On Parameter Estimation of Linear Time Invariant (LTI) Systems Using Bootstrap Filters

2014 ◽  
pp. 1529-1541
Author(s):  
Anshul Goyal ◽  
Arunasis Chakraborty
Keyword(s):  
Parameter Estimation ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Time Invariant

ON EFFICIENCY OF EKF FOR PARAMETER ESTIMATION OF LTI SYSTEM FROM NON-STATIONARY ACCELERATION RESPONSES

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Swarup Mahato ◽  
Arunasis Chakraborty
Keyword(s):  
Parameter Estimation ◽  
Linear Time ◽  
Modal Parameters ◽  
Acceleration Response ◽  
Identification Scheme ◽  
Linear Time Invariant ◽  
Lti System ◽  
Eigen Values ◽  
Predictor Corrector ◽  
Time Invariant

Parameters of the linear time invariant (LTI) dynamic system using extended Kalman filter (EKF) are identified in this work. The efficiency of EKF for parameter estimation of LTI system is studied. For this purpose, a three-story steel frame is used in the laboratory, and the recorded ground motion is applied to measure the acceleration response at different floor levels. Using these responses, the EKF-based predictor-corrector algorithm is used to identify the modal parameters. It has been observed that the EKF-based identification scheme can converge to different system matrices (i.e., mass and stiffness) in different experiments for the same structure. However, their eigen values (i.e., natural frequency and mode) remain the same.

Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Ya Guo ◽  
Jinglu Tan
Keyword(s):  
Parameter Estimation ◽  
State Space ◽  
Linear Time ◽  
Initial Condition ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
Linear Time Invariant ◽  
Forced Responses ◽  
Time Invariant ◽  
Combined Data

AbstractMany systems can be represented as linear time-invariant (LTI) systems in state space with ordinary differential equations (ODE). Forced responses are often used for model parameter estimation; however, some models are not uniquely identifiable from the data of forced responses, or experiments with pure forced response may not be the optimal design. It is thus meaningful to look for other types of data for model parameter estimation through redesigning experiments. In this work, we compare the influence of forced and initial condition responses on the deterministic identifiability of LTI systems in state space with ODEs as model structure. It is clearly demonstrated that one initial condition vector is equivalent to one column vector of the control matrix for constraining system eigenvectors. The combination of forced and initial condition responses can improve the identifiability of models that are not identifiable only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses.

MODAL PARAMETER ESTIMATION OF LTI SYSTEM USING HILBERT-HUANG TRANSFORMATION OF MEASURED WIRELESS SENSOR DATA

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Meda Vinay Teja ◽  
Swarup Mahato ◽  
Arunasis Chakraborty
Keyword(s):  
Parameter Estimation ◽  
Linear Time ◽  
Numerical Study ◽  
Sensor Data ◽  
Modal Parameter ◽  
Linear Time Invariant ◽  
Lti System ◽  
Modal Parameter Estimation ◽  
Time Invariant ◽  
Identification Strategy

An iterative Hilbert-Huang transformation (HHT) based algorithm is developed to extract the modal parameters of a linear time invariant (LTI) system excited by recorded non-stationary ground motion. The acceleration responses are measured using wireless sensors, which are filtered to avoid mode mixing prior to evaluate the instantaneous amplitude and phase using HHT. The band width is adjusted in successive iterations to achieve convergence in modal parameter estimation. The numerical study presented in this work discusses the efficiency of the identification strategy in the light of noise contaminated earthquake responses.

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

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