Identification Of Time-varying Parameters Research Articles

Improvement of and Parameter Identification for the Bimodal Time-Varying Modified Kanai-Tajimi Power Spectral Model

Based on the Kanai-Tajimi power spectrum filtering method proposed by Du Xiuli et al., a genetic algorithm and a quadratic optimization identification technique are employed to improve the bimodal time-varying modified Kanai-Tajimi power spectral model and the parameter identification method proposed by Vlachos et al. Additionally, a method for modeling time-varying power spectrum parameters for ground motion is proposed. The 8244 Orion and Chi-Chi earthquake accelerograms are selected as examples for time-varying power spectral model parameter identification and ground motion simulations to verify the feasibility and effectiveness of the improved bimodal time-varying modified Kanai-Tajimi power spectral model. The results of this study provide important references for designing ground motion inputs for seismic analyses of major engineering structures.

Identification of Time-Varying Parameters of Hybrid Dynamical System Models and Its Application to Driving Behavior

This paper presents a novel identification method for hybrid dynamical system models, where parameters have stochastic and time-varying characteristics. The proposed parameter identification scheme is based on a modified implementation of particle filtering, together with a time-smoothing technique. Parameters of the identified model are considered as time-varying random variables. Parameters are identified independently at each time step, using the Bayesian inference implemented as an iterative particle filtering method. Parameters time dynamics are smoothed using a distribution based moving average technique. Modes of the hybrid system model are handled independently, allowing any type of nonlinear piecewise model to be identified. The proposed identification scheme has low computation burden, and it can be implemented for online use. Effectiveness of the scheme is verified by numerical experiments, and an application of the method is proposed: analysis of driving behavior through identified time-varying parameters.

Recursive identification of discrete-time nonlinear cascade systems with time-varying output hysteresis

A recursive identification method for discrete-time nonlinear cascade systems with a linear dynamic system followed by a time-varying output hysteresis is presented. The mathematical model is based on the application of a special form of Coleman–Hodgdon hysteresis model and a compound operator decomposition technique and is linear-in-parameters. The recursive least-squares algorithm with internal variable estimation is used for the time-varying parameter identification. Simulation studies show the feasibility of proposed approach to estimate the model parameters and track their changes.

A compact self-adaptive recursive least square approach for real-time structural identification with unknown inputs

A new online tracking technique, based on recursive least square with adaptive multiple forgetting factors, is presented in this article which can estimate abrupt changes in structural parameters during excitation and also identify the unknown inputs to the structure, for example, earthquake signal. The method considers an adaptive rule for each of the forgetting factors assigned to each of the unknown parameters and thus enables simultaneous identification of different time-varying parameters of the system. The method is validated through both linear and nonlinear case studies, with different excitations and damage scenarios. The results show that the proposed algorithm can effectively identify the time-varying parameters such as damping, stiffness as well as unknown excitations with high computational efficiency, even when the measured data are contaminated with different levels of noise. However, when damage occurs while the excitation is small, the identification error remains at a small range, and therefore, covariance cannot be amplified to effectively track the changes in unknown parameters.

Smooth Adaptive Internal Model Control Based on U Model for Nonlinear Systems with Dynamic Uncertainties

An improved smooth adaptive internal model control based on U model control method is presented to simplify modeling structure and parameter identification for a class of uncertain dynamic systems with unknown model parameters and bounded external disturbances. Differing from traditional adaptive methods, the proposed controller can simplify the identification of time-varying parameters in presence of bounded external disturbances. Combining the small gain theorem and the virtual equivalent system theory, learning rate of smooth adaptive internal model controller has been analyzed and the closed-loop virtual equivalent system based on discrete U model has been constructed as well. The convergence of this virtual equivalent system is proved, which further shows the convergence of the complex closed-loop discrete U model system. Finally, simulation and experimental results on a typical nonlinear dynamic system verified the feasibility of the proposed algorithm. The proposed method is shown to have lighter identification burden and higher control accuracy than the traditional adaptive controller.

Finite-Time Identification Algorithm based on Time-Varying Homogeneity and Lyapunov Approach

In this paper the problem of time-varying parameter identification is studied. To this aim, an identification algorithm is developed in order to identify time-varying parameters in a finite-time. The convergence proofs are based on a notion of finite-time stability over finite intervals of time, i.e. Short-finite-time stability; homogeneity for time-varying systems; and Lyapunov function approach. The algorithm asks for a condition over the regressor term which is related to the classic identifiability condition corresponding to the injectivity of such a term. Simulation results illustrate the feasibility of the proposed algorithm.

Time-varying modal parameters identification of a spacecraft with rotating flexible appendage by recursive algorithm

The rotation of spacecraft flexible appendage may cause changes in modal parameters. For this time-varying system, the computation cost of the frequently-used singular value decomposition (SVD) identification method is high. Some control problems, such as the self-adaptive control, need the latest modal parameters to update the controller parameters in time. In this paper, the projection approximation subspace tracking (PAST) recursive algorithm is applied as an alternative method to identify the time-varying modal parameters. This method avoids the SVD by signal subspace projection and improves the computational efficiency. To verify the ability of this recursive algorithm in spacecraft modal parameters identification, a spacecraft model with rapid rotational appendage, Soil Moisture Active/Passive (SMAP) satellite, is established, and the time-varying modal parameters of the satellite are identified recursively by designing the input and output signals. The results illustrate that this recursive algorithm can obtain the modal parameters in the high signal noise ratio (SNR) and it has better computational efficiency than the SVD method. Moreover, to improve the identification precision of this recursive algorithm in the low SNR, the wavelet de-noising technology is used to decrease the effect of noises.

An efficient algorithm for simultaneous identification of time-varying structural parameters and unknown excitations of a building structure

When a structure is being damaged under unknown excitations, structural parameters of the damaged elements are actually varying with time. Hence, the simultaneous identification of time-varying structural parameters and unknown excitations is an important task in structural health monitoring. Although some analytical methods for such identifications are available in the literature, they are complicated, time-consuming, or restrained by special requirements. This paper presents an efficient algorithm for identifying time-varying structural parameters of a building structure under unknown excitations. By projecting on to the column space of influence matrix of unknown excitations, the observation equation of the structural system with unknown excitations is transformed from a multiple linear regression equation to a simple linear regression equation. By further introducing a time-varying correction factor matrix, an analytical recursive least-squares estimation algorithm is developed for identifying unknown excitations and time-varying structural parameters such as stiffness and damping. The feasibility and accuracy of the proposed algorithm are finally demonstrated through numerical examples and comparison with the existing methods. The results clearly exhibit that the proposed algorithm can simultaneously identify unknown excitations and time-varying structural parameters efficiently and accurately.

Integration of health monitoring and vibration control for smart building structures with time-varying structural parameters and unknown excitations

When a building structure requires both health monitoring system and vibration control system, integrating the two systems together will be cost-effective and beneficial for creating a smart building structure with its own sensors (nervous system), processors (brain system), and actuators (muscular system). This paper presents a real-time integrated procedure to demonstrate how health monitoring and vibration control can be integrated in real time to accurately identify time-varying structural parameters and unknown excitations on one hand, and to optimally mitigate excessive vibration of the building structure on the other hand. The basic equations for the identification of time-varying structural parameters and unknown excitations of a semi-active damper-controlled building structure are first presented. The basic equations for semi-active vibration control of the building structure with time-varying structural parameters and unknown excitations are then put forward. The numerical algorithm is finally followed to show how the identification and the control can be performed simultaneously. The results from the numerical investigation of an example building demonstrate that the proposed method is feasible and accurate.

Experimental Studies on Finite Element Model Updating for a Heated Beam-Like Structure

An experimental study was made for the identification procedure of time-varying modal parameters and the finite element model updating technique of a beam-like thermal structure in both steady and unsteady high temperature environments. An improved time-varying autoregressive method was proposed first to extract the instantaneous natural frequencies of the structure in the unsteady high temperature environment. Based on the identified modal parameters, then, a finite element model for the structure was updated by using Kriging meta-model and optimization-based finite-element model updating method. The temperature-dependent parameters to be updated were expressed as low-order polynomials of temperature increase, and the finite element model updating problem was solved by updating several coefficients of the polynomials. The experimental results demonstrated the effectiveness of the time-varying modal parameter identification method and showed that the instantaneous natural frequencies of the updated model well tracked the trends of the measured values with high accuracy.

Time-varying physical parameter identification of shear type structures based on discrete wavelet transform

This paper proposed a discrete wavelet transform based method for time-varying physical parameter identification of shear type structures. The time-varying physical parameters are dispersed and expanded at multi-scale as profile and detail signal using discrete wavelet basis. To reduce the number of unknown quantity, the wavelet coefficients that reflect the detail signal are ignored by setting as zero value. Consequently, the time-varying parameter can be approximately estimated only using the scale coefficients that reflect the profile signal, and the identification task is transformed to an equivalent time-invariant scale coefficient estimation. The time-invariant scale coefficients can be simply estimated using regular least-squares methods, and then the original time-varying physical parameters can be reconstructed by using the identified time-invariant scale coefficients. To reduce the influence of the ill-posed problem of equation resolving caused by noise, the Tikhonov regularization method instead of regular least-squares method is used in the paper to estimate the scale coefficients. A two-story shear type frame structure with time-varying stiffness and damping are simulated to validate the effectiveness and accuracy of the proposed method. It is demonstrated that the identified time-varying stiffness is with a good accuracy, while the identified damping is sensitive to noise.

Experimental investigation on the time-varying modal parameters of a trapezoidal plate in temperature-varying environments by subspace tracking-based method

Subspace-based methods for estimation of modal parameters are briefly reviewed in this study and a time-varying modal parameter identification algorithm, based on finite-data-window Projection Approximation Subspace Tracking, is presented to investigate the time-varying modal parameters of a trapezoidal titanium-alloy plate in temperature-varying environments. An experiment conducted on a steel beam with a removable mass is used to confirm the proposed method with a brief discussion on the factors of this method. Two groups of experiments are conducted to reveal the effects of varying temperature and heating speed on the natural frequencies of the plate, and the identified natural frequencies evidently show the effect of thermal stresses caused by temperature gradients in experiment.

Research on Two Kinds of Parameter Identification Methods for Short-Term Time-Varying System

In this paper, two kinds of time varying parameter identification methods which are called identification method of using broken line to approximate time varying parameter and identification algorithm with auto-regulation forgetting factor are studied. The two methods are used for short-term time-varying system parameter identification in simulations. According to the results of the simulations, the applicable conditions of the two kinds of identification methods are analyzed. The results of the simulations indicate the effectiveness of the two methods. Furthermore whether the two kinds of identification methods are sensitive to noise or not is studied by setting different noise levels in the simulations. Finally, experiments of a variable mass cylindrical shell are adopted to demonstrate the efficiency of the two kinds of time varying parameter identification methods.

Identification of Time-Varying Parameters Using the Derivative Formulation of Chebyshev Polynomials

This paper introduces a parameter identification method for linear time-varying systems that is based on the derivative formulation of the Chebyshev polynomial basis. A dynamic system matrix representation is first developed for N-DOF mechanical systems having multiple time-varying parameters. The method is then applied to a numerical simulation of a rotational 1-DOF mechanical system having time-varying stiffness, constant damping, and constant inertia. Results show that the identification quality is significantly increased when the least-square identification is performed only with the center portion of the time basis of the Chebyshev basis used.

Time-varying linear and nonlinear parametric model for Granger causality analysis

Statistical measures such as coherence, mutual information, or correlation are usually applied to evaluate the interactions between two or more signals. However, these methods cannot distinguish directions of flow between two signals. The capability to detect causalities is highly desirable for understanding the cooperative nature of complex systems. The main objective of this work is to present a linear and nonlinear time-varying parametric modeling and identification approach that can be used to detect Granger causality, which may change with time and may not be detected by traditional methods. A numerical example, in which the exact causal influences relationships, is presented to illustrate the performance of the method for time-varying Granger causality detection. The approach is applied to EEG signals to track and detect hidden potential causalities. One advantage of the proposed model, compared with traditional Granger causality, is that the results are easier to interpret and yield additional insights into the transient directed dynamical Granger causality interactions.

Two new fast identification algorithms of time-varying modal parameters based on subspace tracking

The procedure of fast identification algorithms of the time-varying modal parameter based subspace tracking is investigated in this paper.After the pretreatment to the updating input/output data,the problem of fast time-varying modal parameter identification changes to be a subspace tracking problem principally.Adopting the principal subspace tracking algorithms,the fast time-varying modal parameter identification algorithms can be deduced.Replacing PAST by NPI and API,two new versions of time-varying modal parameter identification algorithms are proposed.The performance of the fast modal parameter identification algorithms based on different principal subspace tracking algorithms are compared by applying them on a classical time-varying mechanical system of a moving distributed mass-cantilever beam and a 2-DOF spring-mass model.

Parameter Identification of Time Varying System Using Basic Function Expansion

Time-varying parameters identification in linear system is considered, which can be changed into time-invariant coefficient polynomials after Taylor expansion. Using response data to establish the time-varying autoregressive moving average (TV-ARMA) model, then utilizing least-square algorithm to obtain time-invariant coefficients of time-varying parameters. According to error analysis, to reduce errors and improve accuracy, the estimation time is divided into small internals and the above method is used in each interval. Simulation shows that, under certain error condition, the time-varying parameters obtained by the method have good agreement with the theoretical values; the measures taken have strong anti-interference and high efficiency.

Substructural Time-Varying Parameter Identification Using Wavelet Multiresolution Approximation

Identifying properties of civil engineering structures is an important task for their condition assessment, damage diagnosis, maintenance and repair, and life-cycle management. These structures usually contain a large number of degrees of freedom and exhibit some time-varying or nonlinear behavior, especially under extreme excitation or when damaged. In this study, an offline substructure method based on wavelet multiresolution approximation (WMRA) is proposed for the identification of arbitrary time-varying parameters in a shear-beam building. Assuming that the possible damage location of the building can be identified a priori, a substructural model containing both interface and internal restoring forces can be formulated. The WMRA can then be used to approximate the time-varying damping and stiffness parameters and convert a time-varying parametric identification problem into a time-invariant coefficient estimation problem. To obtain accurate estimation and minimize the computational effort, Akaike’s information criterion is used for the selection of a resolution level and the pruning of insignificant terms. Numerical and experimental results show that the proposed technique can locate and quantify the time-varying parameters in the substructure. The method inherits the wavelet’s excellent capability in the approximation of arbitrary functions and provides a flexible approach for identifying various types of time-varying parameters in shear-beam buildings.

Fast Time-varying modal parameter identification algorithm based on two-layer linear neural network learning for subspace tracking

The key of fast identification algorithm of time-varying modal parameter based on subspace tracking is to find efficient and fast subspace-tracking algorithm. This paper presents a modified version of NIC(Novel Information Criterion) adopted in two-layer linear neural network learning for subspace tracking, which is applied in time-varying modal parameter identification algorithm based on subspace tracking and get a new time-varying modal parameter identification algorithm. Comparing with the original subspace-tracking algorithm, there is no need to set a key control parameter in advance. Simulation experiments show that new time-varying modal parameter identification algorithm has a faster convergence in the initial period and a real experiment under laboratory conditions confirms further its validity of the time-varying modal identification algorithm presented in this paper.

Identification of time-varying hysteretic structures using wavelet multiresolution analysis

In this paper, a wavelet multiresolution technique is proposed to identify time-varying properties of hysteretic structures. It is well known that arbitrary transient functions can be effectively and accurately approximated using wavelet multiresolution expansions due to wavelet's good time–frequency localization property. By decomposing the time-varying parameters with wavelet multiresolution expansion, a time-varying parametric identification problem can be transformed into a time-invariant non-parametric one. The identification in the time-invariant wavelet multiresolution domain can be achieved by choosing a wavelet basis function and performing a suitable parameter estimation technique. Since wavelet representation of arbitrary signal uses only a small number of terms, the orthogonal forward regression algorithm can be adopted for significant term selection and parameter estimation. Single and multiple degrees of freedom Bouc–Wen hysteretic structures with gradual and abrupt varying properties are used to illustrate the proposed approach. Results show that the wavelet multiresolution technique can identify and track the time-varying hysteretic parameters quite accurately. The effect of measurement noise is also studied. It is found that the presence of noise would affect more on the damping ratios and the Bouc–Wen parameters but less on the equivalent stiffness coefficients.