Subspace Identification Research Articles

Investigation of modal parameters of a 600-m-tall skyscraper based on two-year-long structural health monitoring data and five typhoons measurements

On the basis of two-year-long structural health monitoring data, this paper investigates the structural dynamic properties of a 600-m-high supertall building installed with an active tuned mass damper (ATMD) system. The long-term modal parameters such as natural frequencies and damping ratios of the monitored skyscraper are first determined by the stochastic subspace identification approach, and the results generally agree well with those obtained by the finite element method and forced vibration tests. The statistical analysis of the modal parameters indicates that the natural frequencies follow the normal distribution, while the damping ratios fit well with the Gumbel distribution. In addition, the two-year-long variations of the modal parameters with ambient environmental factors are investigated and it is found that both the ambient temperature and humidity have limited effects on the modal parameters of the skyscraper. Moreover, the impacts of the ATMD system on the modal parameters are explored based on the field measurements during five typhoons. The analyzed results demonstrate that the active damper system had significant effects on the modal parameters of the fundamental sway modes, while it had marginal influences on these of higher modes. This study aims to enhance the understanding of structural dynamic properties of supertall buildings and provide useful information for their wind-resistant design.

Practical Implementation of Recursive Subspace Identification on Seismically Excited Structures with Fixed Window

As one of the most catastrophic natural disasters worldwide, earthquakes and their effect on structures are very important to structural health monitoring (SHM), particularly for the ones living around the Pacific ring of fire. In this regard, SHM techniques with real-time or online processing can be used to identify states of structures, track modal parameters, provide a warning message about damage, and help post-earthquake reconnaissance and rehabilitation. For instance, a recursive formulation based on subspace identification (SI) has been demonstrated that it is capable to track system changes. In this study, a recursive subspace identification (RSI) algorithm with a fixed window is proposed to investigate the time-varying dynamic characteristics under seismic excitations. Subsequently, some suggestion is described and discussed for practical implementation. For verifying the proposed algorithm, different datasets from full-scale experiments are applied to examine its applicability. In other words, the practicability of implementing RSI in real-time or online has been developed and examined in this paper.

Modeling and Finite-Horizon MPC for a Boiler-Turbine System Using Minimal Realization State-Space Model

This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively.

Automated operational modal analysis using variational Gaussian mixture model

Automated operational modal analysis is essential for online structural health monitoring without human intervention. It remains a challenging issue due to the need of processing a large number of datasets and the involvement of many user-specified thresholds. This paper proposes a novel automated modal identification approach based on stochastic subspace identification and variational Gaussian mixture model that involves the analysis of the stabilization diagram to automatically identify modal parameters. Two validation criteria are first adopted to eliminate the spurious modes in the stabilization diagram. A Gaussian mixture model (GMM) is then used to probabilistically classify each pole in the stabilization diagram to a specific cluster. The parameters of GMM are estimated using variational inference, giving representatives of each mode, and the optimal number of clusters is automatically determined through the Dirichlet Process. The proposed framework automatically distinguishes physical modes from spurious modes with only two verified and widely used thresholds. Results of a four-story shear and a footbridge with continuous measurements demonstrate the efficacy and robustness of the proposed approach. It shows that the proposed approach can automatically identify modal parameters with high accuracy, including weakly excited and closely spaced modes.

Dynamic response analysis of a real-world operating offshore wind turbine under earthquake excitations

This paper describes the dynamic monitoring campaign conducted on a monopile offshore wind turbine (OWT). An unexpected harvest is that the dynamic responses of the OWT under earthquake excitations were captured. Therefore, particular emphasis is placed on any abnormal behavior of the OWT. Operational modal analysis with the stochastic subspace identification method is used to reveal any variations in the modal parameters before, during and after the earthquake. The influence of the time-varying yaw angle on modal identification is derived. The results indicate that the earthquake had a colossal impact on the OWT as compared to the wind loading. The earthquake allows the identification of some of the high-frequency bending and twisting modes. Another critical finding is that the first frequency of the OWT increased after the earthquake, possibly implying some quick consolidation of the seabed adjacent to the OWT. Although earthquakes are often considered harmful to the safety of OWTs, it is possible for some special cases to improve the bearing capacity and stability of the monopile foundations. This paper could be the first study on the dynamic response of a real-world OWT under earthquake excitations, in which some beneficial effects of an earthquake are observed.

Propeller's operational modal parameters identification based on Fiber Bragg Grating sensing

The propeller will generate a lot of harmful vibration and noise underwater. In order to effectively solve the problem of vibration and noise, it is of great significance to accurately obtain the modal parameters of propeller for the design and optimization of the propeller structure. Since it is difficult to measure the load of propeller when it is running underwater, only operational modal analysis (OMA) method can be used to identify the operational modal parameters of propeller. This paper is aimed at solving this problem by taking the metal propeller as the research object, an open-water test platform was built, and the Fiber Bragg Grating (FBG) sensors were used to obtain the underwater strain information of the propeller. Finally, the operational modal parameters of propeller are identified by the Stochastic subspace identification (SSI) method. In addition, the modal simulation analysis of propeller was carried out by using finite element simulation software, and the experimental results were compared with the simulation results. The results show that the stochastic subspace identification method can accurately identify the operational modal parameters of propeller.

Data-Driven Predictive Control of Exoskeleton for Hand Rehabilitation with Subspace Identification.

This study proposed a control method, a data-driven predictive control (DDPC), for the hand exoskeleton used for active, passive, and resistive rehabilitation. DDPC is a model-free approach based on past system data. One of the strengths of DDPC is that constraints of states can be added to the controller while performing the controller design. These features of the control algorithm eliminate an essential problem for rehabilitation robots in terms of easy customization and safe repetitive rehabilitation tasks that can be planned within certain constraints. Experiments were carried out with a designed hand rehabilitation system under repetitive and various therapy tasks. Real-time experiment results demonstrate the feasibility and efficiency of the proposed control approach to rehabilitation systems.

Finite element model of a cable-stayed bridge updated with vibration measurements and its application to investigate the variation of modal frequencies in monitoring

Ambient vibration measurements of a cable-stayed bridge in Taiwan were first conducted to identify its dominant modal parameters with a reliable stochastic subspace identification algorithm recently developed. A finite element model is then constructed based on the identified frequencies and shape vectors of four vertically bending, one torsional, and one horizontally bending modes. This model is also updated by adjusting the girder-pier connection with the addition of a rotational spring to reflect the actual conditions and its accuracy is demonstrated with less than 1% of error for the first two vertically bending modes. As a solid application for probing the environmental effects in structural health monitoring, the vibration measurements of 24 hours were further conducted and combined with the well calibrated model to investigate the controlling factor for its variation in modal frequencies. It is found that the frequencies of the first two vertically bending modes are closely correlated to the root-mean-square velocity representing the traffic excitation intensity. Moreover, it is shown with the updated model that the daily variations in the frequencies of the first two vertically bending modes can be reasonably simulated by modifying the coefficient of the rotational spring merely in a limited range.

Parametric model-order reduction for radiation transport using multi-resolution proper orthogonal decomposition

For parametric high-fidelity simulations, it is often desirable to utilize a reduced-order model (ROM) to emulate, at a reduced computational cost, parametric solutions of the governing partial differential equations (PDEs) for unseen parameter values. One commonly employed option is to utilize a data-driven, projection-based ROM supplemented with subspace identification via proper orthogonal decomposition (POD). POD discovers the ROM subspace by computing the singular value decomposition (SVD) of a set of training data from the full-order model (FOM). In streaming-dominated radiation transport simulations with localized sources, solutions often greatly vary over the spatial domain by many orders of magnitude. In such cases, machine-precision arithmetic can be insufficient to obtain an accurate SVD, resulting in a poorly performing ROM. We present a method called multiresolution POD (mrPOD) that mitigates these inaccuracies. The mrPOD method works by decomposing the spatial domain into regions and performing proper orthogonal decomposition on the training dataset separately in each region. mrPOD is tested on single energy group and multigroup atmospheric shielding transport problems and is shown to outperform classic POD.

Cover Image

The cover image is based on the Research Article A data-driven combined deterministic-stochastic subspace identification method for condition assessment of roof structures subjected to strong winds by Xuan Liu et al., https://doi.org/10.1002/stc.3031

A robust methodology for output-only modal identification of civil engineering structures

Output-only modal identification has been attracting increasing research efforts in civil engineering community. The aim of this study was to develop a robust output-only modal identification methodology to improve the performance of the existing methods. The proposed method combines the second-order blind identification (SOBI) with the covariance driven stochastic subspace identification (SSI-COV) by introducing a new system model. Instead of employing single degree-of-freedom fitting methods to obtain local modal information of each mode like it usually does in SOBI, modal responses identified by SOBI are regarded as the output of a system to form the block Toeplitz matrix of the SSI-COV. More accurate global modal parameters are expected to be obtained since a parametric system model is included and the contributions of different modes are considered. It is also easy to select physical modes based on the time and frequency characteristics of source signals and thus can avoid the ambiguous work related to the stabilization diagrams. The proposed method is validated by a simulated 8-DOF system with emphasize on identification accuracy and parameter sensitivity. The results confirm the insensitivity of input parameters and demonstrate the high accuracy. It is then applied to estimate the modal parameters of a reinforced concrete shear core building and a concrete arch-gravity dam. It is demonstrated that a total of twelve building modes and six dam modes are successfully identified respectively, and the results in both applications are accord well with the existing modal identification methods, especially SSI-COV. The promising results show that the physical modes can be well separated, and the associated modal parameters can be reliably identified with high accuracy, even if closely-spaced modes and spurious harmonics occur. As expected, the modes discrimination step that associated with the proposed method tends to be more distinct and intuitive than the stabilization diagrams.

Data-Driven Identification of Nonlinear Power System Dynamics Using Output-Only Measurements

In this paper, we propose a novel approach for the data-driven characterization of power system dynamics. The developed method of Extended Subspace Identification (ESI) is suitable for systems with output measurements when all the dynamics states are not observable. It is particularly applicable for power systems dynamic identification using Phasor Measurement Units (PMUs) measurements. As in the case of power systems, it is often expensive or impossible to measure all the internal dynamic states of system components such as generators, controllers and loads. PMU measurements capture voltages, currents, power injection and frequencies, which can be considered as the outputs of system dynamics. The ESI method is suitable for system identification, capturing nonlinear modes, computing participation factor of output measurements in system modes and identifying system parameters such as system inertia. The proposed method is suitable for measurements with a noise similar to realistic system measurements. The developed method addresses some of the known deficiencies of existing data-driven dynamic system characterization methods. The approach is validated for multiple network models and dynamic event scenarios with synthetic PMU measurements.

Full-Field Modal Property Extraction from Motion Video Measurement: Considering Out-of-Plane Motions

Aging problems and potential damage of structures will increase the risks of structural collapse in the upcoming extreme loading events (i.e., earthquakes, hurricanes). Thus, structural health monitoring (SHM) is an essential technique to determine structural soundness through in-situ measurements. However, a successful SHM system requires a dense array of sensors that may be challenging in real-world applications. Alternatively, the structural response can be acquired through motion videos. This measurement method not only overcomes the disadvantages of the conventional SHM systems but also gives the opportunity to investigate more detailed dynamic behavior. In this study, a full-field modal property extraction method based on motion videos is proposed, in particular for out-of-plane motions. The measurements are first padded to reduce the distortion effect caused by the image pyramid. The responses are then compressed and decomposed into sub-bands using an image pyramid decomposition. The modal properties are subsequently extracted using the OMA approach known as frequency-domain stochastic subspace identification. The advantages and limitations of the proposed approach are illustrated numerically using a physics-based graphics model of a continuous beam. Subsequently, experimental validation is conducted for a 3-story model building using the Intel RealSenseTM D415 depth camera. Modal properties are shown to be determined quickly, with high accuracy and noise robustness.

MEMD-Based Hybrid Modal Identification for High-Rise Structures with Multi-Sensor Vibration Measurements

Although widely used in various fields due to its powerful capability of signal processing, empirical mode decomposition has to decompose signals separately, which limits its application for multivariate data such as the structural monitoring data recorded by multiple sensors. In order to avoid this shortcoming, a multivariate extension of empirical mode decomposition is proposed to deal with the multidimensional signals synchronously by employing a real-valued projection on hyperspheres. This study presents a hybrid modal identification method combining the multivariate empirical mode decomposition with stochastic subspace identification and fast Bayesian FFT methods to more conveniently and accurately identify structural dynamic parameters from multi-sensor vibration measurements. Deployed as a preprocessing tool, the multivariate signals are decomposed into several aligned intrinsic mode functions, which contain only a dominant component in the frequency domain. Then, the modal parameters can be identified by advanced fast Bayesian FFT and stochastic subspace identification directly. The combined method is first validated by a numerical illustration of a frame structure and then is applied in a shaking table test and a full-scale measurement under nonstationary earthquake excitation. Compared with the finite element method, the peak–pick, the half-power bandwidth methods, and Hilbert–Huang transform method, the results show that this hybrid method is more robust and reliable in the modal parameters identification. The main contribution of this paper is to develop a more effective integrated approach for accurate modal identification with the output-only multi-dimensional nonstationary signal.

Identification of boundary conditions of railway bridges using artificial neural networks

This article presents a study that aims to identify the boundary conditions of a railway bridge using system identification and artificial neural networks. Vibrations generated by three different train types recorded during a 24-h long measurement campaign is used to identify the modal frequencies and mode shapes of a single-span 50 m long railway bridge. Frequency Domain Decomposition and Stochastic Subspace Identification with Covariance methods were used to identify the modal properties from the recorded vibrations and the effect of the used Operational Modal Analysis on the identified modal properties was evaluated. An initial finite-element (FE) model based on the design drawings was not able to replicate the observed dynamic behavior of the bridge. Using a sensitivity analysis, the key parameters of the finite-element model that impact the vibration frequencies of the bridge was determined. 300 finite-element models were created by changing the values of these key parameters within their effective range and were used to identify the relationship between these parameters and the vibration frequencies using Artificial neural networks (ANNs). Leveraging this relationship, the values of the FE model parameters that minimizes the error between the measured and computed frequencies was determined. As a result, the mean error between the computed and the identified vibration frequencies was reduced from 27.3% for the initial model to 3.0% for the updated model. The study indicates that boundary conditions are among the most influential parameter on the dynamic behavior of bridges and can deviate significantly from the simplistic models generally used in the FE models.

Determining the Dynamic Characteristics of a Multi-Story RC Building Located in Chile: A Comparison of the Results between the Nonparametric Spectral Analysis Method and the Parametric Stochastic Subspace Identification Method

Estimating the dynamic characteristics of instrumented built structures from seismic vibration data collected from built civil structures is essential input information for structural model updating and assessing the health of structures. This study focuses on the earthquake acceleration time histories obtained from several events recorded during its construction phase by accelerometers placed throughout an office building located in Viña del Mar (Chile) to determine its modal features. To this end, the data obtained were analyzed to compare the building’s dynamic properties obtained with two different modal identification techniques. MATLAB programs were developed to implement both methods. The stochastic subspace identification technique for linear systems developed by van Overschee and de Moor was used to study the dynamic properties of the building. In contrast, the nonparametric method employed herein uses correlations and spectral analysis based on the Welch transform in the frequency domain. The investigation demonstrated that both methods identify similar frequencies and that the obtained translational mode shapes exhibit good agreement. Furthermore, the identified frequencies are congruent with the design frequencies.

MLD–MPC for Ultra-Supercritical Circulating Fluidized Bed Boiler Unit Using Subspace Identification

Before carbon capture and storage technologies can truly be promoted and applied, and nuclear or renewable energy power generation can become predominant, it is important to further develop more efficient and ultra-low emission USC units on the basis of leveraging the strengths of CFB technology. In view of this complex system with strong nonlinearity such as the boiler-turbine unit of a thermal power unit, the establishment of a model that is suitable for control is indispensable for the operation and the economics of the process. In this study the form of the nonlinear model after linearization at the steady-state point has been fully considered and an improved subspace identification method, which is based on the steady-state point deviations data, was proposed in order to identify a piecewise affine model. In addition, the construction of the excitation signal in practical applications has been fully considered. The identification results demonstrate that this method has a better adaptability to strong nonlinear systems. The identification normalized root mean square errors of each working condition were almost all less than 10%. On this basis, a framework that is widely applicable to complex system control has been established by combining with the mixed logic dynamic (MLD) model. The canonical form realization was performed in order to transfer the local models into the same state basis. The predictive control was carried out on the boiler-turbine system of a 660-MW ultra-supercritical circulating fluidized bed unit that was based on the above framework. The results indicate that the predictive control performance is closely related to the setting value of the ramp rate and, therefore, prove the effectiveness of the framework.

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.

A hybrid autoencoder framework of dimensionality reduction for brain-computer interface decoding

ObjectiveAs the scale of neural recording increases, Brain-computer interfaces (BCIs) are restrained by high-dimensional neural features, so dimensionality reduction is required as a preprocess of neural features. In this context, we propose a novel framework based on deep learning to reduce the dimensionality of neural features that are typically extracted from electrocorticography (ECoG) or local field potential (LFP). ApproachA high-performance autoencoder was implemented by chaining convolutional layers to deal with spatial and frequency dimensions with bottleneck long short-term memory (LSTM) layers to deal with the temporal dimension of the features. Furthermore, this autoencoder is combined with a fully connected layer to regularize the training. Main resultsBy applying the proposed method to two different datasets, we found that this dimensionality reduction method largely outperforms kernel principal component analysis (KPCA), partial least square (PLS), preferential subspace identification (PSID), and latent factor analysis via dynamical systems (LFADS). Besides, the new features obtained by our method can be applied to various BCI decoders, without significant differences in decoding performance. SignificanceA novel method is proposed as a reliable tool for efficient dimensionality reduction of neural signals. Its high performance and robustness are promising to enhance the decoding accuracy and long-term stability of online BCI systems based on large-scale neural recordings.

A novel direct performance adaptive control of aero-engine using subspace-based improved model predictive control

The direct performance predictive control method can fully improve the engine's operating performance. Compared with the traditional control methods, it has a better control effect. However, it urgently needs to solve the problems of how to achieve the predictive control applicable for any operating point of the engine and how to further reduce the calculation cost of performance parameter estimation. Therefore, this paper first proposes a subspace-based improved model predictive control method. The subspace identification method is used to identify the past I/O data set of the engine offline to obtain the approximate predictive model, and then the predictive model is updated in real-time according to the currently collected I/O data online to adapt to the current actual operating point of the engine. Thus, the engine's direct performance adaptive control is successfully realized based on the predictive control using this obtained predictive model in full life cycle, full envelope, and full state in this paper. This method reduces the online computational burden through the Givens rotation transformation algorithm, and the design process is simple. Compared with the existing methods, it not only improves the robustness, adaptability, and independence of the engine model but also perfects the control performance. Secondly, aiming at the problems, such as complex design and a tremendous amount of calculation of the current direct performance estimator, a high-precision real-time estimation method of nonlinear onboard performance parameters based on spherical unscented Kalman filter is also proposed. Compared with the existing estimation methods, its computational complexity is reduced by one time while maintaining accuracy. Finally, a fully digital simulation system of aero-engine's direct performance adaptive predictive control is established. The simulation results show that the dynamic response time from idle to maximum state is 3.48 s, the steady-state error is ±0.2%, and there is no overshoot. Compared with the traditional control, the dynamic performance is improved by 32%.