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.

scholarly journals Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Zhao ◽  
Baofeng Zhang ◽  
Fangfang Han ◽  
Huan Tian ◽  
Xiao Yu ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Model ◽  
Estimation Method ◽  
Nonlinear Damping ◽  
Torsion Pendulum ◽  
Damping Force ◽  
Restoring Force ◽  
Pendulum System ◽  
The Moment ◽  
The Relationship

The nonlinear model of torsion pendulum is presented by considering the nonlinear damping force and nonlinear restoring force. The analytic solution of the nonlinear model is calculated to analyze the relationship between the characteristics of torsion pendulum and the nonlinear factors. The instantaneous characteristics of nonlinear torsion pendulum are analyzed by instantaneous undamped natural frequency and instantaneous damping coefficient. The instantaneous characteristics can be used for the parameter estimation of nonlinear torsion pendulum system. The nonlinear characteristics of the torsion pendulum are validated by the torsion pendulum based on the air-hovered turntable. The parameter estimation method based on the instantaneous characteristics is validated by the moment of inertia measurement system based on the torsion pendulum.

scholarly journals MODEL DECOMPOSITION BASED ABNORMAL PARAMETER ESTIMATION FOR DISTILLATION COLUMN

2018 ◽  
Vol 48 (2) ◽  
pp. 81-87
Author(s):  
W. D. TIAN ◽  
S. L. SUN
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Model ◽  
Distillation Column ◽  
Estimation Method ◽  
Matrix Analysis ◽  
Physical Parameters ◽  
Time Saving ◽  
Model Decomposition ◽  
Parameter Estimation Method ◽  
Occurrence Matrix

Parameter estimation method can produce useful physical parameters in finding abnormal causes, but nonlinear model makes this method computationally intensive and non-robust for distillation scenario. In this paper, we propose a model decomposition based parameter estimation method for distillation column diagnosis purposes. Nonlinear first principles dynamic model is divided into some disjoint submodels through occurrence matrix analysis. The whole model is used to monitor distillation process and the submodel that gives the highest contribution to the generated residual is selected to perform abnormal parameter estimation. Application results from stripping tower in the popular Tennessee Eastman challenge problem show that the model decomposition based diagnosis scheme is more time-saving and robust than pure nonlinear model based scheme.

scholarly journals Monitoring of drilling conditions using the Hilbert-Huang transformation

2018 ◽  
Vol 148 ◽  
pp. 16003 ◽  
Author(s):  
Piotr Wolszczak ◽  
Grzegorz Litak ◽  
Marek Dziuba
Keyword(s):  
Fourier Transform ◽  
Numerical Simulations ◽  
Hilbert Transform ◽  
Geometrical Parameters ◽  
Drilling Process ◽  
Nonlinear Characteristics ◽  
Different Types ◽  
Fourier Spectra ◽  
Backbone Curves ◽  
Drilling Conditions

The article presents the results of design and monitoring the drilling process. Vibroacoustic sensors were used to observe spindle vibrations. These signals were subjected to a Huang decomposition and a Fourier transform. Results for various conditions were studied and classified with help of Fourier spectra and the envelope curves. Using the additional results of numerical simulations sources of vibration were identified. We considered four different types of drilling which were diversified in terms of geometrical parameters of blades. The application of Hilbert transform enable to find nonlinear characteristics via the deflection profile of resonance backbone curves.

A New Electrode Regulator System Identification of Arc Furnace Based on Time-Variant Nonlinear-Linear-Nonlinear Model

2016 ◽  
Vol 2 (1) ◽  
pp. 32
Author(s):  
Jinfeng Wang ◽  
Shoulin Yin ◽  
Xueying Wang
Keyword(s):  
Nonlinear Model ◽  
Model System ◽  
Time Varying ◽  
Arc Furnace ◽  
Identification Process ◽  
System Parameters ◽  
Online Identification ◽  
Arc Characteristics ◽  
Controlling System ◽  
The Mind

<p>In this paper, we express arc furnace electrode regulator system as a time-variant nonlinear-linear-nonlinear model. On this basis, we propose an online identification method based on nonlinear-linear-nonlinear model system. This new scheme solves the problem of model variation and prediction precision decline causing by time-varying of arc characteristic. In order to dispose the difficulty of parameters separation in the online identification process, this new method adopts the mind of update the parameters of linear parts and nonlinear parts respectively. It realizes the parameters separation of system effectively. Simulation results show that this method can track the changes of arc characteristics effectively. That it achieves the aim of real-time monitoring and controlling system parameters.</p>

scholarly journals Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160759 ◽  
Author(s):  
Robert Szalai ◽  
David Ehrhardt ◽  
George Haller
Keyword(s):  
Nonlinear Model ◽  
Invariant Manifolds ◽  
Model Identification ◽  
Oscillatory System ◽  
Least Square ◽  
Least Square Fit ◽  
Backbone Curves ◽  
Nonlinear Model Identification ◽  
Real Experimental Data ◽  
Spectral Submanifolds

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude–frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. This model identification utilizes Taken’s delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding. The SSMs are then constructed for the sampling map using the parametrization method for invariant manifolds, which assumes that the manifold is an embedding of, rather than a graph over, a spectral subspace. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

SOME REMARKS ON STRUCTURE SELECTION FOR NONLINEAR MODELS

1994 ◽  
Vol 04 (06) ◽  
pp. 1707-1714 ◽  
Author(s):  
LUIS ANTONIO AGUIRRE
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Model ◽  
Nonlinear Models ◽  
Sampling Period ◽  
Information Criteria ◽  
Structure Selection ◽  
Selection For ◽  
Selection Of

This note is concerned with structure selection of nonlinear models. By structure selection it is meant the choice of the model basis prior to parameter estimation. It is argued that the effect of the sampling period and the noise on the data may in some cases preclude adequate structure selection. Other issues which are briefly discussed include the selection of the sampling period and the effectiveness of information criteria in indicating the best size of a nonlinear model.

scholarly journals Calibration for Parameter Estimation of Signals with Complex Noise via Nonstationarity Measure

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhiming Zhou ◽  
Zhengyun Zhou ◽  
Liang Wu
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Calibration Method ◽  
Numerical Studies ◽  
Chaotic Signals ◽  
Inaccurate Estimation ◽  
Non Gaussian ◽  
First Time

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex (such as non-Gaussian noise, strong noise, and chaotic noise). This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types (including random noise and chaotic noise) and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations.

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