Identification Of Time-varying Systems Research Articles

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

Iterative Learning Identification and Control for Discrete-time Linear Time-varying Systems with Iteration Varying Lengths

Iterative Learning Identification and Control for Discrete-time Linear Time-varying Systems with Iteration Varying Lengths

Identification of linear time-varying dynamic systems based on the WKB method

This work proposes a new parameter identification method based on the Wentzel-Kramers-Brillouin (WKB) approximation for slow linear time-varying (LTV) dynamic systems. The considered time period is divided into a series of short time windows. In each time window, the assumption of “short time linearly varying” parameters is employed, and a nonlinear optimization problem is solved using the WKB results for the slow LTV dynamic system. A search algorithm is developed to find the optimal solution. In the identification process, only one type of response signal (displacement, velocity or acceleration) is required. Thus, numerical differentiation or integration of the measured signal, which leads to truncation or cumulative errors in noise environment, is avoided. The accuracy and robustness of the new identification method are validated by applying it to a particular LTV system with time-varying stiffness.

Research and Application of Data-Driven Modeling Method for Gear System Based on Time-Varying Characteristics

The time-varying characteristics of the gear system have an essential influence on its vibration and stability characteristics. Aiming at this characteristic and taking the generalized force caused by load torque as input and dynamic transmission error as output, a data-driven modeling method for gear time-varying system is studied using the periodic time-varying system identification theory. The effectiveness of the proposed method is verified by the lumped mass model of the gear system. This method has high modeling accuracy and can accurately characterize the time-varying characteristics of the gear system. Then, the virtual experimental platform of gear system dynamics is established based on the finite element theory. The method successfully extends to the virtual experimental platform, laying a foundation for analyzing the gear system’s dynamic characteristics.

A novel instantaneous frequency estimation method for operational time-varying systems using short-time multivariate variational mode decomposition

Operational modal identification of time-varying systems plays a crucial role in assessing the health condition and controlling the dynamic properties of engineering structures. However, only the response is measurable, making it challenging. Based on the variational mode decomposition (VMD) theory, this paper presents a short-time multivariate or multi-channel VMD (STMVMD) method for instantaneous frequency (IF) identification of time-varying structures in the case of output-only measurements. The idea of short-time windows overcomes the shortcoming of many VMD-based methods that employ the narrowband assumption of intrinsic mode functions (IMFs) and cannot decompose non-stationary signals involving closely-spaced wideband IMFs. After obtaining the multivariate IMFs by STMVMD, an average scheme is employed to estimate IFs, reducing the noise sensitivity of Hilbert Transform. Moreover, by tracking the center frequencies of STMVMD at different moments, another more noise-robust IF estimation method is also presented. A series of numerical and experimental examples illustrate the advantages of the proposal.

Identification of forced time-varying systems via intrinsic chirp component decomposition

Modal parameter identification is significant in the field of vibration and control for tracking structural vibrations and evaluating structural performances. A novel parameter identification method based on the intrinsic chirp component decomposition (ICCD) and the Hilbert transform is proposed for forced time-varying systems. The developed ICCD decomposes the measured response signal into a limited number of intrinsic chirp components, and instantaneous modal parameters of the system are identified by the Hilbert transform of each intrinsic chirp component. The effectiveness and the accuracy of the proposed approach are investigated in two case studies, that is, a discrete mass-spring-damper oscillator and a cantilever beam. Smooth and periodical parameter variations are discussed in each case. Comparison with the empirical mode decomposition based method validates that the proposed method has better identification ability on estimating the instantaneous natural frequency of the system with the presence of noise. Results demonstrate that the ICCD-based approach could be a reasonable alternative for identification of forced time-varying systems in a noise environment.

Finite-window RLS algorithms

Two recursive least-squares (RLS) adaptive filtering algorithms are most often used in practice, the exponential and sliding (rectangular) window RLS algorithms. This popularity is mainly due to existence of low-complexity versions of these algorithms. However, these two windows are not always the best choice for identification of fast time-varying systems, when the identification performance is most important. In this paper, we show how RLS algorithms with arbitrary finite-length windows can be implemented at a complexity comparable to that of exponential and sliding window RLS algorithms. Then, as an example, we show an improvement in the performance when using the proposed finite-window RLS algorithm with the Hanning window for identification of fast time-varying systems.

Time-Varying System Identification of Precast Segmental Columns Subjected to Seismic Excitations

Precast segmental columns, as one structures, have attracted increasing attention in bridge and building construction. To understand the performance and dynamic characteristics of precast segmental columns subjected to earthquake excitations, this paper develops a novel approach for time-varying system stiffness identification of precast segmental columns under seismic excitations, based on the adaptive unscented Kalman filtering (AUKF) method. In the proposed approach, a precast segmental column model is considered as an equivalent single-degree-of-freedom (SDOF) system with time-varying system parameters. The AUKF method is employed to identify the time-varying stiffness parameters by using measured acceleration responses and then calculate dynamic displacement responses of the SDOF system to verify the accuracy of the identified stiffness parameters. Since the system parameter identification process and measurement noise covariance matrices are updated at each time step, the estimated results can be reliably obtained to evaluate the conditions of segmental columns subjected to seismic excitations. To verify the feasibility and effectiveness of using the proposed approach for time-varying system stiffness identification of segmental columns, numerical studies on a planar precast segmental column subjected to different intensities of ground motion excitations are conducted. Shake table tests on a scaled precast segmental column and a scaled monolithic column subjected to earthquake excitations are conducted in the laboratory to further verify the performance of the proposed approach. Measured acceleration responses are used for time-varying system identification. Both numerical and experimental results demonstrate that the proposed approach can successfully identify the time-varying stiffness values of precast segmental columns subjected to earthquake excitations, and the displacement responses of these columns are predicted accurately as compared with the measured ones.

A experimental study of a cable-pulleys spring-damper energy dissipation system for buildings

An energy dissipation mechanism made of a cable-pulleys system placed in series with a spring-damper device (fluid viscous) is experimentally studied. The system aims to provide high damping ratios for all the structural modes by using a unique spring-damper device to dissipate the seismic energy of the entire structure (and all its structural modes). Shake table tests and pull-back tests are carried out on a scaled five-story structure to compare the dissipation capabilities provided by the proposed system. Therefore, the same structure is tested under different configurations that included: i) the structure itself without any energy mitigation device, ii) the structure with viscous dampers installed on each story, iii) the structure with the proposed cable-pulleys and the spring-damper system, and iv) the structure with the cable-pulleys system but without any dissipation device. The experimental results showed that the structure with the proposed system exhibits a highly nonlinear response (mainly explained by the cable-pulleys interaction) evidenced by the significant change of the structure's dynamic properties during the time. The Short-Time Transfer Function plots show that the structure's natural frequencies change significantly when the cable-pulleys system is included. Complementarily, a novel time-variant system identification approach, termed Mod-ζ(var), is proposed, which allows estimating the time-variant evolution of the structure's dynamic properties during seismic tests (natural frequencies, damping ratios, and mode shapes). Moreover, the Mod-ζ(var) approach also enables computing relevant engineering quantities such as the empirical response spectrum from experimental data. It is found that the analyzed energy dissipation system provides high damping ratios (>10%) for all the structural modes, allowing reducing the seismic demands in terms of the empirical response spectrum, inter-story drifts, inter-story shear forces, peak accelerations, and Housner Intensities at each floor.

Multi-Layered Recursive Least Squares for Time-Varying System Identification

Traditional recursive least squares (RLS) adaptive filtering is widely used to estimate the impulse responses (IR) of an unknown system. Nevertheless, the RLS estimator shows poor performance when tracking rapidly time-varying systems. In this paper, we propose a multi-layered RLS (m-RLS) estimator to address this concern. The m-RLS estimator is composed of multiple RLS estimators, each of which is employed to estimate and eliminate the misadjustment of the previous layer. It is shown that the mean squared error (MSE) of the m-RLS estimate can be minimized by selecting the optimum number of layers. We provide a method to determine the optimum number of layers. A low-complexity implementation of m-RLS is discussed and it is indicated that the complexity order of the proposed estimator can be reduced to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(M)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> is the IR length. Through simulations, we show that m-RLS outperforms the classic RLS and the RLS methods with a variable forgetting factor.

Online identification of time-varying dynamical systems for industrial robots based on sparse Bayesian learning

Online identification of time-varying dynamical systems for industrial robots based on sparse Bayesian learning

Autoregressive spectrum-guided variational mode decomposition for time-varying modal identification under nonstationary conditions

Modal identification is an important research subject in structural health monitoring. It is a mature subject for modal identification of time-invariant and stationary conditions. Because time-varying properties are valuable for damage detection and time-varying system identification, and because the environmental loads do not always satisfy the assumption of stationarity, it is necessary to develop accurate identification methods for time-varying structures, structures under nonstationary excitations, or the coupling of the two conditions. The variational mode decomposition (VMD) method, which adaptively decomposes the signal into narrow-band intrinsic modes, shows the potential for time-varying and nonstationary conditions. However, parameter selection greatly affects the accuracy of mode decomposition. In this study, a new modal identification method based on an autoregressive spectrum-guided variational mode decomposition method is proposed for the application of time-varying and nonstationary conditions. First, the determination of the initial center frequencies for VMD is proposed using an autoregressive spectrum-guided method to greatly improve the accuracy. Second, a method to select the optimal balancing factor is developed to improve the decomposition accuracy by controlling the proper bandwidth. Subsequently, an instantaneous frequency identification method is presented by detecting the ridge of the time–frequency distribution. Finally, studies of numerical and actual structures demonstrate the capacity of the proposed method for practical applications of time-varying cases and nonstationary conditions.

Identification of Linear Time-Variant Systems Based on Ensemble Empirical Mode Decomposition and Hilbert Transform

This paper proposes an identification method based on ensemble empirical mode decomposition (EEMD) and Hilbert transform. The main procedures are: First, the system responses of an n degrees of freedom (DOFs) system are decomposed into intrinsic mode functions (IMFs) and residues by EEMD. The obtained ensemble mean IMFs and residues are then analysed by the Hilbert Transform to form the corresponding analytical signals. Second, the analytical signals of the n IMFs and the residue of each system response of each DOF are added to form a new analytical response. Third, the system equation of motion is rewritten into complex matrix equations for parameter identification. Numerical simulations are carried out on multi-DOFs systems with varying system parameters to demonstrate good robustness, effectiveness and accuracy of the proposed method, which attempts to offer a new means to study identification for linear time variant systems.

Iterative reference-driven S-transform time-varying parameter identification for bridges under moving vehicle

Traditional bridge health monitoring is both expensive and time-consuming because of the need for installing a large quantity of sensors on the bridge. The indirect monitoring method as a feasible alternative has become popular over the last decade, as useful information can be gathered from moving vehicles installed with sensors by considering vehicle-bridge interaction. This paper describes an indirect time-varying modal parameter identification method for bridges under a moving test vehicle. A novel reference-driven S-transform is proposed for the parametric modal identification of time-varying structural systems with non-stationary characteristics based on a multisensory arrangement, comprising a fixed reference sensor installed on the bridge and another movable sensor installed on a moving test vehicle. By the phase-preservation property of S-transform and the multisensory time-frequency analysis, the proposed iterative reference-driven S-transform can be used to extract the time-varying modal parameters of the vehicle-bridge system when the vehicle moves on the bridge. Based on the coherence between measurements from the sensors mounted on the bridge and vehicle, one can track the time-varying characteristics by combining the spatial and time-frequency information obtained by the multisensory array. The efficiency of the proposed reference-driven S-transform method is validated by numerical simulations and laboratory experiments using a simply supported beam with a moving vehicle. The effects of the vehicle property, driving speed, road roughness and measurement noise are discussed. The numerical and experimental results have demonstrated that the proposed method is useful for time-varying parameter extraction with a multisensory system. This will be useful to structural condition monitoring of bridges.

Application of regularized Savitzky–Golay filters to identification of time-varying systems

Savitzky–Golay (SG) filtering is a classical signal smoothing technique based on the local least squares approximation of the analyzed signal by a linear combination of known functions of time (originally — powers of time, which corresponds to polynomial approximation). It is shown that the regularized version of the SG algorithm can be successfully applied to identification of time-varying finite impulse response (FIR) systems. Such a solution is possible owing to the recently proposed preestimation technique, which converts the problem of identification of a time-varying FIR system into the problem of smoothing of the appropriately generated preestimates of system parameters. The resulting fast regularized local basis function estimators, optimized using the empirical Bayes approach, have very good parameter tracking capabilities, favorably comparing with the state-of-the-art in terms of accuracy, computational complexity and numerical robustness.

Novel tensor subspace system identification algorithm to identify time-varying modal parameters of bridge structures

Subspace-based system identification algorithms have been developed as an advanced technique for performing modal analysis. We introduce a novel tensor subspace-based algorithm to identify the time-varying modal parameters of bridge structures. A new time dimension is introduced in the traditional Hankel matrix, and a mathematical model of tensor subspace decomposition is established. Combined with the stabilization diagram, tensor parallel factor decomposition is used to estimate the frequencies, mode shapes, and modal damping ratios. The effectiveness of the proposed algorithm is validated by comparing it with the classical sliding-window–based stochastic subspace algorithm on a model cable-stayed bridge dynamic test. The proposed algorithm is further applied to process the dynamic responses of a real bridge health monitoring system to identify its time-varying modal frequencies. Our results demonstrated that the proposed algorithm significantly reduces computational efforts and extends the range of solution ideas for future out-only time-varying system identification problems.

Identification of linear time-varying fractional order systems using block pulse functions based on repetitive principle

A novel method for identifying linear time-varying fractional order systems based on a repetitive principle is proposed in this study. According to the repetitive principle, the system operates repetitively for several times, so the time-varying parameters are invariant on the fixed time for different operations. In the identification process, the time-varying parameters, independent from the input/output signals, are expanded onto some block pulse functions. The system is then converted to an algebraic system via the fractional differential operational matrix of the block pulse functions. Finally, recursive least square and instrumental variable recursive least square algorithms along the iteration axis are designed to identify the time-varying parameters without and with noise. Simulation results demonstrate that our proposed method is powerful in tracking time-varying parameters.

Study of modal parameter estimation of time-varying mechanical system in time-frequency domain based on output-only method

With increasing mobile instrument inspection systems like mobile inspection cameras applied in modern industrial automation lines, their time-varying modal parameters need to be thoroughly studied since they are operating under various random vibration excitations which are mostly unpredictable and unrepeatable. This paper investigates modal parameter identification of time-varying mobile mechanical systems through a poly-reference expansion based on output-only method in time-frequency domain. The poly-reference parametric model is presented through a time-frequency-domain right matrix fraction description. Based on the poly-reference parametric model, a poly-reference least square estimator and a poly-reference maximum likelihood estimator of modal parameters of time-varying systems are developed. For the case of only one batch of measurements, a novel approach to estimate the covariance matrix for the poly-reference maximum likelihood estimator by non-repeatable measurement is also proposed in this paper. A numerical example demonstrates the advantageous performance of the proposed estimators, such as the estimation of the close-coupled modes. Finally, a laboratory experiment validates these proposed estimators via a comparative way.

Application of decoupled ARMA model to modal identification of linear time-varying system based on the ICA and assumption of “short-time linearly varying”

A new approach for time-varying (TV) modal parameters identification is proposed in this research. In the identification process, the entire signal is divided into successive short time windows, where the structure response under white noise excitation is transformed into modal coordinates by the Independent Component Analysis (ICA) method. The decoupled time-varying Auto-Regressive Moving-Average (ARMA) model based on the new assumption of “short-time linearly varying” (STLV) is established with the extracted modal coordinates. The TV parameters can be obtained by solving a nonlinear least squares problem. The main motivation of the proposed approach is to simplify the model and reduce the computational difficulty. The effectiveness and accuracy are validated via both the numerical example and experiment.