scholarly journals Identification of time-varying systems with partial acceleration measurements by synthesis of wavelet decomposition and Kalman filter

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093046
Author(s):  
Siyi Chen ◽  
Jubin Lu ◽  
Ying Lei
Keyword(s):  
Kalman Filter ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Parametric Identification ◽  
Identification Problem ◽  
Structural Systems ◽  
Wavelet Expansion ◽  
Time Varying ◽  
Multiresolution Decomposition ◽  
Original Time

Structural systems often exhibit time-varying dynamic characteristics during their service life due to serve hazards and environmental erosion, so the identification of time-varying structural systems is an important research topic. Among the previous methodologies, wavelet multiresolution analysis for time-varying structural systems has gained increasing attention in the past decades. However, most of the existing wavelet-based identification approaches request the full measurements of structural responses including acceleration, velocity, and displacement responses at all dynamic degrees of freedom. In this article, an improved algorithm is proposed for the identification of time-varying structural parameters using only partial measurements of structural acceleration responses. The proposed algorithm is based on the synthesis of wavelet multiresolution decomposition and the Kalman filter approach. The time-varying structural stiffness and damping parameters are expanded at multi-scale profile by wavelet multiresolution decomposition, so the time-varying parametric identification problem is converted into a time-invariant one. Structural full responses are estimated by Kalman filter using partial observations of structural acceleration responses. The scale coefficients by the wavelet expansion are estimated via the solution of a nonlinear optimization problem of minimizing the errors between estimated and observed accelerations. Finally, the original time-varying parameters can be reconstructed. To demonstrate the efficiency of the proposed algorithm, the identification of several numerical examples with various time-varying scenarios is studied.

scholarly journals Wavelet multi-resolution approximation of time-varying frame structure

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879559 ◽  
Author(s):  
Min Xiang ◽  
Feng Xiong ◽  
Yuanfeng Shi ◽  
Kaoshan Dai ◽  
Zhibin Ding
Keyword(s):  
Parameter Estimation ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Identification Problem ◽  
Frame Structure ◽  
Structural Parameter ◽  
Time Varying ◽  
Engineering Structures ◽  
Time Frequency ◽  
Non Parametric

Engineering structures usually exhibit time-varying behavior when subjected to strong excitation or due to material deterioration. This behavior is one of the key properties affecting the structural performance. Hence, reasonable description and timely tracking of time-varying characteristics of engineering structures are necessary for their safety assessment and life-cycle management. Due to its powerful ability of approximating functions in the time–frequency domain, wavelet multi-resolution approximation has been widely applied in the field of parameter estimation. Considering that the damage levels of beams and columns are usually different, identification of time-varying structural parameters of frame structure under seismic excitation using wavelet multi-resolution approximation is studied in this article. A time-varying dynamical model including both the translational and rotational degrees of freedom is established so as to estimate the stiffness coefficients of beams and columns separately. By decomposing each time-varying structural parameter using one wavelet multi-resolution approximation, the time-varying parametric identification problem is transformed into a time-invariant non-parametric one. In solving the high number of regressors in the non-parametric regression program, the modified orthogonal forward regression algorithm is proposed for significant term selection and parameter estimation. This work is demonstrated through numerical examples which consider both gradual variation and abrupt changes in the structural parameters.

A Two-stage Parametric Identification of Strong Nonlinear Structural Systems with Incomplete Response Measurements

2016 ◽  
Vol 16 (04) ◽  
pp. 1640022 ◽  
Author(s):  
Lijun Liu ◽  
Ying Lei ◽  
Mingyu He
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Structural Parameters ◽  
Nonlinear Problems ◽  
Parametric Identification ◽  
Structural Systems ◽  
Two Stage ◽  
Incomplete Response ◽  
Nonlinear Structural ◽  
Structural Responses

Compared with the identification of linear structural parameters, it is more difficult to conduct parametric identification of strong nonlinear structural systems, especially when only incomplete structural responses are available. Although the extended Kalman filter (EKF) is useful for structural identification with partial measurements of structural responses and can be extended for the identification of nonlinear structures, EKF approximates nonlinear system through Taylor series expansion and is therefore not effective for the identification of strong nonlinear structural systems. Other approaches such as the unscented Kalman filter (UKF) have been proposed for the identification of strong nonlinear problems. Based on the fact that nonlinearities exist in local areas of structures, a straightforward two-stage identification approach is proposed in this paper for the identification of strong nonlinear structural parameters with incomplete response measurements. In the first stage, the locations of nonlinearities are identified based on the EKF for the identification of the equivalent linear structures. In the second stage, the UKF is utilized to identify the parameters of strong nonlinear structural systems. Therefore, the parametric identification of strong nonlinear structural parameters is simplified by the proposed approach. Several numerical examples with different nonlinear models and locations are used to validate the proposed approach.

Identification of Time-Varying Time Constants of Thermocouple Sensors and Its Application to Temperature Measurement

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Kenneth Kar ◽  
Akshya K. Swain ◽  
Robert Raine
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Time Constant ◽  
Identification Problem ◽  
Basis Functions ◽  
New Technique ◽  
Ratio Test ◽  
Time Varying ◽  
Time Constants ◽  
Orthogonal Least Squares

The present study addresses the problem of estimating time-varying time constants associated with thermocouple sensors by a set of basis functions. By expanding each time-varying time constant onto a finite set of basis sequences, the time-varying identification problem reduces to a parameter estimation problem of a time-invariant system. The proposed algorithm, to be called as orthogonal least-squares with basis function expansion algorithm, combines the orthogonal least-squares algorithm with an error reduction ratio test to include significant basis functions into the model, which results in a parsimonious model structure. The performance of the method was compared with a linear Kalman filter. Simulations on engine data have demonstrated that the proposed method performs satisfactorily and is better than the Kalman filter. The new technique has been applied in a Stirling cycle compressor. The sinusoidal variations in time constant are tracked properly using the new technique, but the linear Kalman filter fails to do so. Both model validation and thermodynamic laws confirm that the new technique gives unbiased estimates and that the assumed thermocouple model is adequate.

On the Uniqueness of Solutions for the Identification of Linear Structural Systems

2005 ◽  
Vol 73 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Guillermo Franco ◽  
Raimondo Betti ◽  
Richard W. Longman
Keyword(s):  
Prior Knowledge ◽  
Degrees Of Freedom ◽  
Identification Problem ◽  
Minimum Amount ◽  
Structural Systems ◽  
Structural System ◽  
Uniqueness Of Solutions ◽  
Stiffness Identification ◽  
Shear Type ◽  
Forced Excitation

This work tackles the problem of global identifiability of an undamped, shear-type, N degrees of freedom linear structural system under forced excitation without any prior knowledge of its mass or stiffness distributions. Three actuator/sensor schemes are presented, which guarantee the existence of only one solution for the mass and stiffness identification problem while requiring a minimum amount of instrumentation (only 1 actuator and 1 or 2 sensors). Through a counterexample for a 3DOF system it is also shown that fewer measurements than those suggested result invariably in non-unique solutions.

Identification of Two Degree of Freedom Robot Arm’s Joints’ Time-Varying Stiffness

2012 ◽  
Vol 241-244 ◽  
pp. 1880-1884
Author(s):  
Rui Xu ◽  
Qiang Chen ◽  
Guo Lai Yang
Keyword(s):  
Degrees Of Freedom ◽  
Least Square Method ◽  
Identification Problem ◽  
Degree Of Freedom ◽  
Least Square ◽  
Analytical Mechanics ◽  
Time Varying ◽  
Robot Arm ◽  
Whole Process ◽  
Two Degree Of Freedom

This paper is concerned with the identification problem of two degree of freedom robot arm’s joints’ time-varying stiffness. The dynamic equation of two degrees of freedom robot arm can be obtained by using analytical mechanics method. Then by choosing limited memory least square method, time-varying stiffness can be identified. Finally, the calculative stiffness is compared to the “real” stiffness which is simulated in ADAMS. The whole process shows that the robot arm’s dynamic model and the method of identification are both effective.

Uniqueness of Solutions for the Identification of Linear Reduced Order Structural Systems

2004 ◽  
Author(s):  
Guillermo Franco ◽  
Jun Yu ◽  
Raimondo Betti
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Identification Problem ◽  
Structural Systems ◽  
Uniqueness Of Solutions ◽  
Reduced Order ◽  
Theoretical Approaches ◽  
Uniqueness Of The Solution ◽  
Minimum Number ◽  
Output Information

The problem of identification of structural systems is an inverse problem that uses input (say force excitation) and output information (accelerations, for instance) to obtain an optimal model to describe the system’s behavior. Since a full instrumentation setup is expensive, situations usually arise where only partial measurements are available. Uniqueness of the solution in these circumstances might not be guaranteed. This paper analyzes the minimum number of measurements required to ensure that only one solution exists for the identification problem of mass, damping and stiffness distributions of shear-type N degrees of freedom linear structures. Three typical configurations of measurements are studied with two distinct theoretical approaches, one based on classical polynomial theory, the other based on reduced order model theory. Both these approaches lead to the conclusion that only one input and one or two output measurements are sufficient to guarantee uniqueness of identification, depending on the selected location of the input measurement. Additionally, the identification of a 3DOF system is carried out analytically with the usage of Sylvester’s Dyalitic Elimination to show that fewer measurements than the ones proposed lead to non-unique identification. This fact is also illustrated with the usage of a recently developed optimization technique, with which convergence to the different solutions is observed depending on the initial estimate used.

A gradient algorithm for the identification of interconnected discrete time varying systems

2019 ◽  
Vol 37 (3) ◽  
pp. 909-928
Author(s):  
Yamna Ghoul
Keyword(s):  
Discrete Time ◽  
Parametric Identification ◽  
Identification Problem ◽  
Gradient Algorithm ◽  
Interconnected Systems ◽  
Time Varying ◽  
Content Type ◽  
Time Varying Parameters ◽  
Time Varying Systems ◽  
Vector Observation

Purpose An identification scheme to identify interconnected discrete-time (DT) varying systems. Design/methodology/approach The purpose of this paper is the identification of interconnected discrete time varying systems. The proposed technique permits the division of global system to many subsystems by building a vector observation of each subsystem and then using the gradient method to identify the time-varying parameters of each subsystem. The convergence of the presented algorithm is proven under a given condition. Findings The effectiveness of the proposed technique is then shown with application to a simulation example. Originality/value In the past decade, there has been a renewed interest in interconnected systems that are multidimensional and composed of similar subsystems, which interact with their closest neighbors. In this context, the concept of parametric identification of interconnected systems becomes relevant, as it considers the estimation problem of such systems. Therefore, the identification of interconnected systems is a challenging problem in which it is crucial to exploit the available knowledge about the interconnection structure. For time-varying systems, the identification problem is much more difficult. To cope with this issue, this paper addresses the identification of DT dynamical models, composed by the interconnection of time-varying systems.

scholarly journals Sign Restrictions in Structural Vector Autoregressions: A Critical Review

2011 ◽  
Vol 49 (4) ◽  
pp. 938-960 ◽  
Author(s):  
Renée Fry ◽  
Adrian Pagan
Keyword(s):  
Model Identification ◽  
Parametric Identification ◽  
Identification Problem ◽  
Structural Systems ◽  
Impulse Responses ◽  
Vector Autoregressions ◽  
Sign Restrictions ◽  
Unique Model ◽  
Jel C32 ◽  
Structural Vector

The paper provides a review of the estimation of structural vector autoregressions with sign restrictions. It is shown how sign restrictions solve the parametric identification problem present in structural systems but leaves the model identification problem unresolved. A market and a macro model are used to illustrate these points. Suggestions have been made on how to find a unique model. These are reviewed. An analysis is provided of whether one can recover the true impulse responses and what difficulties might arise when one wishes to use the impulse responses found with sign restrictions. (JEL C32, C51, E12)

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.

Sign in / Sign up

Export Citation Format

Share Document