Stochastic Subspace Method Research Articles

FLC-Based Ultra-Low-Frequency Oscillation Suppression Scheme for Interconnected Power Grids

The appearance of ultra-low-frequency oscillations in the grid at the sending end, after asynchronous grid interconnection, poses a significant threat to the stable operation of the system. For post-asynchronous interconnection in a multi-DC transmission system, an investigation is conducted to analyze the causes of ultra-low-frequency oscillations and the utilization of a Frequency Limit Controller (FLC) which aims to suppress these oscillations. Furthermore, a method is developed to rank DC sensitivity, considering the hydroelectric distribution in the sending-end grid, by combining the DC FLC impact factor and DC control sensitivity. Subsequently, a novel approach for ultra-low-frequency oscillation suppression is proposed. This approach employs the stochastic subspace method for parameter estimation and the NSGA-II optimization algorithm to convert the multi-DC optimization challenge into multiple sequential cyclic optimization problems, each focusing on a single DC, ensuring a more effective suppression of ultra-low-frequency oscillations. The proposed scheme’s effectiveness is validated through simulations using a specific locations’ interconnected power grid.

A bootstrap-based stochastic subspace method for modal parameter identification and uncertainty quantification of high-rise buildings

This paper proposes a bootstrap-based stochastic subspace method for modal parameter identification and uncertainty quantification of high-rise buildings. Firstly, the stochastic subspace method in combination with the bootstrap technique enables the estimation of multiple sets of modal parameters from raw data series. Then, a bootstrap-based stabilization diagram is used to extract the physical modes. Finally, the modal identification and associated uncertainty quantification results are determined via statistical analysis. Through a numerical study of high-rise buildings, the performance of the proposed method is validated, demonstrating that it can provide reliable modal parameter identification and uncertainty quantification as well as has good noise immunity. Furthermore, the developed approach is employed to identify modal parameters of a 600-m-tall skyscraper during a typhoon, proving its applicability to field measurements and structural health monitoring of high-rise buildings. This paper aims to present a novel tool for modal parameter identification and associated uncertainty quantification of high-rise buildings.

Identification of modal parameters and relaxation parameter for exponential non-viscous damping system using stochastic subspace method

Non-viscous damping parameters can be identified approximately based on the frequency response function of structures. However, it is difficult or expensive to perform vibration test and layout enough amount measured points for structures. The stochastic subspace method can identify modal damping parameters only using responses data from partial measured points. This paper extends the stochastic subspace method from the viscous damping system to non-viscous damping system. In addition, the eigenvalues of the second-order form equation of motion are proved equally to the state space formulation. The identified procedure of the proposed method is given in detail. Finally, the method is validated using three numerical examples for assessing its accuracy.

Modal Identification of 38 Supertall Buildings and Establishment of Predictive Models

Information on natural frequencies and damping ratios is essential for structural dynamic analysis. To develop predictive models of modal parameters applicable for modern high-rise buildings with increasing heights, an advanced interferometric radar system was employed to measure the displacement responses of 38 supertall buildings with heights ranging from 200 to 600 m under ambient excitations. Then, a combined approach of the stochastic subspace method and an uncertainty bound estimation method are adopted for modal identification, and its accuracy is validated by a numerical simulation study. By applying the modal identification method to the field measurements, modal parameters of the 38 supertall buildings are identified. Based on these results, predictive models for fundamental natural frequency and damping ratio of supertall buildings are accordingly proposed, which are more applicable for the wind-resistant serviceability assessment or design of high-rise buildings with heights over 200 m than existing empirical models.

MODAL IDENTIFICATION OF BASE-FIXED MODEL USING STOCHASTIC SUBSPACE METHOD

A two-step system identification is presented to estimate modal properties of a base-fixed model from ambient vibration records on a multi-story building with soil-structure interaction (SSI). In the first step the output-only identification of the stochastic subspace method is employed for estimating modal properties with SSI. In the second step the modal properties of the base-fixed model are modified from the first estimates, by using theoretical relations between the multi-degree-of-freedom model with SSI and its equivalent base-fixed model derived in the paper. Two examples in numerical and real-world tests are demonstrated to show applicability in the two-step system identification.

Monitoring of Wind Effects on a Super-Tall Building under a Typhoon

Field measurements are critical to further understand the structural behavior of super-tall buildings under strong wind actions. This paper presents field measurements that reflect the wind characteristics and wind effects on Leatop Plaza under Typhoon Vicente. Wind field characteristics, including the turbulence intensity, gust factor, and power spectral density of wind speed in an urban area, were obtained on the basis of a statistical analysis of measured wind data. Subsequently, measured wind-induced accelerations were used to evaluate the dynamic characteristics of the building and the effects of wind on it. On the basis of the first several modes, the modal properties, i.e., the natural frequency and damping ratio, were identified via the fast Bayesian fast Fourier transform method and compared with those identified using the stochastic subspace method. The discrepancy between the identified results and finite element model predictions is presented and discussed. Finally, the variation in the modal parameters with respect to time and the vibration amplitude was analyzed while considering the associated posterior uncertainty.

Influence of Hankel matrix dimension on system identification of structures using stochastic subspace algorithms

In stochastic subspace methods, the modal analysis results are highly dependent on the dimensions of the Hankel matrix. Increasing the dimensions of the Hankel matrix (especially the number of rows) improves the estimation of the modal features by decreasing the impact of noise effects. Due to processing time and memory use, it is impossible to adjust the size of the Hankel matrix to the maximum compatible value. Therefore, this study uses a sensitivity analysis of the dimensions of the Hankel matrix to pick models with the slightest estimate error in the data-driven (DD-SSI) method. First, using the condition number criteria, the desirable models in which the effects of system errors are not predominating are determined. Second, the modal properties of desired models are validated by clustering the damping ratios and modal frequencies using the Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and assessing the complexity of shape modes with the Modal Complexity Factor (MCF). Finally, the optimum models are identified by analyzing the estimated error of modal properties (particularly damping ratio) and the coefficient of variation (CV) of damping of validated clusters. The proposed method was investigated for a two-dimensional simulated concrete building frame, a three-dimensional experimental model, and the Namin city Overpass Bridge ambient vibration tests. Sensitivity analysis was performed for canonical correlation analysis (SSI-CCA) and canonical variate analysis (SSI-CVA) methods. Analyses of computational and laboratory models revealed that the likelihood of non-physical modes arising outside the system's maximum order is relatively high. Also, the MCF is valuable for identifying computational and noise modes. These criteria accurately detected the flexural mode of the foundation set, which was clustered as the stable mode of the slab deck in the practical bridge. Furthermore, the CV analysis revealed that the desired dimension obtained from the condition number could be a reasonable estimate of the optimal system dimension.

Monitor wind characteristics and wind‐induced responses of a skyscraper during two typhoons

SummarySkyscrapers are wind‐sensitive structures due to their large slenderness ratio and good flexibility. Understanding the wind characteristics and wind‐induced response from the actual data provides first‐hand information for wind resistance design. This paper reports the wind properties and dynamic performance of a 632 m high‐rise building in Shanghai during the passage of typhoons Jongdari and Rumbbia. Field measurements obtained from the structural health monitoring system include acceleration and wind speed. The data analysis of turbulence intensity, turbulence integral length, and gust factor are compared and discussed. For the identification of dynamic characteristics, the stochastic subspace method and enhanced frequency domain decomposition method are employed to identify the modal parameters. Besides, the comfort assessment using peak value and root mean square of accelerations is compared with different standards. Studying the wind characteristics during the passage of typhoons and their impact on high‐rise buildings in a metropolis is expected to gain an insight into the dynamic mechanism of high‐rise buildings and collect a database for wind resistance design in typhoon‐prone regions.

A Comparative Study of the Data-Driven Stochastic Subspace Methods for Health Monitoring of Structures: A Bridge Case Study

Subspace system identification is a class of methods to estimate state-space model based on low rank characteristic of a system. State-space-based subspace system identification is the dominant subspace method for system identification in health monitoring of the civil structures. The weight matrices of canonical variate analysis (CVA), principle component (PC), and unweighted principle component (UPC), are used in stochastic subspace identification (SSI) to reduce the complexity and optimize the prediction in identification process. However, researches on evaluation and comparison of weight matrices’ performance are very limited. This study provides a detailed analysis on the effect of different weight matrices on robustness, accuracy, and computation efficiency. Two case studies including a lumped mass system and the response dataset of the Alamosa Canyon Bridge are used in this study. The results demonstrated that UPC algorithm had better performance compared to two other algorithms. It can be concluded that though dimensionality reduction in PC and CVA lingered the computation time, it has yielded an improved modal identification in PC.

Modal identification of civil structures via covariance-driven stochastic subspace method.

It is usually of great importance to identify modal parameters for dynamic analysis and vibration control of civil structures. Unlike the cases in many other fields such as mechanical engineering where the input excitation of a dynamic system may be well quantified, those in civil engineering are commonly characterized by unknown external forces. During the last two decades, stochastic subspace identification (SSI) method has been developed as an advanced modal identification technique which is driven by output-only records. This method combines the theory of system identification, linear algebra (e.g., singular value decomposition) and statistics. Through matrix calculation, the so-called system matrix can be identified, from which the modal parameters can be determined. The SSI method can identify not only the natural frequencies but also the modal shapes and damping ratios associated with multiple modes of the system simultaneously, making it of particular efficiency. In this study, main steps involved in the modal identification process via the covariance-driven SSI method are introduced first. A case study is then presented to demonstrate the accuracy and efficiency of this method, through comparing the corresponding results with those via an alternative method. The effects of noise contaminated in output signals on identification results are stressed. Special attention is also paid to how to determine the mode order accurately.

Modal identification of arch dams using balanced stochastic subspace identification

Dynamic characteristics extracted from ambient and forced vibration tests are always associated with some level of uncertainties because of unknown nature of applied forces, existence of ambient noises as well as measurement errors. Stochastic Subspace Methods are among the most accurate and consistent methods within the domain of operational modal analysis. In this research, a new technique for Operational Modal Analysis is proposed using Stochastic Realization Theory and Canonical Correlation Analysis, which in comparison with previous methodologies, identification process are directly performed in the prediction space by extracting orthonormal vectors of data space. Considering its optimized nature, the proposed method is expected to have superior accuracy in terms of elimination of unstable poles as well as low time consumption analysis. To indicate the efficiency and accuracy of the proposed algorithm, it is applied to reanalyze the results of the forced vibration tests performed on the Shahid-Rajaee arch dam in northern Iran. These tests were conducted via steady-state sinusoidal stimulation method. More accurate natural frequencies are obtained compared to those of previously reported results, besides the fact that the first three modes of the structure were identified by the new approach, while they were not observed via the previous one. In order to examine the capabilities of the proposed method for processing of ambient vibration records, the dynamic characteristics of the Pacoima dam was identified using the recorded responses during 2001 earthquake in San Fernando, California. The results indicated good accuracy in the obtained frequencies and damping ratios compared to those obtained via data driven subspace method. Time consumption of identification process were reduced significantly (up to 50%) for both case studies indicating a faster convergence rate provided by the proposed method.

Mode matching pursuit for estimating dominant modes in bulk power grid

This study presents a general approach to identify dominant oscillation modes in bulk power system by using wide-area measurement system. To automatically identify the dominant modes without artificial participation, spectral characteristic of power system oscillation mode is applied to distinguish electromechanical oscillation modes which are calculated by stochastic subspace method, and a proposed mode matching pursuit is adopted to discriminate the dominant modes from the trivial modes, then stepwise-refinement scheme is developed to remove outliers of the dominant modes and the highly accurate dominant modes of identification are obtained. The method is implemented on the dominant modes of China Southern Power Grid which is one of the largest AC/DC paralleling grids in the world. Simulation data and field-measurement data are used to demonstrate high accuracy and better robustness of the dominant modes identification approach.

Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method

Abstract Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.

Modal Parameter Identification of Concrete Filled Steel Tube Arch Bridge Based on Stochastic Subspace Method

Based on stochastic subspace method, the natural frequency of the bridge arch rib, damping ratios and vibration mold parameter was obtained by modal parameter identification of a concrete filled steel tubular arch bridge under ambient excitation, and the Midas Civil finite element software was used to establish a computational model of the bridge. Measured results and calculated results were compared, and the reliability of the identification results have been verified, the identified dynamic properties can be served as the basis in the finite element model updating, damage detection, condition assessment and health monitoring of the bridge.

DETECTION OF CHANGES OF THE SYSTEM TECHNICAL STATE USING STOCHASTIC SUBSPACE OBSERVATION METHOD

System diagnostics based on vibroacoustics signals, carried out by means of stochastic subspace methods was undertaken in the hereby paper. Subspace methods are the ones based on numerical linear algebra tools. The considered solutions belong to diagnostic methods according to data, leading to the generation of residuals allowing failure recognition of elements and assemblies in machines and devices. The algorithm of diagnostics according to the subspace observation method was applied – in the paper – for the estimation of the valve system of the spark ignition engine. Keyworda: system diagnostic, subspace method, vibroacoustic.

Estimation of the electromechanical characteristics of power systems based on a revised stochastic subspace method and the stabilization diagram

Estimating low-frequency oscillation modes and the corresponding mode shapes based on ambient data from WAMS measurements has a promising prospect in power system analysis and control. Based on the stochastic subspace method, this paper proposes a revised stochastic subspace method by introducing reference channels, which can estimate the modes and the mode shapes simultaneously with great computational efficiency. Meanwhile, the accuracy of the estimated results is not degraded. To discriminate the real modes from the spurious ones, the stabilization diagram is introduced. A novel algorithm is designed to deal with the stabilization diagram which can detect the real modes automatically. Tests conducted on the IEEE-118 system indicate that the proposed method has good performance in terms of both computational efficiency and accuracy, and has the potential of being used on-line.

Stochastic Krylov subspace methods for flow in random porous media

AbstractThe present work establishes a comparative analysis of two different Krylov‐based methods for assessing uncertainty in porous media flow applications. They are: (1) the stochastic reduced basis method (SRBM) and the (2) Krylov‐Karhunen‐Loeve moment equation (KKLME). The former relies on the construction of an orthogonal basis from which projectors may be realized to perform the uncertainty analysis on a lower‐dimensional space. The second approach relies on the idea of expressing input and corresponding outputs in terms of stochastic and perturbative polynomial expansions. By grouping terms and moments of the same order, the original stochastic equation is replaced by successive (and parallel) solutions of a set of deterministic equations. We provide a set of numerical experiments illustrating the capabilities of SRBM and KKLME against Monte Carlo simulations (MCS) on stationary permeability cases. We show that KKLME is superior to SRBM. Furthermore, KKLME appears to be also a more efficient alternative than MCS for non‐stationary permeability field distributions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Identification of 18 flutter derivatives by covariance driven stochastic subspace method

For the slender and flexible cable supported bridges, identification of all the flutter derivatives for the vertical, lateral and torsional motions is essential for its stability investigation. In all, eighteen flutter derivatives may have to be considered, the identification of which using a three degree-of-freedom elastic suspension system has been a challenging task. In this paper, a system identification technique, known as covariance-driven stochastic subspace identification (COV-SSI) technique, has been utilized to extract the flutter derivatives for a typical bridge deck. This method identifies the stochastic state-space model from the covariances of the output-only (stochastic) data. All the eighteen flutter derivatives have been simultaneously extracted from the output response data obtained from wind tunnel test on a 3-DOF elastically suspended bridge deck section-model. Simplicity in model suspension and measurements of only output responses are additional motivating factors for adopting COV-SSI technique. The identified discrete values of flutter derivatives have been approximated by rational functions.

MODAL IDENTIFICATION AND DAMAGE DETECTION USING THE DATA-DRIVEN STOCHASTIC SUBSPACE AND ARMAV METHODS

This paper presents results of modal identification and damage detection on the Steel-Quake structure using the autoregressive moving average vector and data-driven stochastic subspace methods. The methods directly work with the recorded time signals and allow to analyse linear systems where only the system output is measured, while the input is unknown but produced by uncorrelated random signals. These techniques can also be used directly to analyse data obtained from the free response of linear systems.

IDENTIFICATION OF MODAL PARAMETERS FROM MEASURED OUTPUT DATA USING VECTOR BACKWARD AUTOREGRESSIVE MODEL

In this paper, a modal identification system that is based on the vector backward autoregressive (VBAR) model has been developed for the identification of natural frequencies, damping ratios and mode shapes of structures from measured output data. The modal identification using forward autoregressive approach has some problems in discriminating the structure modes from spurious modes. On the contrary, the VBAR approach provides a determinate boundary for the separation of system modes from spurious modes, and an eigenvalue filter for the selection of physical modes is existent in the proposed method. For convenience of application, the backward state equation established from VBAR model is transformed into a forward state equation, which is termed as transformed VFAR model in this paper. In addition, the extraction of equivalent system matrix of state equation of motion for structures from the transformed VFAR model has been developed, and then the normal modes can be calculated from the identified equivalent system matrix. Two examples of modal identification are carried out to demonstrate the availability and effectiveness of the proposed backward approach: (1) Numerical modal identification for a three-degree-of-freedom dynamic system with noise level in 20% of r.m.s of measured output data; (2) experimental modal identification of a cantilever beam. Finally, to show the advantage of the proposed VBAR approach on the selection of physical modes, the modal identification by stochastic subspace method was performed. The results from both methods are compared.