scholarly journals Online Identification of Time-Variant Structural Parameters Under Unknown Inputs Basing On Extended Kalman Filter

2021 ◽  
Author(s):  
Xiaoxiong Zhang ◽  
Jia He ◽  
Xugang Hua ◽  
Zhengqing Chen ◽  
Ou Yang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Structural Parameters ◽  
Optimization Procedure ◽  
Unbiased Estimation ◽  
Time Varying ◽  
Time Step ◽  
Varying Parameters ◽  
Unknown Inputs ◽  
Time Varying Parameters

Abstract To date, a number of parameter identification methods have been developed for the purpose of structural health monitoring and vibration control. Among them, the extended Kalman filter (EKF) series methods are attractive in view of the efficient unbiased estimation in recursive manner. However, most of these methods are performed on the premise that the parameters are time-invariant and/or the loadings are known. To circumvent the aforementioned limitations, an online EKF with unknown input (OEKF-UI) approach is proposed in this paper for the identification of time-varying parameters and the unknown excitation. A revised observation equation is obtained with the aid of projection matrix. To capture the changes of structural parameters in real-time, an online tracking matrix (OTM) associated with the time-varying parameters is introduced and determined via an optimization procedure. Then, based on the principle of EKF, the recursive solution of structural states including the time-variant parameters can be analytically derived. Finally, using the estimated structural states, the unknown inputs are identified by means of least-squares estimation (LSE) at the same time-step. The effectiveness of the proposed approach is validated via linear and nonlinear numerical examples with the consideration of parameters being varied abruptly.

scholarly journals Experimental validation of the proposed extended Kalman filter with unknown inputs algorithm based on data fusion

2019 ◽  
Vol 39 (4) ◽  
pp. 835-849 ◽  
Author(s):  
Jinshan Huang ◽  
Xianzhi Li ◽  
Xiongjun Yang ◽  
Zhupeng Zheng ◽  
Ying Lei
Keyword(s):  
Kalman Filter ◽  
Data Fusion ◽  
Extended Kalman Filter ◽  
Experimental Validation ◽  
Structural Parameters ◽  
Wide Band ◽  
Unknown Inputs ◽  
Filter Methods ◽  
Filter Approach ◽  
Shear Building

The extended Kalman filter is a useful tool in the research of structural health monitoring and vibration control. However, the traditional extended Kalman filter approach is only applicable when the information of external inputs to structures is available. In recent years, some improved extended Kalman filter methods applied with unknown inputs have been proposed. The authors have proposed an extended Kalman filter with unknown inputs based on data fusion of partially measured displacement and acceleration responses. Compared with previous approaches, the drifts in the estimated structural displacements and unknown external inputs can be avoided. The feasibility of proposed extended Kalman filter with unknown inputs has been demonstrated by some numerical simulation examples. However, experimental validation of the proposed extended Kalman filter with unknown inputs has not been conducted. In this paper, an experiment is conducted to validate the effectiveness of the proposed approach. A five-story shear building model subjected to an unknown external excitation of wide-band white noise is conducted. Moreover, the data fusion of partially measured strain and acceleration responses from the building is adopted as it is difficult to accurately measure structural displacement in practice. Identified results show that the recently proposed extended Kalman filter with unknown inputs can be applied to identify structural parameters, structural states, and the unknown inputs in real time.

STATISTICAL LEARNING WITH TIME-VARYING PARAMETERS

2003 ◽  
Vol 7 (1) ◽  
pp. 119-139 ◽  
Author(s):  
Bruce McGough
Keyword(s):  
Stochastic Process ◽  
Kalman Filter ◽  
Statistical Learning ◽  
Rational Expectations ◽  
Stability Parameter ◽  
Time Varying ◽  
Rational Expectations Equilibrium ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
The Stability

In their landmark paper, Bray and Savin note that the constant-parameters model used by their agents to form expectations is misspecified and that, using standard econometric techniques, agents may be able to determine the time-varying nature of the model's parameters. Here, we consider the same type of model as employed by Bray and Savin except that our agents form expectations using a perceived model with parameters that vary with time. We assume agents use the Kalman filter to form estimates of these time-varying parameters. We find that, under certain restrictions on the structure of the stochastic process and on the value of the stability parameter, the model will converge to its rational expectations equilibrium. Further, the restrictions on the stability parameter required for convergence are identical to those found by Bray and Savin.

scholarly journals A time-varying parameter estimation approach using split-sample calibration based on dynamic programming

2021 ◽  
Vol 25 (2) ◽  
pp. 711-733
Author(s):  
Xiaojing Zhang ◽  
Pan Liu
Keyword(s):  
Dynamic Programming ◽  
Data Assimilation ◽  
River Basin ◽  
Optimal Parameter ◽  
Time Varying ◽  
Time Step ◽  
Changing Environment ◽  
Varying Parameters ◽  
Split Sample ◽  
Time Varying Parameters

Abstract. Although the parameters of hydrological models are usually regarded as constant, temporal variations can occur in a changing environment. Thus, effectively estimating time-varying parameters becomes a significant challenge. Two methods, including split-sample calibration (SSC) and data assimilation, have been used to estimate time-varying parameters. However, SSC is unable to consider the parameter temporal continuity, while data assimilation assumes parameters vary at every time step. This study proposed a new method that combines (1) the basic concept of split-sample calibration, whereby parameters are assumed to be stable for one sub-period, and (2) the parameter continuity assumption; i.e. the differences between parameters in consecutive time steps are small. Dynamic programming is then used to determine the optimal parameter trajectory by considering two objective functions: maximization of simulation accuracy and maximization of parameter continuity. The efficiency of the proposed method is evaluated by two synthetic experiments, one with a simple 2-parameter monthly model and the second using a more complex 15-parameter daily model. The results show that the proposed method is superior to SSC alone and outperforms the ensemble Kalman filter if the proper sub-period length is used. An application to the Wuding River basin indicates that the soil water capacity parameter varies before and after 1972, which can be interpreted according to land use and land cover changes. A further application to the Xun River basin shows that parameters are generally stationary on an annual scale but exhibit significant changes over seasonal scales. These results demonstrate that the proposed method is an effective tool for identifying time-varying parameters in a changing environment.

Identification of Linear Time-Varying Systems

2010 ◽  
pp. 221-237
Author(s):  
Vinayak G. Asutkar ◽  
Balasaheb M. Patre
Keyword(s):  
Kalman Filter ◽  
Physical Situation ◽  
Time Varying ◽  
Varying Parameters ◽  
System Parameters ◽  
Optimal Estimator ◽  
Time Varying Parameters ◽  
Time Varying Systems ◽  
Filter Approach ◽  
Kalman Filter Method

This chapter deals with identification of time-varying systems using Kalman filter approach. Most physical systems exhibit some degree of time-varying behaviour for many reasons. These systems cannot effectively be modelled using time invariant models. A time-varying autoregressive with exogenous input (TVARX) model is good to model these time-varying systems. The Kalman filter approach is a superior way to estimate the system parameters. This approach can track the time-varying parameters and is suitable for recursive estimation. It works well even when there are abrupt changes in the system parameters. Kalman filter is known to be an optimal estimator even when there is significant noise. In the proposed approach, for the purpose of simulation, we employ first order TVARX model and its parameters are estimated using recursive Kalman filter method. The system parameters are varied in continuous and abruptly changing manner to reveal the physical situation. To show the efficacy of the proposed approach, the time-varying parameters are estimated for different noise conditions. The performance is evaluated by calculating error performance measures. The results are found to be satisfactory with reasonable accuracy for noisy conditions even for fast changing parameters. The numerical examples illustrate efficacy of the proposed Kalman filter based approach for identification of time-varying systems.

Experimental Study on Impact-Induced Damage Detection Using an Improved Extended Kalman Filter

2014 ◽  
Vol 14 (05) ◽  
pp. 1440007 ◽  
Author(s):  
Ying Lei ◽  
Zhilu Lai ◽  
Songye Zhu ◽  
Xiao-Hua Zhang
Keyword(s):  
Experimental Study ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Structural Damage ◽  
Shaking Table Test ◽  
Impact Load ◽  
Structural Parameters ◽  
Optimization Procedure ◽  
Shaking Table ◽  
Improved Performance

This paper presents an experimental study on using an improved extended Kalman filter (EKF) to identify impact-induced structural damage. By introducing the optimization of estimated residual error into the classical EKF, this real-time approach demonstrates an excellent capability to identify the abrupt changes of structural parameters instantly and accurately. The optimization procedure is activated when a prescribed threshold is exceeded. A shaking table test of a three-story steel frame subjected to abrupt damage induced by impact load was conducted to validate the improved EKF approach. The results clearly reveal its improved performance and good anti-noise ability in identifying time-variant structural parameters.

Synchronization of Chaotic Systems with Uncertain Time-Varying Parameters

2015 ◽  
Vol 9 (6) ◽  
pp. 568
Author(s):  
Ahmad Al-Jarrah ◽  
Mohammad Ababneh ◽  
Suleiman Bani Hani ◽  
Khalid Al-Widyan
Keyword(s):  
Chaotic Systems ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Uncertain Time
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