-Raphson methods was used to solve the nonlinear equation system. The propagation of the plastic zone was calculated based on the flow theory of plasticity. Elastoplastic behavior and effective material properties were determined according to the TTO model. Numerical investigations have shown that functionally graded beams behave quite differently from homogeneous beams under torsion. Yielding of the material starts at the outer boundaries of the section of the homogeneous beams, and the plastic zone propagates symmetrically. On the other hand, yielding and propagation of plastic zones tend to shift to regions with more ceramic volume with higher effective Young modulus in functionally graded beams. Unlike homogeneous beams, the largest shear stresses can occur within the section rather than at the outer boundaries of the section. In beams graded from ceramic to metal using the power law, the section moves along the transverse direction in addition to the rotation. This transverse displacement occurs in the grading direction, and its magnitude is about 3% of the thickness at 12.5° rotation angle. Also, the shear stresses are not zero in the section's midpoint. The effects of material distribution on displacements, stresses, and plastic zone propagation were examined, and essential points were reported.

Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws.

Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang-Shu) weighting; however, the smoothness indicator of the 5-point stencil adopts a special design with a higher-order leading term similar to the τ in Z weighting. The design maintains that the nonlinear weights satisfy sufficient conditions for the scheme to avoid degradation even near extreme points. By adjusting the linear weights to a specific value and using the τ in Z weighting, the method can be degraded to Z weighting. Analysis of linear weights shows that they do not affect the accuracy in the smooth region, and they can also adjust the resolution and discontinuity-capturing capability. Numerical tests of different hyperbolic conservation laws are conducted to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show that there are no obvious oscillations near the discontinuity, and the resolution of both the discontinuity and smooth regions is better than that of Z weights.

New Weibull Log-Logistic grey forecasting model for a hard disk drive failures

Forecasting the failure of hard disk drives is important in server operation and has attracted increasing attention. However, current disk drive warning systems suffer from high false positive rates and high resource consumption when dealing with hard disk drive overall failure. Therefore, to accurately and stably predict hard disk drive overall failure, this paper develops a new Weibull Log-Logistic grey forecasting model with multiple interaction effects. Firstly, to capture and fit the trend of hard disk failure data flexibly and reduce the volatility, a new accumulation generation operator is established by introducing the Weibull Log-Logistic mixture distribution. Secondly, the proposed model constructs a multiple interaction term to describe the nonlinear relationship of the dependent variables on the system behavior series and the multiple interaction effects between the independent variables. Then, the parameter estimation method is designed to improve the fitting accuracy of the new model, in which linear estimation method, nonlinear estimation method, and meta-heuristic optimization algorithm are used to calculate the parameter values according to their categories. Finally, four varieties of hard disk drive data sets from BackBlaze are selected as study cases to validate the effectiveness of the proposed model. The results show that the mean MAPE of the proposed method is 2.1181 %, 2.2306 %, 8.1712 %, and 4.3417 %, respectively, corresponding to (hard disk drives ST8000NM0055, ST12000NM0007, ST10000NM0086, and ST14000NM0138), and the average value of the evaluation metrics are optimal in all competing models. Furthermore, it is observed that the number of reallocated sectors has the greatest influence in causing the failure of hard disk drives.

Electromagnetic telemetry signal denoising: An interference elimination via parameter estimation

Electromagnetic telemetry has emerged as a promising technique for the real-time acquisition of downhole data. However, the transmission of electromagnetic waves through the formation encounters attenuation, leading to a weakened received signal at the surface, typically registering at the microvolt level. The growing presence of surface electrical equipment in well-site environments has engendered heightened electromagnetic interference, thus deteriorating the signal-to-noise ratio (SNR) of received signals. The conventional linear filtering method can effectively eliminate the electromagnetic interference at the wellsite, but it has no effect on the low frequency interference close to the carrier frequency, especially the common low-frequency pulse interference (LPI) and power line interference (PLI). To mitigate the adverse effects of surface noise, we propose a nonlinear processing method based on parameter estimation algorithms. Generally, the proposed method entails reconstructing the interference by accurate parameter estimation and subtracting it from the received signal, aiming to enhance the SNR of the received signal. Simulation data and real noise data collected in the field are processed to verify the effectiveness of the proposed method. The results demonstrate the superiority of this approach over traditional filtering techniques in effectively eradicating surface interference.

Study of the kurtoses transmission of linear structures under stationary non-Gaussian random loadings

Recent research has discovered that the kurtoses of non-Gaussian stress loadings can significantly impact the fatigue life of in-service structures. To predict potential damage, a fatigue life estimation method based on Gaussian damage and a kurtosis-related corrective coefficient has been developed. However, the transmission of kurtoses from excitations to responses has not been well studied, particularly in multi-input cases. This hinders efforts to accelerate fatigue damage by controlling input kurtoses. Therefore, this paper aims to establish a kurtoses transmission model for a linear structure under multiple uncorrelated stationary non-Gaussian excitations generated by zero-memory non-linear method. Firstly, a single-input kurtosis transmission equation is proposed to establish the relationship between excitation kurtosis and response kurtosis. Using this equation, the response kurtosis is formulated with input kurtosis and the system parameters of a linear structure. Secondly, the response kurtosis of multi-input cases is deduced, and the study shows that the response kurtosis is the weighted sum of the kurtosis induced by each excitation. Finally, numerical validation and experimental studies are conducted to verify the accuracy of both the single-input and multi-input kurtoses transmission models. The validations demonstrate that the proposed models can predict the response kurtoses with satisfactory precision, regardless of the input spectral shape and the number of uncorrelated input forces.

Quantitative and intelligent methods for economic forecasts (birth rate time series (Ntl))

The models proposed in the field of time series forecasting are numerous. However, accurate forecasting is still one of the main challenging problems faced by decision makers in various fields, especially in financial markets. Anticipatory and intelligent methods play a crucial role in economic forecasting, helping to increase the accuracy and reliability of forecasts. This is the main reason that many researchers have in the focus of their research the development of methods for improving the performance of forecasts. Using only a linear or non-linear method is not enough to recognize and model all features and functions of the data. In addition to quantitative techniques as well as intelligent techniques that have been developed recently as a result of technological developments, a new technique or hybridization of these two techniques behaves as a very efficient approach. For this reason, in the study it is proposed to improve the modeling and forecasting results by combining a linear A RIMA method with an intelligent non-linear method, the artificial neural network -ANN. Several ARIMA-ANN hybrid model architectures are known, but in this thesis a new A RIMA-ANN technique with improving features of the existing hybrid methods is proposed. The time series under study are the birth rate in Albania obtained by INSTAT and the Bank of Albania with monthly frequencies. Time series analysis goes through three phases: defining characteristics, modeling and forecasting. The analysis is performed with ARIMA, ANN and the proposed ARIMA-ANN method. Data mining, sentiment analysis, and natural language processing (NLP) techniques are used to analyze unstructured data sources. The models, either quantitative or intelligent, give satisfactory results, but the hybrid model shows much higher performance in all series. From the measurement indicators of the prediction performance, the hybrid method has resulted with high efficiency. The ARIMA-ANN model produced much better results than the ARIMA and ANN models. These results are a consequence of the combination of the two techniques and from which results a good recognition of the different structures of the data modes. This study contributes to the field of time series forecasts in Albania and intelligent or quantitative modeling by developing a new forecast model, that of hybridization.

Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

The Influence of Short-Term High Temperature Environment on the Non-Uniform Distribution of Ferrite Grain Size in 40 mm-thick Q345 Steel

In order to reveal the non-uniform distribution of grain size in thick direction for engineering heavy plate, microstructure of 40 mm-thick Q345 steel was observed and measured under different short-term high temperature environments formed by fire. Moreover, the influence of the short-term high temperature environment was revealed on the distribution of ferrite grain size in the Q345 steel. Under different fire service environments, there was a log-normal distribution relationship between the distribution parameter Nf (number of ferrite grains) and df (average grain diameter), as well as ρAf (area fraction density) and df, at different positions along the thickness direction. However, the statistical results are greatly affected by the length of the statistical interval. When df is about 4 to 6 times the length of the statistical interval, the statistical accuracy is higher. By using nonlinear fitting method, multiple non-uniform distribution empirical models including Nf-df empirical formulas and ρAf-df empirical formulas were established at different positions along thick direction under various fire environments. Furthermore, the interrelationships between fire temperature T and Nf , T and ρAf , fire duration t and Nf , t and ρAf were revealed, respectively.

Characterisation of coherent ultrasonic nonlinear imaging

Nonlinear ultrasonic imaging methods for non-destructive testing have shown sensitivity to early damage formation. Among those, the Fundamental wave Amplitude Difference (FAD) technique has been proposed in the literature as a nonlinearity mapping method for defect visualisation. It does so by calculating the residual between a low and high nonlinearity image, which is achieved by some modulation of the focal spot amplitude. This is realised either through different input voltages or alternating the element-wise firing scheme. This paper assesses the sensitivity of FAD through different techniques used for the generation of the low nonlinearity images, using both theoretical and experimental approaches. These techniques include (1) Different-Voltage FAD (DV-FAD); (2) Odd-Even FAD (OE-FAD) and; (3) Parallel–Sequential FAD (PS-FAD). Formulae are derived that allow the different firing sequences and image corrections to be compared. The FAD techniques are then experimentally evaluated against the theory, showing a 50% amplitude gain at the crack tip when comparing PS-FAD to OE-FAD and DV-FAD. Additionally, the instrument behaviour is assessed by considering the image correction required to improve the image contrast for the visualisation of the crack tip. Finally, it is shown that all FAD techniques are equivalent in terms of nonlinear detection but additional work is required in comparing the performance of other array controllers when using FAD.

Impact of environmental policy stringency on sectoral GHG emissions: evidence from Finland and Sweden by nonlinear quantile-based methods

ABSTRACT The growing societal concern regarding environmental matters has led to the implementation of many environmental measures intended to protect the environment and address global warming by lessening emissions and mitigating climate change. In line with this movement, this study scrutinizes the impact of these environmental measures on greenhouse gas (GHG) emissions to analyze the cases of Finland and Sweden. More specifically, the study employs the Environmental Policy Stringency (EPS) index as a proxy for environmental measures, explores sector-specific GHG emissions by employing nonlinear quantile-based methodologies (including quantile-on-quantile regression and Granger causality-in-quantiles methods as the primary model and quantile regression for robustness checking) spanning the period from 1991/Q1 to 2020/Q4. The findings show that: (i) EPS lessens GHG emissions from fuel exploitation, industrial combustion, and the power industry sector at lower and middle quantiles in Finland and Sweden; (ii) EPS decreases GHG emissions from processes, transportation, and waste sectors in Finland but increases them in Sweden at higher quantiles; (iii) EPS leads to an increase in GHG emissions from the agriculture and construction sectors at higher quantiles; (iv) EPS has a causal effect on sector-specific GHG emissions across different quantiles; (v) the robustness of the findings is largely confirmed. Hence, the study underscores the varying impacts of EPS on sectoral GHG emissions based on quantiles, sectors, and countries, emphasizing the need for policymakers to adopt environmental policies to comprise these differences and adjust the policy framework accordingly.

A new passive‐based active disturbance rejection control for PMSG system with saturation constraints

AbstractThe disturbance in wind energy conversion system has a serious negative impact on the maximum power tracking performance of the system, and the saturation constraint problem also seriously restricts the stability of the control system. Therefore, a novel model compensation passive‐based active disturbance rejection control strategy is proposed to suppress the disturbance and saturation constraints, thus improving the tracking performance of the permanent magnet synchronous generator system in this paper. Taking advantage of the fact that active disturbance rejection control technology can estimate and compensate for the disturbances of the system in real time, a model compensation active disturbance rejection control method is proposed to make the system more robust to the changes in its own parameters and external disturbance. At the same time, the control input signal of the controller is given. A model compensation passive‐based active disturbance rejection controller is designed by using the passive control method, and the nonlinear sector method is introduced to solve the saturation constraint problem of the system. Simulation results show that the control strategy can effectively reduce overshoot, improve the system's response speed, have a good anti‐interference ability, and effectively suppress the influence of saturation constraints on the system.

Fault-Tolerant Control for Aircraft with Structural Damage Using Sparse Online Gaussian Process Regression

AbstractThis paper presents the design of data-driven fault-tolerant control using sparse online Gaussian process regression (SOGPR) to stabilize an aircraft with left-wing damage. The structural damage causes changes in mass, moment of inertia, center of gravity, and aerodynamic coefficients. These parameter variations deteriorate the performance of model-based nonlinear control methods. Hence, Gaussian process-based nonlinear dynamic inversion (GP-NDI) is proposed to compensate for uncertainties in situations of structural damage. Unlike parametric adaptive control approaches, Gaussian process regression is a non-parametric method that does not need prior information about uncertainties. And the proposed method implements SOGPR to reduce computational time and memory by incrementally updating the mean and variance. To compensate for the error in the estimated uncertainty, a robust control input is designed. In addition, a weighted delete score is used to improve the transient response. Numerical simulation results are compared with model reference adaptive control (MRAC) and nonlinear disturbance observer (NDO) to analyze a stabilizing and tracking performance in a structural damage situation.

Interpretation of autoencoder-learned collective variables using Morse-Smale complex and sublevelset persistent homology: An application on molecular trajectories.

Dimensionality reduction often serves as the first step toward a minimalist understanding of physical systems as well as the accelerated simulations of them. In particular, neural network-based nonlinear dimensionality reduction methods, such as autoencoders, have shown promising outcomes in uncovering collective variables (CVs). However, the physical meaning of these CVs remains largely elusive. In this work, we constructed a framework that (1) determines the optimal number of CVs needed to capture the essential molecular motions using an ensemble of hierarchical autoencoders and (2) provides topology-based interpretations to the autoencoder-learned CVs with Morse-Smale complex and sublevelset persistent homology. This approach was exemplified using a series of n-alkanes and can be regarded as a general, explainable nonlinear dimensionality reduction method.

Land Use Sustainability: Assessment of the Dynamic Response of Typical Bedrock-Buried-Hill Earth Fissure Sites in the Su-Xi-Chang Area

Disaster prevention and the mitigation of earth fissures is a key issue in the sustainable development of urban land. Structures directly avoiding earth fissures are not conducive to the rational planning and efficient utilization of urban construction. The Su-Xi-Chang area, which consists of the cities of Suzhou, Wuxi, and Changzhou, surrounded by Taihu Lake, has developed bedrock buried-hill earth fissures that are rare in the rest of the country. Existing research results have identified the genesis mechanisms, distribution patterns, and developmental characteristics of this type of fissure. Not only does the slow-variable activity of earth fissures cause direct damage to surface and underground structures, but in addition, when an earthquake occurs, the presence of earth fissures may cause the seismic response of the site to be altered or even strengthened, leading to unknown damage or the possible destruction of structures near the fissures. However, no studies have been conducted to assess the dynamic effects of bedrock-buried-hill earth fissure sites. Therefore, in this research, based on six typical bedrock-buried-hill-type earth fissures in the Su-Xi-Chang area, and in order to accurately reveal the dynamic amplification effect law of the earth fissure sites, systematic spectral analyses and comparisons of the microtremor signals were carried out by using the linear analysis method (Direct Fourier Transform Analysis) and the nonlinear analysis method (Hilbert–Huang Transform). The results show that bedrock-buried-hill-type earth fissures have a significant amplification effect on the dynamic response of the site; the amplification effect of bedrock-buried-hill fissure sites follows the same attenuation pattern, and the furthest range of the dynamic response on the site is about 25 m, beyond which the original seismic fortification level can be maintained; the extreme value of the amplification factor of the two sides of this type of site, as derived from the Fourier and HHT methods, is about double, and the nearest earth fissure region should be considered to have a raised seismic fortification intensity of more than double the original. The Hilbert–Huang transform method has good applicability for processing microtremor data, and nonlinear signal analysis methods can be considered comprehensive for future microtremor signal processing.

Study of the adsorption isotherm of 2-mercaptobenzothiazole by activated carbon based on grape marc: linear and non-linear method

The adsorption performance of 2-mercaptobenzothiazole from an aqueous solution on activated carbon synthesized through grape marc was explored. In this research, the agricultural waste was chemically treated with phosphoric acid (40% H3PO4, 170 °C, 3 h), then pyrolyzed at 650 °C for 2 h, to obtain the GMAC-650 to be used as an adsorbent. The resulting material was characterized by Fourier-transform infrared spectroscopy, X-ray diffraction, and Brunauer–Emmett–Teller (BET). Maximum uptake (∼99%) is obtained under ideal conditions: an adsorbent dose of 0.8 g L−1 and pH = 8 for an initial concentration of 10 mg L−1 at 45 °C. The adsorption equilibrium data were fitted to the following isotherm models: Langmuir and Freundlich. For optimal equilibrium isotherm selection, a comparison of linear and non-linear methods for the adsorption of MBT. It was based on four error functions: the coefficient of determination R 2, the sum of squared errors, the Chi-square (χ 2), and the root mean square error. The current work has shown that the non-linear method is a more adequate method for estimating the parameters of the isotherm compared with the linear method. The comparative analysis of the models shows that the Freundlich model is more appropriate for describing equilibrium data.

Accurate Temperature Reconstruction in Radiofrequency Ablation for Atherosclerotic Plaques Based on Inverse Heat Transfer Analysis.

Radio frequency ablation has emerged as a widely accepted treatment for atherosclerotic plaques. However, monitoring the temperature field distribution in the blood vessel wall during this procedure presents challenges. This limitation increases the risk of endothelial cell damage and inflammatory responses, potentially leading to lumen restenosis. The aim of this study is to accurately reconstruct the transient temperature distribution by solving a stochastic heat transfer model with uncertain parameters using an inverse heat transfer algorithm and temperature measurement data. The nonlinear least squares optimization method, Levenberg-Marquardt (LM), was employed to solve the inverse heat transfer problem for parameter estimation. Then, to improve the convergence of the algorithm and reduce the computational resources, a method of parameter sensitivity analysis was proposed to select parameters mainly affecting the temperature field. Furthermore, the robustness and accuracy of the algorithm were verified by introducing random noise to the temperature measurements. Despite the high level of temperature measurement noise (ξ = 5%) and larger initial guess deviation, the parameter estimation results remained closely aligned with the actual values, with an overall ERMS consistently below 0.05. The absolute errors between the reconstruction temperature at the measurement points TC1, TC2, and TC3, and the actual temperature, remained within 0.33 °C, 2.4 °C, and 1.17 °C, respectively. The Levenberg-Marquardt algorithm employed in this study proficiently tackled the ill-posed issue of inversion process and obtained a strong consistency between the reconstructed temperature the actual temperature.

Energy analysis of a nonlinear gas-spring dynamic vibration absorber subjected to seismic excitations

Nonlinear control methods and devices have been widely used in seismic vibration reduction of engineering structures. A nonlinear gas-spring dynamic vibration absorber (NGSDVA) has been recently proposed by the authors and demonstrates a wideband vibration suppression capability across various excitation amplitudes. In this study, an energy analysis method for a multi-story structure with NGSDVA attached under seismic excitation is proposed through experimental and numerical simulation analysis. The energy distribution of the controlled structure and the energy transmission process between the main structure and the damping system are analyzed. It is found that the intermodal energy transfer phenomenon occurs in the five-story steel frame structure during the energy transmission process, while the first-order modal energy is converted to high-order modal energy simultaneously. A series of energy-based parametric studies are further conducted, and the consistency of the parameter influence rules under four different seismic waves is proved, indicating the advantages of energy evaluation indicators for optimizing the design of this nonlinear damper with amplitude-frequency characteristics.

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill