Identification Of Time-varying Parameters Research Articles

A novel inertial parameter identification method for the ship-mounted Stewart platform based on a wave compensation platform

To meet the requirement of time-varying inertial parameter identification of control algorithms for shipborne Stewart wave compensation platforms, this study proposes an innovative inertial parameter identification method based on a non-inertial system. Unlike traditional Stewart identification methods with a fixed frame, the proposed method does not require designing excitation trajectories to consider the condition number of the observation matrix. Namely, the proposed method requires only performing two-dimensional dynamic parameter collection for parameter identification in a six-dimensional non-inertial motion. In addition, a coupling error dimension reduction method is developed to improve the identification accuracy under the condition of coupling motion. Finally, experiments are conducted to verify the effectiveness of the proposed identification method. The experimental results show that under the coupling motion conditions, the coupling errors of the corrected singularity points are reduced by 7.9–28.1% compared to before correction, and the axial force average error correction is below 5.32%.

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

Identification of Time-Varying Conceptual Hydrological Model Parameters with Differentiable Parameter Learning

The parameters of the GR4J-CemaNeige coupling model (GR4neige) are typically treated as constants. However, the maximum capacity of the production store (parX1) exhibits time-varying characteristics due to climate variability and vegetation coverage change. This study employed differentiable parameter learning (dPL) to identify the time-varying parX1 in the GR4neige across 671 catchments within the United States. We built two types of dPL, including static and dynamic parameter networks, to assess the advantages of the time-varying parameter. In the dynamic parameter network, we evaluated the impact of potential evapotranspiration (PET), precipitation (P), temperature (T), soil moisture (SM), and normalized difference vegetation index (NDVI) datasets on the performance of dPL. We then compared dPL with the empirical functional method (fm). The results demonstrated that the dynamic parameter network outperformed the static parameter network in streamflow estimation. There were differences in streamflow estimation among the dynamic parameter network driven by various input features. In humid catchments, simultaneously incorporating all five factors, including PET, P, T, SM, and the NDVI, achieved optimal streamflow simulation accuracy. In arid catchments, it was preferable to introduce PET, T, and the NDVI separately for improved performance. dPL significantly outperformed the empirical fm in estimating streamflow and uncalibrated intermediate variables, like evapotranspiration (ET). Both the derived parX1 from dPL and the empirical fm exhibited significant spatiotemporal variation across 671 catchments. Notably, compared to parX1 obtained through the empirical fm, parX1 derived from dPL exhibited a distinct spatial clustering pattern. This study highlights the potential of dPL in enhancing model accuracy and contributes to understanding the spatiotemporal variation characteristics of parX1 under the influence of climate factors, soil conditions, and vegetation change.

Time-varying parameters from the same period in previous years to improve runoff forecasting

The time-varying parameter functional (TVPF) method has shown promise in improving runoff forecasting under climate change and human activities. However, it has three notable limitations: data availability, increased model complexity, and the inability to update with newly measured data. To address these challenges, this study proposes an improved runoff forecasting method that relies solely on time-varying parameters from the same period in previous years. The proposed method comprises four steps: (1) identification of time-varying parameters from historical observations; (2) estimation of the current-year parameters by averaging the time-varying parameters from the same period in previous years; (3) runoff forecasts using the estimated current-year parameters; (4) continuous identification and estimation of parameters with newly measured data for each year, enabling a rolling forecast of runoff. The proposed method is compared with both the constant parameter method and TVPF method, using the Xun River and Zuo River basins as case studies. The results reveal that (1) parameters from the same period in the previous three years yield the best runoff forecasts in the Xun River basin, while parameters from the same period in the previous five years produce the best runoff forecasts in the Zuo River basin; (2) the proposed method significantly improves the water balance index (WBI) compared to the TVPF method, providing either superior or comparable performance in structural risk minimization (SRM) evaluation. Overall, this study provides an approach to forecast runoff in a changing environment that reduces data requirements, simplifies model complexity, and improves WBI performance.

Identification of time-varying inertia tensor parameters of a space solar power satellite based on a robust weighted recursive algorithm under impulsive disturbance

Considering changes in the structural size and mass caused by the on-orbit assembly process in a planar space solar power satellite, this study proposes an improved robust recursive algorithm to identify the time-varying inertia tensor parameters of the system. In this algorithm, to decrease the effect of impulsive disturbance on inertial parameter identification during the on-orbit assembly and improve computational accuracy, robust weighted factor and multi-innovation theory are involved. Then, the time-varying inertia tensor parameters of this large flexible structure are identified based on the distributed measurement results of multiple attitude sensors. The simulation results indicate that the proposed algorithm improves the identification accuracy and has better robustness than the original method under the impulsive disturbance. The relative values of the average relative error caused by the impulsive disturbance under the proposed algorithm are approximately 27.8–73.0% less than those under the original method. Additionally, the results also demonstrate that the proposed algorithm has higher noise immunity than the classical recursive least-squares method in a time-varying system. When the impulsive disturbance and zero-mean Gaussian white noise are applied to the system, compared with the conventional recursive least-squares method, the proposed algorithm yields lower absolute and relative values of the average relative error by approximately 4.2% and 44.9%, respectively.

Time-varying nonlinear parameters identification of high-speed train suspension system based on WMA

The parameters identification of suspension components provides a foundation for health assessment of the high-speed train. Considering the time-varying nonlinearity of suspension parameters caused by changing temperature, this work identifies the time-varying nonlinear parameters based on the wavelet multiresolution analysis (WMA) combined with the proposed improved Akaike information criterion (AIC). Firstly, the parameters variation law against time-temperature are fitted based on test data and the vibration responses of a two-degree-of-freedom suspension model are obtained. Secondly, the time-varying nonlinear parameters are expanded into scale coefficients using WMA. Thus, the identification of time-varying nonlinear parameters is transformed into the identification of time-invariant wavelet scale coefficients. Then the improved AIC is utilized to select the optimal basis functions and decomposition scales in noisy environments. The identified parameters vectors are used by the improved AIC as evaluation index of identification model to reduce the effect of noise. Finally, the time-varying nonlinear parameters are reconstructed based on the optimal wavelet scale coefficients. The results show that the time-varying nonlinear stiffness and damping coefficients can be accurately identified based on the WMA combined with the proposed improved AIC.

Time-varying modal identification using multi-channel measurements based on multivariate variational mode decomposition

Structural modal parameters are essential to provide dynamic information for data analysis of structural health monitoring (SHM) system. Because of the variation of the physical properties or the influence of the environment, the structural modal parameters may change with time during the operation, showing time-varying characteristics. Therefore, accurate identification of time-varying modal parameters shows to be an important issue for SHM. In this paper, a time-varying modal identification method is proposed by improving the multivariate variational mode decomposition (MVMD) method with autoregressive power spectrum and windowed principal component analysis (PCA). Firstly, the method for determination of initial center frequency is proposed by autoregressive power spectrum to improve the efficiency of MVMD. Secondly, intrinsic mode function for each mode is extracted using multi-channel responses by MVMD. Subsequently, instantaneous frequencies are identified through detecting the ridgeline of the synchro-squeezed short-time Fourier transform (SSTFT). Moreover, identification method for time-varying mode shapes is proposed by using the windowed PCA of the multi-channel intrinsic modes. Finally, the proposed method is verified by the numerical and practical studies. The results of the numerical study show that the method is effective for continuously varying modal parameters under impulse and random excitations. Through the data analysis of practical bridge, the capability for practical application is demonstrated.

Sequential Ensemble Monte Carlo Sampler for On-Line Bayesian Inference of Time-Varying Parameter in Engineering Applications

Abstract Several on-line identification approaches have been proposed to identify parameters and evolution models of engineering systems and structures when sequential datasets are available via Bayesian inference. In this work, a robust and “tune-free” sampler is proposed to extend one of the sequential Monte Carlo implementations for the identification of time-varying parameters which can be assumed constant within each set of data collected but might vary across different sequences of datasets. The proposed approach involves the implementation of the affine-invariant Ensemble sampler in place of the Metropolis–Hastings sampler to update the samples. An adaptive-tuning algorithm is also proposed to automatically tune the step-size of the affine-invariant ensemble sampler which, in turn, controls the acceptance rate of the samples across iterations. Furthermore, a numerical investigation behind the existence of inherent lower and upper bounds on the acceptance rate, making the algorithm robust by design, is also conducted. The proposed method allows for the off-line and on-line identification of the most probable models under uncertainty. The proposed sampling strategy is first verified against the existing sequential Monte Carlo sampler in a numerical example. Then, it is validated by identifying the time-varying parameters and the most probable model of a nonlinear dynamical system using experimental data.

Simultaneous Identification of Time-Varying Parameters and External Loads Based on Extended Kalman Filter: Approach and Validation

Online identification of time-variant parameters without knowledge of external loads is an important but challenging task for structural health monitoring and vibration control. In this study, a two-stage approach, named extended Kalman filter with forgetting factor matrix under unknown inputs (EKF-FFM-UI), is proposed for simultaneously identifying the time-variant parameters and external loads. In stage 1, an extended Kalman filter under unknown inputs (EKF-UI) approach previously proposed by the authors is employed for estimating the structural states and unknown loads. This EKF-UI approach is solely suitable for time-invariant system identification. Therefore, the aim of stage 2 is to improve this approach for the purpose of possessing tracking capability. In this stage, the acceleration responses are first reconstructed by using the differential equation of motion and employed for improving the accuracy of estimated structural states. A forgetting factor matrix is introduced into the priori estimation error covariance matrix to track time-varying parameters. The square errors between the measurements and the corresponding estimates are defined as an index and used for detecting the damage time instant. Then, a covariance resetting technique is employed to assure that such changes in structural parameters can be efficiently captured. A shear-type building structure without/with magneto-rheological (MR) dampers and a fixed beam structure are used as numerical examples for validating the effectiveness of the proposed approach. Experimental tests on a six-story building model are also conducted. Results show the time-varying parameters and unknown inputs can be simultaneously identified with acceptable accuracy.

Identification of Time-Varying Parameters of Distributed Hydrological Model in Wei River Basin on Loess Plateau in the Changing Environment

In the watershed hydrological model, the parameters represent the characteristics of the watershed. Usually, the parameters are assumed to be constant in the stable environment. However, in the changing environment, the parameters may change and the constant parameters would not represent the change of the characteristics of the runoff generation and routing in the watershed. The identification of the time-varying characteristics of the watershed hydrological model parameters will help to improve the performance of the simulation and prediction of hydrological models in changing environments. Based on the measured data at the ground stations in the Wei River Basin on the Loess Plateau in China, the temporal and spatial evolution of the ecohydrological and meteorological factors was analyzed, and the SWAT model was used to identify the relationship between the model parameters and the factors, such as precipitation, potential evapotranspiration, NDVI and the other environmental characterization factors of the river basin. The results showed that the annual precipitation in the basin showed a decreasing trend, and the annual potential evapotranspiration, the annual average temperature, the annual runoff and the annual average NDVI all showed an increasing trend. The model parameters fluctuated with time during the study period. The change of the soil evaporation compensation coefficient (ESCO) was similar with the annual potential evapotranspiration, and the model parameters all showed a certain correlation with the potential evaporation of the basin, which indicates that the changes of the hydrological model parameters in the upper reach of the Wei River are closely related to the changes of the basin potential evapotranspiration. Potential evapotranspiration is a characterization factor for dynamic changes of the hydrological model parameters in the upper reach of the Wei River.

Robust Conservation Voltage Reduction Evaluation Using Soft Constrained Gradient Analysis

Evaluation of conservation voltage reduction (CVR) factor is critical to peak load reduction, 556 energy conservation, and many CVR-related power system control/optimization strategies. This paper proposes a novel robust CVR factor evaluation method using soft constrained gradient analysis based on time-varying load modeling and real utility field measurements. Firstly, the time-varying ZIP parameter identification is formulated as an over-determinant problem composed of first-order gradient with respect to each coefficient and soft constraints representing temporal correlation of loads in each time step, in order to improve the robustness and smoothness of CVR factor evaluation. Then, problems in time series are coordinated with a sliding window approach. A necessary condition for selecting the smallest window size is proposed and strictly proved to guarantee the existence and uniqueness of the solution of time-varying load modeling problem. Finally, time-varying CVR factors are accurately and robustly calculated with field measurements and the identified load model. Case studies are performed using sufficient field measurements obtained from two real utilities. Unlike existing methods that require a large number of measurements to obtain precise estimation of CVR factor, the proposed method is sufficiently accurate even when the measurements are limited or of low time resolution. Further, the accuracy and robustness of the proposed approach are validated under different types of uncertainties and compared with other existing data processing and CVR factor evaluation methods.

Output-Only Time-Varying Modal Parameter Identification Method Based on the TARMAX Model for the Milling of a Thin-Walled Workpiece.

The process parameters chosen for high-performance machining in the milling of a thin-walled workpiece are determined by a stability prediction model, which needs accurate modal parameters of the machining system. However, the in-process modal parameters are different from the offline modal parameters and are difficult to precisely obtain due to material removal. To address this problem, an accurate time-dependent autoregressive moving average with an exogenous input (TARMAX) method is proposed for the identification of the modal parameters in the milling of a thin-walled workpiece. In this process, a TARMAX model considering external force excitation is constructed to characterize the actual condition in the milling of a thin-walled workpiece. Then, recursive method and sliding window recursive method are used to identify TARMAX model parameters under time-varying cutting conditions. Subsequently, a three-degree of freedom (3-DOF) time-varying structure numerical model under theoretical milling forces and white-noise excitation is established, and the computational results show that the predicted natural frequencies using the proposed method are in close agreement with the simulated values. Finally, several experiments are designed and carried out to validate the effectiveness of the proposed method. The experimental results show that the predicted accuracy of the proposed method using actual cutting forces is 95.68%. Good agreement has been drawn in the numerical simulation and machining experiments. Our further research objectives will focus on the prediction of the damping ratios, modal stiffness, and modal mass.

Time-varying frequency parameter identification of space solar power satellites based on an improved recursive subspace algorithm and optimal sensor placement

This study focuses on the time-varying modal frequency identification of space solar power satellites. Accordingly, an improved recursive subspace identification algorithm based on the variable forgetting factor is proposed to enhance the tracking adaptability of the original method in time-varying systems. Considering the changes in the structural configuration induced by the rotation of the solar concentrator mirror, a time-varying attitude-vibration coupling dynamic model of a space solar power satellite with an integrated symmetrical concentrator configuration is developed based on the modal synthesis technology and the substructure method. Moreover, based on the projection subspace theory, the time-varying forgetting factor is determined by minimizing the mean square deviation of the system estimator. Subsequently, the variable forgetting factor subspace algorithm is adopted to recursively identify the time-varying pseudo modal frequency parameters. A finite element model of the space solar power satellite is established via numerical simulations, and several optimal sensor placement methods are applied to determine the positions of the vibration sensors. Based on the output signals obtained from the optimal sensor placement results, the time-varying frequency parameters of the system are obtained using the proposed algorithm. The computational results reveal that a decrease in the average relative error by 4.2% compared with that obtained via the conventional recursive subspace method is observed when the signal-to-noise-ratio of the measured output is selected as 15 dB. In addition, the results also reveal that an average relative error reduction of approximately 0.4%–1.4%, over two other methods with a fixed forgetting factor, can be achieved using the proposed algorithm when the rotation speed of the solar concentrator mirror is increased. The findings of this study confirm that the proposed algorithm demonstrates a high noise-immune ability and tracking performance for fast time-varying systems.

Online identification of time-variant structural parameters under unknown inputs basing on extended Kalman filter

To date, many parameter identification methods have been developed for the purpose of structural health monitoring and vibration control. Among them, the extended Kalman filter 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 extended Kalman filter with unknown input 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 associated with the time-varying parameters is introduced and determined via an optimization procedure. Then, based on the principle of extended Kalman filter, 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 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.

A substructural and wavelet multiresolution approach for identifying time-varying physical parameters by partial measurements

Currently, most wavelet multiresolution based methods for the identification of time-varying structural physical parameters request the full measurements of all structural responses. All physical parameters including time-varying and time-invariant parameters are expanded by wavelet multiresolution, so it is only applicable to structures with a few degree-of-freedoms. In this paper, based on the substructural identification technique, a novel two-step approach is proposed to identify the time-varying physical parameters of linear structures with more degree-of-freedoms under unknown excitations using only partially measured responses. The whole structure is divided into several substructures. For a substructure concerned, the unknown interaction forces from neighboring structures are treated as ‘additional unknown inputs’ to the substructure, so the identification of complete structure can be transformed to the identification of each substructure with parallel computing in two steps. In the first step, the fading-factor generalized extended Kalman filter under unknown input algorithm is proposed to locate the time-varying physical parameters. In the second step, a synthesized method is developed for the quantitative identification of time-varying physical parameters based on the integration of wavelet multiresolution analysis and the generalized Kalman filter under unknown input. The time-varying structural physical parameters distinguished in the first step are expanded by wavelet multiresolution analysis. Then, the time-invariant physical parameters and the scale coefficients of time-varying physical parameters are identified by performing a nonlinear optimization with an objective function established by the extended Kalman filter under unknown input. Finally, the estimated scale coefficients are used to reconstruct the original time-varying structural physical parameters. Several numerical examples are used to demonstrate the effectiveness of the proposed approach.

Simultaneously Robust Chaos Synchronization and Identification of Unknown Parameters for Nonlinear Gyro System

This paper concerns robust synchronization and parameter identification for nonlinear gyroscope systems. Gyros are widely utilized in navigational applications where synchronization plays a vital role. A system of nonlinear dynamical equations with some parameters presents a model of gyro systems. The parameters of gyro can vary in time, which can lead to desynchronization of the gyro systems. In this paper, we assume that a gyro system has bounded time-varying unknown parameters and the synchronization problem is considered in two situations. First, the synchronization of two gyroscopes with identical dynamical model and, second, the synchronization of a gyroscope with the Rossler system. The Lyapunov stability theory with control terms is employed to cope with the problem. Also, the identification of time-varying unknown parameters is the side goal of the paper. The proposed scheme synchronizes chaotic nonlinear systems in both situations appropriately. In addition, the slave parameters converge to the nominal values of master parameters despite uncertainty. Simulation results illustrate the superiority of the proposed method.

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.

Identification of time-varying nonlinear structural physical parameters by integrated WMA and UKF/UKF-UI

Identification of time-varying nonlinear structural physical parameters by integrated WMA and UKF/UKF-UI

Identification and prediction of time-varying parameters of COVID-19 model: a data-driven deep learning approach

Data-driven deep learning provides efficient algorithms for parameter identification of epidemiology models. Unlike the constant parameters, the complexity of identifying time-varying parameters is largely increased. In this paper, a variant of physics-informed neural network is adopted to identify the time-varying parameters of the Susceptible-Infectious-Recovered-Deceased model for the spread of COVID-19 by fitting daily reported cases. The learned parameters are verified by utilizing an ordinary differential equation solver to compute the corresponding solutions of this compartmental model. The effective reproduction number based on these parameters is calculated. Long Short-Term Memory neural network is employed to predict the future weekly time-varying parameters. The numerical simulations demonstrate that PINN combined with LSTM yields accurate and effective results.

Identification of time-varying signals in quantum systems

The identification of time-varying parameters (e.g., directly inaccessible in situ signals in vacuum and low-temperature environments) is prevalent for characterizing the dynamics of quantum processes. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with specially designed probe systems can the parameters be explicitly read out, and a rigorous identifiability analysis is lacking, i.e., whether the measurement data are sufficient for unambiguous identification. In this paper we formulate this problem as the invertibility of the input-output mapping associated with the quantum system for which an algebraic identifiability criterion is derived based on the system's relative degree. The invertibility analysis also leads to an inversion-based algorithm for numerically identifying the parameters, which is computationally much more efficient than nonlinear regression methods. The effectiveness of the criterion are demonstrated by numerical examples.