Data-driven Stochastic Subspace Identification Research Articles

Modal identification of Canton Tower under uncertain environmental conditions

The instrumented Canton Tower is a 610 m high-rise structure, which has been considered as a benchmark problem for structural health monitoring (SHM) research. In this paper, an improved automatic modal identification method is presented based on a natural excitation technique in conjunction with the eigensystem realization algorithm (NExT/ERA). In the proposed modal identification method, damping ratio, consistent mode indicator from observability matrices (CMI_O) and modal amplitude coherence (MAC) are used as criteria to distinguish the physically true modes from spurious modes. Enhanced frequency domain decomposition (EFDD), the data-driven stochastic subspace identification method (SSI-DATA) and the proposed method are respectively applied to extract the modal parameters of the Canton Tower under different environmental conditions. Results of modal parameter identification based on output-only measurements are presented and discussed. User-selected parameters used in those methods are suggested and discussed. Furthermore, the effect of environmental conditions on the dynamic characteristics of Canton tower is investigated.

Effects of changing ambient temperature on finite element model updating of the Dowling Hall Footbridge

In this paper, effects of changing ambient temperatures on finite element (FE) model updating of the Dowling Hall Footbridge are investigated. The Dowling Hall Footbridge is located on the Tufts University campus in Medford, Massachusetts. The footbridge is equipped with a continuous monitoring system that records vibration and temperature of the bridge once an hour or when triggered by large vibrations. Natural frequencies, mode shapes, and modal damping ratios of the structure are extracted from measured ambient vibration data using an automated data-driven stochastic subspace identification algorithm. The identified natural frequencies and mode shapes are then used for calibration/updating of an initial FE model of the bridge. However, the identified natural frequencies show significant variability with changing ambient temperature. This variability propagates through the FE model updating process and therefore yields uncertainty in the FE model updating results. A static polynomial model is estimated to represent the relationship between identified natural frequencies and measured temperatures. This model is then used to “remove” the temperature effects from the identified natural frequencies. Two sets of FE models are updated in this study based on 17weeks of hourly-identified modal parameters, before and after removing the temperature effects. The proposed approach is successful in minimizing the effects of changing ambient temperature on FE model updating of the Dowling Hall Footbridge. Accounting for the temperature effects in the FE model updating process reduces the variability of temperature-sensitive updating parameters and therefore decreases the probability of missed identification of damage.

An improved stochastic subspace identification for operational modal analysis

An improved stochastic subspace identification algorithm is introduced to solve the low computational efficiency problem of the Data-driven stochastic subspace identification. Compared with the conventional algorithm, it needs much less cost of memory and computing time because it does not have a process of the QR decomposition of Hankel matrix. Model similarity index is proposed to measure the reliability of the modes obtained by the improved stochastic subspace identification. Furthermore, the stabilization diagram in combination with the modal similarity index is adopted to effectively indicate spurious modes resulting from noise and model redundancy. A criterion named the modal norm is introduced to indicate the dominating mode. A numerical example on the parameter estimation of a linear time-invariant system of 7 degrees of freedom and one experimental example on the parameter estimation of Chaotianmen bridge model in Chongqing are presented to demonstrate the efficacy of the method.

Structural damage diagnosis based on on-line recursive stochastic subspace identification

This paper presents a recursive stochastic subspace identification (RSSI) technique foron-line and almost real-time structural damage diagnosis using output-only measurements.Through RSSI the time-varying natural frequencies of a system can be identified. Toreduce the computation time in conducting LQ decomposition in RSSI, the Givensrotation as well as the matrix operation appending a new data set are derived. Therelationship between the size of the Hankel matrix and the data length in each shiftingmoving window is examined so as to extract the time-varying features of the systemwithout loss of generality and to establish on-line and almost real-time systemidentification. The result from the RSSI technique can also be applied to structuraldamage diagnosis. Off-line data-driven stochastic subspace identification was usedfirst to establish the system matrix from the measurements of an undamaged(reference) case. Then the RSSI technique incorporating a Kalman estimator isused to extract the dynamic characteristics of the system through continuousmonitoring data. The predicted residual error is defined as a damage feature andthrough the outlier statistics provides an indicator of damage. Verification ofthe proposed identification algorithm by using the bridge scouring test data andwhite noise response data of a reinforced concrete frame structure is conducted.

System identification of a super high-rise building via a stochastic subspace approach

System identification is a fundamental step towards the application of structural health monitoring and damage detection techniques. On this respect, the development of evolved identification strategies is a priority for obtaining reliable and repeatable baseline modal parameters of an undamaged structure to be adopted as references for future structural health assessments. The paper presents the identification of the modal parameters of the Guangzhou New Television Tower, China, using a data-driven stochastic subspace identification (SSI-data) approach complemented with an appropriate automatic mode selection strategy which proved to be successful in previous literature studies. This well-known approach is based on a clustering technique which is adopted to discriminate structural modes from spurious noise ones. The method is applied to the acceleration measurements made available within the task I of the ANCRiSST benchmark problem, which cover 24 hours of continuous monitoring of the structural response under ambient excitation. These records are then subdivided into a convenient number of data sets and the variability of modal parameter estimates with ambient temperature and mean wind velocity are pointed out. Both 10 minutes and 1 hour long records are considered for this purpose. A comparison with finite element model predictions is finally carried out, using the structural matrices provided within the benchmark, in order to check that all the structural modes contained in the considered frequency interval are effectively identified via SSI-data.

Data-driven stochastic subspace identification of flutter derivatives of bridge decks

Most of the previous studies on flutter derivatives have used deterministic system identification techniques, in which the buffeting forces and the associated responses are considered as noises. In this paper, one of the most advanced stochastic system identification, the data-driven stochastic subspace identification technique (SSI-DATA) was proposed to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of the stochastic method is that it considers the buffeting forces and the responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under a smooth flow by the free decay and the buffeting tests were used to validate the applicability of the SSI-DATA method. The results were compared with those from the widely used covariance-driven SSI method. Wind tunnel tests of a two-edge girder blunt type of Industrial-Ring-Road Bridge deck (IRR) were then conducted under both smooth and turbulent flows. The identified flutter derivatives of the thin plate model based on the SSI-DATA technique agree well with those obtained theoretically. The results from the thin plate and the IRR Bridge deck helped validate the reliability and applicability of the SSI-DATA technique to various experimental methods and wind flow conditions. The results for the two-edge girder blunt type section show that applying the SSI-DATA yields better results than those of the SSI-COV. The results also indicate that turbulence tends to delay the onset of flutter compared with the smooth flow case.

Application of Modal Identification Methods to Spatial Structure Using Field Measurement Data

Modal identification with output-only measurements plays a key role in vibration-based damage detection, model updating, and structural health monitoring in civil engineering. This paper addresses the application of modal identification method to a triangle steel tube truss natatorium using the field measurement data. To obtain dynamic characteristics of the spatial structure, four different output-only system identification methods are employed. They are natural excitation technique–eigensystem realization algorithm, data-driven stochastic subspace identification method, frequency-domain decomposition/frequency-spatial domain decomposition method, and half spectra/rational fractional orthogonal polynomial method. First an analytical modal analysis was performed on the three-dimensional finite element model according to the factual layout design to obtain the calculated frequencies and mode shapes. Then the whole procedure of the field vibration tests on the natatorium was presented. Finally, practical issues and efficiency of the four output-only modal identification techniques are investigated, and compared with the results from a finite element model. The system identification results demonstrate that both methods can provide reliable information on dynamic characteristics of the spatial structure. The frequency-domain methods, however, can quickly identify the modal parameters, but the leakage error introduced by power-spectral density estimation is existent due to the limited length of data. And the time-domain methods can avoid the leakage error, but the computational modes and the computational cost are the main two drawbacks in application. The conclusion is that several system identification methods should be consulted to ensure the accuracy of the estimated modal parameters.

System Identification of Alfred Zampa Memorial Bridge Using Dynamic Field Test Data

The Alfred Zampa Memorial Bridge (AZMB), a newly built long-span suspension bridge, is located 32km northeast of San Francisco on interstate Highway I-80. A set of dynamic field tests were conducted on the AZMB in November 2003, just before the bridge opening to traffic. These tests provided a unique opportunity to identify the modal properties of the bridge in its as-built condition with no previous traffic loads or seismic excitation. A benchmark study on modal identification of the AZMB is performed using three different state-of-the-art system identification algorithms based on ambient as well as forced vibration measurements. These system identification methods consist of: (1) the multiple-reference natural excitation technique combined with the eigensystem realization algorithm, (2) the data-driven stochastic subspace identification method, and (3) the enhanced frequency domain decomposition method. Overall, the modal parameters identified using these system identification methods are found to be in very good agreement for each type of tests (ambient and forced vibration tests). For most vibration modes, the natural frequencies and mode shapes identified using the two different types of test data also match very well. However, the modal damping ratios identified from forced vibration test data are in general higher than those estimated from ambient vibration data. The identified natural frequencies and mode shapes are finally compared with their analytical counterparts from a three-dimensional finite element model of the AZMB. The modal properties of the AZMB presented in this paper can be used as baseline in future health monitoring studies of this bridge.

Dynamic Testing of Alfred Zampa Memorial Bridge

This paper describes a set of dynamic field tests performed on the Alfred Zampa Memorial Bridge (AZMB), also known as the New Carquinez Bridge, which is located 32km northeast of San Francisco on interstate Highway I-80. The AZMB, opened to traffic in November 2003, is the first suspension bridge in the United States with an orthotropic steel deck, reinforced concrete towers, and large-diameter drilled shaft foundations. The dynamic field tests described herein were conducted just before the bridge opening to traffic. They included ambient vibration tests, mainly wind induced, and forced vibration tests based on controlled traffic loads and vehicle-induced impact loads. Four different controlled traffic load patterns and seven different vehicle-induced impact load configurations were used in the forced vibration tests. The dynamic response of the bridge was measured through an array of 34 uniaxial and 10 triaxial force-balanced accelerometers deployed along the whole length of the bridge. These dynamic field tests provided a unique opportunity to determine the dynamic (modal) properties of the bridge in its as-built (baseline) condition with no previous traffic loads or seismic excitation. Such properties could be used to validate and/or update the finite element models used in the design phase of this bridge. They could also be used as baseline for future health monitoring studies of this bridge. At the end of the paper, the ambient vibration test data were used to identify the bridge modal parameters (natural frequencies, damping ratios, and mode shapes) using the data-driven stochastic subspace identification method.

Optimal sensor placement for spatial lattice structure based on genetic algorithms

Optimal sensor placement technique plays a key role in structural health monitoring of spatial lattice structures. This paper considers the problem of locating sensors on a spatial lattice structure with the aim of maximizing the data information so that structural dynamic behavior can be fully characterized. Based on the criterion of optimal sensor placement for modal test, an improved genetic algorithm is introduced to find the optimal placement of sensors. The modal strain energy (MSE) and the modal assurance criterion (MAC) have been taken as the fitness function, respectively, so that three placement designs were produced. The decimal two-dimension array coding method instead of binary coding method is proposed to code the solution. Forced mutation operator is introduced when the identical genes appear via the crossover procedure. A computational simulation of a 12-bay plain truss model has been implemented to demonstrate the feasibility of the three optimal algorithms above. The obtained optimal sensor placements using the improved genetic algorithm are compared with those gained by exiting genetic algorithm using the binary coding method. Further the comparison criterion based on the mean square error between the finite element method (FEM) mode shapes and the Guyan expansion mode shapes identified by data-driven stochastic subspace identification (SSI-DATA) method are employed to demonstrate the advantage of the different fitness function. The results showed that some innovations in genetic algorithm proposed in this paper can enlarge the genes storage and improve the convergence of the algorithm. More importantly, the three optimal sensor placement methods can all provide the reliable results and identify the vibration characteristics of the 12-bay plain truss model accurately.

Challenges in the Application of Stochastic Modal Identification Methods to a Cable-Stayed Bridge

This paper presents an analysis of the data collected in the ambient vibration test of the International Guadiana cable-stayed Bridge, which links Portugal and Spain, based on different output-only identification techniques: peak-picking, frequency domain decomposition, covariance-driven stochastic subspace identification, and data-driven stochastic subspace identification. The purpose of the analysis is to compare the performance of the four techniques and evaluate their efficiency in dealing with specific challenges involved in the modal identification of the tested cable-stayed bridge, namely the existence of closely spaced modes, the perturbation produced by the local vibration of stay-cables, and the variation of modal damping coefficients with wind velocity. The identified natural frequencies and mode shapes are compared with the corresponding modal parameters provided by a previously developed numerical model. Additionally, the variability of some modal damping coefficients is related with the vari...

Experimental investigation of damage evolution by data-driven stochastic subspace identification and iterative finite element model updating

In civil and mechanical engineering, the monitoring of structures is still a frequently investigated research topic. The basis of the present monitoring concept is the analysis of non-destructive measurements taken at regular time intervals to provide information about the current state of damage in a structure. The approach includes two steps: First, a data-driven stochastic subspace identification is applied to obtain a mathematical description of the system. Using a special state-space transformation, we transfer this result into physically meaningful system properties. Thereby the modal information can be separated into a part which describes the undamped system response and a second contribution which represents the influence of the damping. In the second step, we discretise the experimental setup by means of finite elements and apply an iterative finite element model updating algorithm to localise and to determine the damage. One important innovative aspect of the contribution lies in the updating of an entire damage evolution in order to estimate the lifetime of the structure. The experimental laboratory setup is based on a cantilever beam which is damaged locally and progressively with the help of a special device.

Process for preparing group IB-IIIA-VIA semiconducting films

This paper is about development and use of a research based stereo vision system for vibration and operational modal analysis on a parked, 1-kW, 3-bladed vertical axis wind turbine (VAWT), tested in a wind tunnel at high wind. Vibrations were explored experimentally by tracking small deflections of the markers on the structure with two cameras, and also numerically, to study structural vibrations in an overall objective to investigate challenges and to prove the capability of using stereo vision. Two high speed cameras provided displacement measurements at no wind speed interference. The displacement time series were obtained using a robust image processing algorithm and analyzed with data-driven stochastic subspace identification (DD-SSI) method. In addition of exploring structural behaviour, the VAWT testing gave us the possibility to study aerodynamic effects at Reynolds number of approximately 2 × 105. VAWT dynamics were simulated using HAWC2. The stereo vision results and HAWC2 simulations agree within 4% except for mode 3 and 4. The high aerodynamic damping of one of the blades, in flatwise motion, would explain the gap between those two modes from simulation and stereo vision. A set of conventional sensors, such as accelerometers and strain gauges, are also measuring rotor vibration during the experiment. The spectral analysis of the output signals of the conventional sensors agrees the stereo vision results within 4% except for mode 4 which is due to the inaccuracy of spectral analysis in picking very closely spaced modes. Finally, the uncertainty of the 3D displacement measurement was evaluated by applying a generalized method based on the law of error propagation, for a linear camera model of the stereo vision system.