Simple Nonlinear Model Research Articles

Tribological Models for Advanced Ball Bearing Simulation

Advanced ball bearing simulations require the use of accurate tribological models, starting with the calculation of the ball-race contact load and pressure in potentially truncated contacts. Ball—cage and cage—guiding ring contact stiffness models are suggested using the Hertzian contact stiffness and/or a structural stiffness. The central ball-race film thickness, a hydrodynamic rolling force, and normal load increase are calculated using relationships respecting miscellaneous lubrication regimes, including iso-viscous-rigid or piezo-viscous-elastic. A drag force acting at the ball center is included, and its magnitude discussed for claiming that the contribution from drag to the final rolling resistance is smaller than the one from hydrodynamic rolling acting at the ball-race contact. The central film thickness and sliding speed are used for defining shear rate, shear stress, and, hence, final sliding force, using a nonlinear visco-elastic-plastic lubricant rheological model including viscosity, elastic lubricant shear modulus, and limiting shear stress, which are all functions of the pressure and temperature. Elastic effects are approximated using a simple nonlinear visco-plastic model with apparent viscosity. The temperature is defined as the sum of the operating temperature and several other sources of temperature increase. It is observed that when adopting Roelands viscosity model and a simple nonlinear visco-plastic model, the final lubricant traction coefficient and its gradient with respect to sliding speed decrease as the rolling speed increases, mostly reducing the need for a lubricant elastic shear modulus. Appropriate experimental results are highlighted to support these analytical models.

Establishing a Green Economy Accounting Method with Modified GDP

The purpose of this paper is to give a method for calculating GGDP, namely the Environmental Economic Accounting System (SEEA), which can measure the impact of climate environment on GDP, and can be used as an indicator to replace GDP as whether economic development is green and healthy. Meanwhile, establishing a simple nonlinear statistical model to estimate the impact of GGDP on climate environment. Among them, the weight of pollutants is solved by parameter iteration method. After it, the change of pollutants (including water pollution, air pollution, solid waste pollution, etc.) is used to measure the impact of GGDP on climate and environment compared with previous.

An approach of micro-slip modeling based on asymmetric contact pressure distribution and its application in nonlinear boundary beam system

A novel micro-slip friction modeling approach based on the Iwan model is presented here. The normal load and tangential stiffness are reassigned reasonably to obtain the tangential force–displacement expression, and the relationship between the asymmetry of contact pressure distribution and the Iwan density function is established. The micro-slip model depends on the distribution of contact pressure, and has the ability to degenerate into a macro-slip model. Based on the model, a simplified non-linear dynamics model of a rotating blade with a dovetail joint is developed, and its effectiveness is verified by comparing it with a relevant reference. The first-order bending vibration of the blade under distributed excitation is analyzed. The results indicate that the pressure distribution of the contact interface has a significant effect on the amplitude–frequency response of the blade and the contact behavior on the joint interface. Compared with the proposed micro-slip model, the single point contact model overestimates the response amplitude. The amplitude–frequency curve obtained by this model is obviously different from the macro-slip model. It is proved that the micro-slip model can more accurately simulate the nonlinear vibration characteristics of tenoned blades, which provides new insights for the study of the vibration characteristics of tenoned blades.

An enlarged polygon method without binary variables for obstacle avoidance trajectory optimization

In this article, an Enlarged Polygon/Polyhedron (ELP) method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance (CPOA) constraints in trajectory optimization. First, the equivalent condition of a point outside the convex set is given and proved rigorously. Then, the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables, and its geometric meaning is explained. Finally, the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary variables. The effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model (unmanned aerial vehicle) and complex nonlinear dynamic model (hypersonic glide vehicle). Comparison indicates the computational time of ELP method is only 1%-20% of that of the traditional Mixed-Integer Programming (MIP) method.

Novel fiber-based seismic response modelling and design method of partially CFST bridge piers considering local buckling effect

Considering the prohibitive computation time and convergence problems of shell-solid models in seismic analysis of partially concrete-filled steel tubular (CFST) bridge piers, a simple fiber-based nonlinear modelling method is proposed and calibrated in this study intended for large-scale seismic analyses. The local buckling effect of the outer steel tube is considered in the proposed method. By comparing the results of the numerical modelling with those from the experiments, the proposed fiber models are demonstrated to capture the hysteretic behavior of CFST piers with a comparable effectiveness but an enhanced efficiency and analysis time and effort over the shell-solid models. Based on the proposed fiber models, extensive cyclic pushover and time-history analyses are conducted to investigate the effect of critical design parameters on seismic performance of partially CFST piers. The analysis results indicate that the parameters of steel tube and infilled concrete should be properly designed in a combined way to mitigate the local buckling of the steel tube and thus improve the overall seismic performance of partially CFST piers. A novel design method using layered concrete filling is proposed for partially CFST piers, which can achieve an improved structural seismic performance. Furthermore, this method is validated to be especially efficient for seismic retrofit of existing hollow steel piers, which can significantly enhance the pier deformation capacity without imposing much extra force demands on pier foundations.

Implementation of non-linear mixed effects models defined by fractional differential equations.

Fractional differential equations (FDEs), i.e. differential equations with derivatives of non-integer order, can describe certain experimental datasets more accurately than classic models and have found application in pharmacokinetics (PKs), but wider applicability has been hindered by the lack of appropriate software. In the present work an extension of NONMEM software is introduced, as a FORTRAN subroutine, that allows the definition of nonlinear mixed effects (NLME) models with FDEs. The new subroutine can handle arbitrary user defined linear and nonlinear models with multiple equations, and multiple doses and can be integrated in NONMEM workflows seamlessly, working well with third party packages. The performance of the subroutine in parameter estimation exercises, with simple linear and nonlinear (Michaelis-Menten) fractional PK models has been evaluated by simulations and an application to a real clinical dataset of diazepam is presented. In the simulation study, model parameters were estimated for each of 100 simulated datasets for the two models. The relative mean bias (RMB) and relative root mean square error (RRMSE) were calculated in order to assess the bias and precision of the methodology. In all cases both RMB and RRMSE were below 20% showing high accuracy and precision for the estimates. For the diazepam application the fractional model that best described the drug kinetics was a one-compartment linear model which had similar performance, according to diagnostic plots and Visual Predictive Check, to a three-compartment classic model, but including four less parameters than the latter. To the best of our knowledge, it is the first attempt to use FDE systems in an NLME framework, so the approach could be of interest to other disciplines apart from PKs.

Multi-million-year cycles in modelled δ13C as a response to astronomical forcing of organic matter fluxes

Abstract. Along with 400 kyr periodicities, multi-million-year cycles have been found in δ13C records over different time periods. An ∼ 8–9 Myr periodicity is found throughout the Cenozoic and part of the Mesozoic. The robust presence of this periodicity in δ13C records suggests an astronomical origin. However, this periodicity is barely visible in the astronomical forcing. Due to the large fractionation factor of organic matter, its burial or oxidation produces large δ13C variations for moderate carbon variations. Therefore, astronomical forcing of organic matter fluxes is a plausible candidate to explain the oscillations observed in the δ13C records. So far, modelling studies forcing astronomically the organic matter burial have been able to produce 400 kyr and 2.4 Myr cycles in δ13C but were not able to produce longer cycles, such as 8–9 Myr cycles. Here, we propose a mathematical mechanism compatible with the biogeochemistry that could explain the presence of multi-million-year cycles in the δ13C records and their stability over time: a preferential phase locking to multiples of the 2.4 Myr eccentricity period. With a simple non-linear conceptual model for the carbon cycle that has multiple equilibria, we are able to extract longer periods than with a simple linear model – more specifically, multi-million-year periods.

Machine learning-based prediction of elastic properties of amorphous metal alloys

The Young’s modulus E is the key mechanical property that determines the resistance of solids to tension/compression. In the present work, the correlation of the quantity E with such characteristics as the total molar mass M of alloy components, the number of components n forming an alloy, the yield stress σy and the glass transition temperature Tg has been studied in detail based on a large set of empirical data for the Young’s modulus of different amorphous metal alloys. It has been established that the values of the Young’s modulus of metal alloys under normal conditions correlate with such a mechanical characteristic as the yield stress as well as with the glass transition temperature. As found, the specificity of the “chemical formula” of alloy, which is determined by molar mass M and number of components n, does not affect on elasticity of the material. The machine learning algorithm identified both the quantities M and n as insignificant factors in determining E. A simple non-linear regression model is obtained that relates the Young’s modulus with Tg and σy, and this model correctly reproduces the experimental data for metal alloys of different types. This obtained regression model generalizes the previously presented empirical relation E≃49.8σy for amorphous metal alloys.

A Foreground Mismatch and Memory Harmonic Distortion Calibration Algorithm for TIADC

This paper proposes a foreground digital calibration algorithm that estimates and corrects the offset, gain, and time-skew mismatches for time-interleaved analog-to-digital converters (TIADCs) furthermore our algorithm is designed to correct for harmonic distortion introduced by the presence of a nonlinear front-end. We propose a novel simplified non-linear model in place of the more complex conventional Volterra series based structure. The mismatch estimation technique based on the Fast Fourier Transform (FFT) is proposed to estimate the various time-interleaving mismatches simultaneously. A Taylor-based technique is applied to compensate for these mismatches. We also consider the choice of an appropriate time reference for the time-skew correction algorithm by theoretical analysis. The nonlinear distortion correction technique is based on estimating and inverting an assumed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\text {rd}}$ </tex-math></inline-formula> order nonlinearity with a fractional delay. To do this, we design a customized filter in an offline process. Our algorithms are designed to operate in any Nyquist zone. The proposed techniques are verified by a Xilinx Zynq UltraScale+ RFSoC ZCU111 evaluation kit containing a 12-bit, 4.096 GHz TI-ADC with 8 sub-ADCs operating in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{\text {nd}}$ </tex-math></inline-formula> Nyquist zone. Accordingly, we observed an improvement in SFDR of 14 dB for mismatch calibration alone and up to another 12 dB with nonlinear correction enabled.

Mathematical modeling and simulation of SEIR model for COVID-19 outbreak: A case study of Trivandrum

In this study, we formulated a mathematical model of COVID-19 with the effects of partially and fully vaccinated individuals. Here, the purpose of this study is to solve the model using some numerical methods. It is complex to solve four equations of the SEIR model, so we introduce the Euler and the fourth-order Runge–Kutta method to solve the model. These two methods are efficient and practically well suited for solving initial value problems. Therefore, we formulated a simple nonlinear SEIR model with the incorporation of partially and fully vaccinated parameters. Then, we try to solve our model by transforming our equations into the Euler and Runge–Kutta methods. Here, we not only study the comparison of these two methods, also found out the differences in solutions between the two methods. Furthermore, to make our model more realistic, we considered the capital of Kerala, Trivandrum city for the simulation. We used MATLAB software for simulation purpose. At last, we discuss the numerical comparison between these two methods with real world data.

Nonlinear Flutter Analysis of Labyrinth Seals

Abstract A simple nonlinear model to describe labyrinth seal flutter has been developed to assess the aeromechanic stability of straight-through labyrinth seals subjected to large gap variations. The model solves the one-dimensional integral mass, momentum, and energy equations of the seal for a prescribed motion numerically until a periodic state is reached. The model accounts for the effect, previously neglected, of high clearance variations on the stability. The results show that when the vibration amplitudes are small, the work-per-cycle coincides with the prediction of the Corral and Vega model (2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) and Corral et al. (2021, “Higher-Order Conceptual Model for Seal Flutter,” ASME J. Turbomach., 143(7), p. 071006), but for large vibration amplitudes nonlinearities alter the stability limit. In realistic cases, when the discharge time of the seal is much longer than the vibration period, the nonlinear effects are significant and tend to increase the unstable range of operating conditions. Furthermore, seals supported either on the high-pressure or low-pressure sides, stable for small vibration amplitudes, can destabilize when the vibration amplitude increases. The linear stability, though close in many situations to the nonlinear threshold, is not conservative, and attention must be paid to nonlinear effects.

Collapsing Response of a Nonlinear Shear-Beam Building Model Excited by a Strong-Motion Pulse at Its Base

We present a simple nonlinear model of a shear-beam building that experiences large nonlinear deformations and collapse when excited by large pulses of strong earthquake ground motion. In this paper, we introduce the model and show that its properties can be selected to be consistent with the damage observed in a seven-story hotel in San Fernando Valley of the Los Angeles metropolitan area during the 1994 Northridge earthquake. We also show an example of excitation that leads to the collapse of the model. We illustrate the response only for a sequence of horizontal pulses. We will describe the response of the same model to horizontal, vertical, and rocking motions at its base, as well as for more general excitation by strong earthquake ground motion, in future papers.

Quantum Computers for Weather and Climate Prediction: The Good, the Bad, and the Noisy

Abstract Over the past few years, quantum computers and quantum algorithms have attracted considerable interest and attention from numerous scientific disciplines. In this article, we aim to provide a nontechnical yet informative introduction to key aspects of quantum computing. We discuss whether quantum computers one day might become useful tools for numerical weather and climate prediction. Using a recently developed quantum algorithm for solving nonlinear differential equations, we integrate a simple nonlinear model. In addition to considering the advantages that quantum computers have to offer, we shall also discuss the challenges one faces when trying to use quantum computers for real-world problems involving “big data,” such as weather prediction.

Experimental-numerical assessment of laterally-loaded CFS frames with steel sheathing and K-shaped braces

In this study, the behavior of cold-form steel (CFS) frames equipped with various configurations of steel sheathing, and K-shaped braces are experimentally investigated. Low lateral resistance is a major problem with the CFS shear walls. Despite their advantages, such as being lightweight, ease of fabrication, and an environmentally friendly system, their lack of adequate lateral strength prevents engineers from widely using them, especially in areas with medium to high seismicity or mid-rise buildings. In this regard, a total of seven full-scale specimens with different configurations of steel sheathing and k-braced, with and without cladding, were tested to investigate their seismic behavior. The effect of gravity loading on the lateral resistance of the CFS frames was tested using three specimens. The gravity loadings of the CFS specimens were determined assuming an ordinary two-story CFS frame building. The effect of different CFS frame configurations on the energy dissipation, secant stiffness, and ductility factor of those frames was evaluated. The failure modes observed in this study can be classified into brace connection failure, brace element failure, sheathing, and chord stud failure. Moreover, using a calibrated simplified nonlinear model, the seismic behavior of different CFS configurations under earthquake excitation was examined. Based on the obtained experimental and numerical results, it can be concluded that the proposed dual CFS frame and shear wall configuration has a better performance both in the cyclic test and the numerical studies compared to the CFS walls with steel sheathing or bracing alone.

Simplified nonlinear modeling for estimating the seismic response of buildings

Simplified nonlinear modeling for estimating the seismic response of buildings has the advantages of providing structural perception and computational efficiency. Therefore, such modeling is useful for preliminary structural design and seismic simulation of large numbers of buildings. The generalized building model (GBM), which consists of a pure shear stick, a pure flexural stick, and N lumped masses, has been satisfactorily used for elastic seismic analyses of N-story buildings in previous research. The present study develops the inelastic properties of the sticks of all stories in the GBM so that the enhanced GBM can be used for nonlinear response history analysis of buildings. The effectiveness of the enhanced GBM is verified by comparing the seismic responses of a three-story reinforced concrete building and a nine-story steel building estimated using the GBM with those obtained from corresponding finite element models.

Ajuste de modelos não lineares mistos no crescimento dos frutos de amora-preta

Abstract Blackberry fruits belong to the genus Rubus, are fruits more cultivated in temperate climate in the summer, with low luminosity and low temperature in the winter. These fruits have as characteristic the quickperishingafter harvest and regression models, more specifically, nonlinear models, single or double sigmoid growth curve, are more recommended to model the growth of living beings. Several authors have used these models, considering only the average data of individuals under study; however, they do not consider the variability between them. One way to better capture the variability between individuals is by using mixed-effects nonlinear models that, by definition, combine the fixed and random part in the same model. Data used in this work were diameter and length of ‘Choctaw’ blackberry fruits, . The random effects of models were tested on parameters, with some steps, in order to reach the most appropriate model. For fixed-effects models, the least squares method was used, and for mixed models, the restricted likelihood was used. To reach the model that best fits data, the fit quality criteria (R2, AIC c and TRV) were used. For fruit diameter, the simple sigmoid nonlinear model was the logistic with random effect in ß1 and ß2, and for fruit length, the model was the Logistic + Logistic, with random effect in ß1 and ß4.

Multi-resolution dynamic mode decomposition for damage detection in wind turbine gearboxes

Abstract We introduce an approach for damage detection in gearboxes based on the analysis of sensor data with the multi-resolution dynamic mode decomposition (mrDMD). The application focus is the condition monitoring of wind turbine gearboxes under varying load conditions, in particular irregular and stochastic wind fluctuations. We analyze data stemming from a simulated vibration response of a simple nonlinear gearbox model in a healthy and damaged scenario and under different wind conditions. With mrDMD applied on time-delay snapshots of the sensor data, we can extract components in these vibration signals that highlight features related to damage and enable its identification. A comparison with Fourier analysis, time synchronous averaging, and empirical mode decomposition shows the advantages of the proposed mrDMD-based data analysis approach for damage detection.

UAV based adaptive trajectory tracking control with input saturation and unknown time‐varying disturbances

AbstractThis paper proposes an adaptive control method for an underactuated complex nonlinear system, that is, unmanned aerial vehicle (UAV), to realize high‐precision trajectory tracking under input saturation constraint and other disturbances via artificial neural network and anti‐saturation auxiliary system. First, the rigid body motion theory is applied to establish a simplified nonlinear dynamic model of the UAV. Then a Lyapunov function is designed with the error surface to form the preliminary control law based on dynamic surface control. Afterwards, a radical basis function neural network is developed and used to estimate and compensate the disturbance, while the input saturation is also addressed via the designed anti‐saturation auxiliary system. Thus the stability and signal consistency of the closed‐loop UAV control system can be proved via the Lyapunov stability theory with appropriately tuned parameters. Simulation experiments are performed to verify that the proposed control algorithm can be used for UAV high‐precision trajectory tracking under time‐varying disturbances.

Algal Biomass Accumulation in Waste Digestate after Anaerobic Digestion of Wheat Straw

Cultivation of microalgae in waste digestate is a promising cost-effective and environmentally friendly strategy for algal biomass accumulation and valuable product production. Two different digestates obtained as by-products of the anaerobic fermentation at 35 °C and 55 °C of wheat straw as a renewable source for biogas production in laboratory-scale bioreactors were tested as cultivation media for microalgae after pretreatment with active carbon for clarification. The strains of microalgae involved were the red marine microalga Porphyridium cruentum, which reached 4.7 mg/mL dry matter when grown in thermophilic digestate and green freshwater microalga-Scenedesmus acutus, whose growth was the highest—7.3 mg/mL in the mesophilic digestate. During cultivation, algae reduced the available nutrient components in the liquid digestate at the expense of increasing their biomass. This biomass can find further applications in cosmetics, pharmacy, and feed. The nitrogen and phosphorus uptake from both digestates during algae cultivation was monitored and modeled. The results led to the idea of nonlinear dynamic approximations with an exponential character. The purpose was to develop relatively simple nonlinear dynamic models based on available experimental data, as knowing the mechanisms of the considered processes can permit creating protocols for industrial-scale algal production toward obtaining economically valuable products from microalgae grown in organic waste digestate.

A Combination of Near-Infrared Hyperspectral Imaging with Two-Dimensional Correlation Analysis for Monitoring the Content of Alanine in Beef.

Alanine (Ala), as the most important free amino acid, plays a significant role in food taste characteristics and human health regulation. The feasibility of using near-infrared hyperspectral imaging (NIR-HSI) combined with two-dimensional correlation spectroscopy (2D-COS) analysis to predict beef Ala content quickly and nondestructively is first proposed in this study. With Ala content as the external disturbance condition, the sequence of chemical bond changes caused by synchronous and asynchronous correlation spectrum changes in 2D-COS was analyzed, and local sensitive variables closely related to Ala content were obtained. On this basis, the simplified linear, nonlinear, and artificial neural network models developed by the weighted coefficient based on the feature wavelength extraction method were compared. The results show that with the change in Ala content in beef, the double-frequency absorption of the C-H bond of CH2 in the chemical bond sequence occurred prior to the third vibration of the C=O bond and the first stretching of O-H in COOH. Furthermore, the wavelength within the 1136-1478 nm spectrum range was obtained as the local study area of Ala content. The linear partial least squares regression (PLSR) model based on effective wavelengths was selected by competitive adaptive reweighted sampling (CARS) from 2D-COS analysis, and provided excellent results (R2C of 0.8141, R2P of 0.8458, and RPDp of 2.54). Finally, the visual distribution of Ala content in beef was produced by the optimal simplified combination model. The results show that 2D-COS combined with NIR-HSI could be used as an effective method to monitor Ala content in beef.