scholarly journals An Optimization-Based Framework for Nonlinear Model Selection and Identification

Vibration ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 311-331 ◽  
Author(s):  
Javad Taghipour ◽  
Hamed Haddad Khodaparast ◽  
Michael I. Friswell ◽  
Hassan Jalali
Keyword(s):  
Nonlinear Model ◽  
Electromagnetic Force ◽  
Nonlinear Models ◽  
Taylor Series Expansion ◽  
Nonlinear Damping ◽  
Linear Quadratic ◽  
Nonlinear Force ◽  
Linear Damping ◽  
Vibration Tests ◽  
Fifth Order

This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results.

Multiple regression and nonlinear models

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Regression Analysis ◽  
Social Science ◽  
Multiple Regression ◽  
Nonlinear Model ◽  
Nonlinear Models ◽  
Good Strategy ◽  
Science Journal ◽  
Golf Putting ◽  
Social Science Journal ◽  
To Come

This chapter covers multiple regression and links statistical inference to general topics such as lurking variables that arose earlier. Many examples can be used to illustrate multiple regression, but we have found it useful to come to class prepared with a specific example, with computer output (since our students learn to run the regressions on the computer). We have found it is a good strategy to simply use a regression analysis from some published source (e.g., a social science journal) and go through the model and its interpretation with the class, asking students how the regression results would have to differ in order for the study’s conclusions to change. The chapter includes examples that revisit the simple linear model of height and income, involve the class in models of exam scores, and fit a nonlinear model (for more advanced classes) for golf putting.

Dynamics of a Supported Cylinder in Axial Flow

2011 ◽  
Vol 99-100 ◽  
pp. 1059-1062
Author(s):  
Ji Duo Jin ◽  
Ning Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Numerical Simulations ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Friction Drag ◽  
Flutter Instability ◽  
Nonlinear Force

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

scholarly journals Optimal Attack against Autoregressive Models by Manipulating the Environment

2020 ◽  
Vol 34 (04) ◽  
pp. 3545-3552
Author(s):  
Yiding Chen ◽  
Xiaojin Zhu
Keyword(s):  
Predictive Control ◽  
Linear Models ◽  
Nonlinear Models ◽  
Linear Quadratic Regulator ◽  
Black Box ◽  
Combine System ◽  
Linear Quadratic ◽  
Time Series Forecast ◽  
Forecast Models ◽  
Adversarial Attack

We describe an optimal adversarial attack formulation against autoregressive time series forecast using Linear Quadratic Regulator (LQR). In this threat model, the environment evolves according to a dynamical system; an autoregressive model observes the current environment state and predicts its future values; an attacker has the ability to modify the environment state in order to manipulate future autoregressive forecasts. The attacker's goal is to force autoregressive forecasts into tracking a target trajectory while minimizing its attack expenditure. In the white-box setting where the attacker knows the environment and forecast models, we present the optimal attack using LQR for linear models, and Model Predictive Control (MPC) for nonlinear models. In the black-box setting, we combine system identification and MPC. Experiments demonstrate the effectiveness of our attacks.

scholarly journals Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

2014 ◽  
Vol 11 (7) ◽  
pp. 1817-1831 ◽  
Author(s):  
Y. P. Wang ◽  
B. C. Chen ◽  
W. R. Wieder ◽  
M. Leite ◽  
B. E. Medlyn ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Microbial Biomass ◽  
Soil Carbon ◽  
Nonlinear Model ◽  
Linear Models ◽  
Nonlinear Models ◽  
Oscillatory Behavior ◽  
Carbon Pools ◽  
Carbon Decomposition ◽  
Pool Model

Abstract. A number of nonlinear models have recently been proposed for simulating soil carbon decomposition. Their predictions of soil carbon responses to fresh litter input and warming differ significantly from conventional linear models. Using both stability analysis and numerical simulations, we showed that two of those nonlinear models (a two-pool model and a three-pool model) exhibit damped oscillatory responses to small perturbations. Stability analysis showed the frequency of oscillation is proportional to √(ϵ−1−1) Ks/Vs in the two-pool model, and to √(ϵ−1−1) Kl/Vl in the three-pool model, where ϵ is microbial growth efficiency, Ks and Kl are the half saturation constants of soil and litter carbon, respectively, and /Vs and /Vl are the maximal rates of carbon decomposition per unit of microbial biomass for soil and litter carbon, respectively. For both models, the oscillation has a period of between 5 and 15 years depending on other parameter values, and has smaller amplitude at soil temperatures between 0 and 15 °C. In addition, the equilibrium pool sizes of litter or soil carbon are insensitive to carbon inputs in the nonlinear model, but are proportional to carbon input in the conventional linear model. Under warming, the microbial biomass and litter carbon pools simulated by the nonlinear models can increase or decrease, depending whether ϵ varies with temperature. In contrast, the conventional linear models always simulate a decrease in both microbial and litter carbon pools with warming. Based on the evidence available, we concluded that the oscillatory behavior and insensitivity of soil carbon to carbon input are notable features in these nonlinear models that are somewhat unrealistic. We recommend that a better model for capturing the soil carbon dynamics over decadal to centennial timescales would combine the sensitivity of the conventional models to carbon influx with the flexible response to warming of the nonlinear model.

Nonlinear Modeling of a Rigid Rotor Supported on Rolling Element Bearings With Localized Defects

2010 ◽  
Author(s):  
Karthik Kappaganthu ◽  
C. Nataraj
Keyword(s):  
Nonlinear Model ◽  
Nonlinear Models ◽  
Nonlinear Modeling ◽  
Rolling Element Bearings ◽  
Rigid Rotor ◽  
Rolling Element ◽  
Localized Defects ◽  
Bearing Race ◽  
Overall Performance ◽  
Bearing System

In this paper a nonlinear model for defects in rolling element bearings is developed. Detailed nonlinear models are useful to detect, estimate and predict failure in rotating machines. Also, accurate modeling of the defect provides parameters that can be estimated to determine the health of the machine. In this paper the rotor-bearing system is modeled as a rigid rotor and the defects are modeled as pits in the bearing race. Unlike the previous models, the motion of the rolling element thorough the defect is not modeled as a predetermined function; instead, it is dynamically determined since it depends on the clearance and the position of the shaft. Using this nonlinear model, the motion of the shaft is simulated and the effect of the rolling element passing through the defect is studied. The effect of shaft parameters and the defect parameters on the precision of the shaft and the overall performance of the system is studied. Finally, suitable measures for health monitoring and defect tracking are suggested.

An Accurate Linearization of Electromagnetic Force of Heteropolar Magnetic Bearings With Redundant Structures

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Cheng Xin ◽  
Cheng Baixin ◽  
Liu Han ◽  
Allen G. M
Keyword(s):  
Current Distribution ◽  
Electromagnetic Force ◽  
High Performance ◽  
Fault Tolerant ◽  
Taylor Series Expansion ◽  
Magnetic Bearings ◽  
Optimization Approach ◽  
Rotor Position ◽  
Distribution Matrix ◽  
Emf Model

Abstract Fault tolerance is one of the practical and effective approaches to improve the reliability of magnetic bearings. The linearization of the electromagnetic force (EMF) from the redundant structures is the crucial basis of the design of a fault-tolerant controller. In this paper, we propose an accurate linearization approach for the heteropolar magnetic bearings with redundant structures by solving the Taylor series expansion equation of the current distribution matrix (W) in the nonequilibrium position and introducing a set of displacement compensation matrices to establish a unified accurate EMF model including the controlled current and rotor position. The proposed approach can effectively decrease the EMF error between the actual physical model and the linearized model compared with the existing methods for the consideration of the rotor position. Moreover, the solutions of the current distribution matrix and the relevant optimization approach have been presented on the basis of the proposed approach to help to design a high-performance fault-tolerant controller in the entire rotor displacement range. The numerical results demonstrated the noticeable accuracy advantages of the proposed EMF model.

On the Expansion of Nonlinear Models Using Bell-Shaped Basis Functions

2003 ◽  
Author(s):  
Kiriakos Kiriakidis
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Model ◽  
Upper Bound ◽  
Nonlinear Models ◽  
Approximation Error ◽  
Basis Functions ◽  
Model Set

We propose a method that approximates any nonlinear model, without regard to complexity, by minimizing its distance from a rich model set. The method produces, potentially through an automated procedure, the approximation of the nonlinear dynamics in the form of a finite expansion associated with certain basis functions and provides an upper bound on the approximation error.

scholarly journals Estimate of Alabama argillacea (Hübner) (Lepidoptera: Noctuidae) development with nonlinear models

2003 ◽  
Vol 63 (4) ◽  
pp. 589-598 ◽  
Author(s):  
R. S. Medeiros ◽  
F. S. Ramalho ◽  
J. C. Zanuncio ◽  
J. E. Serrão
Keyword(s):  
Relative Humidity ◽  
Gossypium Hirsutum ◽  
Nonlinear Model ◽  
Nonlinear Models ◽  
Gossypium Hirsutum L ◽  
Developmental Rates ◽  
Alabama Argillacea ◽  
The Relationship ◽  
Lepidoptera Noctuidae

The objective of this work was to evaluate which nonlinear model [Davidson (1942, 1944), Stinner et al. (1974), Sharpe & DeMichele (1977), and Lactin et al. (1995)] best describes the relationship between developmental rates of the different instars and stages of Alabama argillacea (Hübner) (Lepidoptera: Noctuidae), and temperature. A. argillacea larvae were fed with cotton leaves (Gossypium hirsutum L., race latifolium Hutch., cultivar CNPA 7H) at constant temperatures of 20, 23, 25, 28, 30, 33, and 35ºC; relative humidity of 60 ± 10%; and photoperiod of 14:10 L:D. Low R² values obtained with Davidson (0.0001 to 0.1179) and Stinner et al. (0.0099 to 0.8296) models indicated a poor fit of their data for A. argillacea. However, high R² values of Sharpe & DeMichele (0.9677 to 0.9997) and Lactin et al. (0.9684 to 0.9997) models indicated a better fit for estimating A. argillacea development.

Application of a Hilbert Transform-Based Algorithm for Parameter Estimation of a Nonlinear Ocean System Roll Model

1997 ◽  
Vol 119 (4) ◽  
pp. 239-243 ◽  
Author(s):  
O. Gottlieb ◽  
M. Feldman
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Model ◽  
Hilbert Transform ◽  
Random Noise ◽  
Nonlinear Damping ◽  
Model System ◽  
Field Calibration ◽  
Calibration Test ◽  
Fishing Boat ◽  
Backbone Curves

We combine an averaging procedure with a Hilbert transform-based algorithm for parameter estimation of a nonlinear ocean system roll model. System backbone curves obtained from data are compared to those obtained analytically and are found to be accurate. Sensitivity of the results is tested by introducing random noise to a nonlinear model describing roll response of a small fishing boat. An example field calibration test of a small semisubmersible exhibiting nonlinear damping is also considered.

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