The identification of coherent generator groups via EMD and SSI

This paper evaluates the performance of data-and covariance- based Stochastic Subspace Identification (SSI) methods for simultaneous estimation of forced oscillations and system modes. Recent events in North American power grid point to resonant interactions of forced oscillations and electromechanical oscillatory modes of the system that can be problematic. In such cases, simultaneous estimation of both natural and forced oscillation characteristics is of great importance in understanding and analyzing the phenomena. In this paper, simulation cases are investigated to show the ability of different types of SSI methods in simultaneous estimation of forced oscillation estimates and natural mode estimates in the system when both kinds have their frequencies close to each other. Kundur two- area test system is used as the study system for simulations. In all the simulated cases, the frequency of the forced oscillation is very close to an inter-area or a local mode of the system. It is shown that even with the lowest possible model order, both system mode and forced oscillation are estimated by SSI methods and this is not related to the mode splitting phenomenon or high model orders. Furthermore, it is shown that although both SSI methods are capable of estimating the forced oscillation and system mode, bias in damping estimation of data- based SSI may be a challenge, especially for well- damped modes.

The Yingxian wooden tower in China is currently the tallest wooden tower in the world. It was built in 1056 AD and is 65.86 m high. Field measurements of wind speed and wind-induced response of this tower are conducted. The wind characteristics, including the average wind speed, wind direction, turbulence intensity, gust factor, turbulence integral length scale and velocity spectrum are investigated. The power spectral density and the root-mean-square wind-induced acceleration are analyzed. The structural modal parameters of this tower are identified with two different methods, including the Empirical Mode Decomposition (EMD) combined with the Random Decrement Technique (RDT) and Hilbert transform technique, and the stochastic subspace identification (SSI) method. Results show that strong wind is coming predominantly from the West-South of the tower which is in the same direction as the inclination of the structure. The Von Karman spectrum can describe the spectrum of wind speed well. Wind-induced torsional vibration obviously occurs in this tower. The natural frequencies identified by EMD, RDT and Hilbert Transform are close to those identified by SSI method, but there is obvious difference between the identified damping ratios for the first two modes.

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

In electromechanical modal analysis of power systems using Wide Area Measurement System (WAMS) based setup, signal processing is complex as the signals are non-stationary and non-linear in nature. In order to get accurate modal parameters, as a first step, it is required to remove the non-linear trend of the signal. In the literature, many conventional methods such as filtering, averaging and peak detection techniques are employed for removing trend. In this paper, Empirical Mode Decomposition (EMD) method, an iterative algorithm is presented to detrend a signal. The EMD method and its variant are compared with another popularly used peak detection method referred to as the Zhou’s detrending algorithm to find the efficacy of the EMD methods. To test the algorithms, a four machine, two-area power system with three-wind farms is modeled and simulated to generate the power system signals which bring out non-linear and non-stationary nature. Further, the modal characterization is carried out employing Prony analysis.

This paper aims to verify the extraction of modal parameters from angle signals using the stochastic subspace identification (SSI) method. The use of angle signal-based mode shapes can reduce the loss of node information and enhance the robustness in curva-ture-based damage detection. In this regard, the system identification of angle signals should be first conducted prior to the damage detection. For large structures, an out-put-only system identification method should be considered for the modal analysis of an-gle signals, because artificial shaking excitation or impact excitation is practically impos-sible. In order to achieve this, the SSI method is used; it is one of the most powerful tools among the output-only system identification methods because it does not cover nonlinear problems. In order to demonstrate the system identification process of angle signals using the SSI method, the transformation matrix is assumed to represent the relationship be-tween the angular displacement and the normal displacement. Next, the modified block Hankel matrix that consists of angle signals, which can be expressed as a multiplication between the transformation matrix and displacement series vector, is constructed. The observability matrix can be estimated using the singular value decomposition for the pro-jection of the future part onto the past part of the modified block Hankel matrix. Finally, the natural frequencies and angle signal-based mode shapes are calculated using the state and observation matrices. In order to verify the results of the analytical studies, the modal properties estimated from the numerical simulation and the SSI method using angu-lar-velocity measurements are compared.

EMD-based stochastic subspace identification of structures from operational vibration measurements

In this paper comparative analysis of digital image stabilization (DIS) is proposed. For comparison purpose Basic Empirical Mode Decomposition (EMD), Improved EMD, Ensemble Empirical Mode Decomposition (EEMD) and Complete Ensemble Empirical Mode Decomposition (CEEMD) methods are considered. Method used for digital image stabilization is of fully data driven approach. With the comparative analysis best version of the EMD for DIS on the basis of low RMSE error is decided. The concept used to determine jitter is high frequency and low amplitude property. Combination of each EMD method and Hilbert Transform is used for the analysis. Various methods of EMD give the different results the better method for digital image stabilization is decided and parameters of EEMD and CEEMD method are globalised.

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.

This paper presents some selected results obtained from the field measurements of wind effects on Guangzhou International Sports Arena (GISA) during the passage of Typhoon Fanapi in September, 2010. The field data such as wind speed, wind direction and acceleration responses, etc., were simultaneously and continuously recorded during the typhoon. The measured acceleration data are analyzed to obtain the information on dynamic characteristics and wind-induced response of the large-span roof structure. The first four natural frequencies and vibration mode shapes of the roof are identified on the basis of the field measurements using the stochastic subspace identification (SSI) method and comparisons with those calculated from the computational model of the roof are made. The damping ratios of the roof are also identified by the SSI method and compared with those estimated by the random decrement method, and the amplitude-dependent damping characteristics are presented and discussed. Furthermore, the field measurement results are compared with the wind tunnel test results to examine the accuracy of the model test results and the adequacy of the techniques used in wind tunnel tests.

Operational modal analysis of an eleven-span concrete bridge subjected to weak ambient excitations

Full-scale measurements are regarded as the most reliable method to evaluate wind effects on large buildings and structures. Some selected results are presented in this paper from the full-scale measurement of wind effects on a long-span steel roof structure during the passage of Typhoon Fanapi. Some field data, including wind speed and direction, acceleration responses, etc., were continuously and simultaneously recorded during the passage of the typhoon. Comprehensive analysis of the measured data is conducted to evaluate the typhoon-generated wind characteristics and its effects on a long-span steel roof. The first four natural frequencies and their vibration mode shapes of the Guangzhou International Sports Arena (GISA) roof are evaluated by the stochastic subspace identification (SSI) method and comparisons with those from finite element (FE) analysis are made. Meanwhile, damping ratios of the roof are also identified by the SSI method and compared with those identified by the random decrement method; the amplitude-dependent damping behaviors are also discussed. The fullscale measurement results are further compared with the corresponding wind tunnel test results to evaluate its reliability. The results obtained from this study are valuable for academic and professional engineers involved in the design of large-span roof structures.

Modal parameter identification for a roof overflow powerhouse under ambient excitation

Cosine window-based boundary processing method for EMD and its application in rubbing fault diagnosis

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

Envelope modified versions of the empirical mode decomposition (EMD) method such as the B‐spline interpolation‐based EMD (B‐EMD) method and cardinal spline interpolation‐based EMD (C‐EMD) method have been proposed recently for purpose of improving its effectiveness. To shed further light on their performance, the behaviours of these EMD‐type methods in the presence of white Gaussian noises are investigated in this study based on extensive numerical experiments. Similarly to the EMD method, it turns out that the envelope modified EMD methods also act as filter banks essentially. However, the spectra among the first several intrinsic mode functions of the B‐EMD method have fewer overlaps than those of the EMD and C‐EMD methods, which indicate that the B‐EMD method has a better ability to alleviate the mode mixing problem for signals with higher frequencies. On the other hand, the C‐EMD method is shown to perform better than the EMD and B‐EMD methods on separating tones with lower frequencies.