Data-driven Stochastic Subspace Identification Method Research Articles

Modal parameter identification of a multiple-span post-tensioned concrete bridge using hybrid vibration testing data

The paper describes and evaluates application of output-only system identification to an eleven-span post-tensioned concrete bridge using hybrid excitation. A linear chirp sweeping force, induced by two light-weight electro-dynamic shakers, augmented environmental sources to excite the bridge during the hybrid testing exercise. To obtain the modal characteristics of the structure, two output-only time domain system identification methods were employed, namely auto-regressive (AR) time series model and eigensystem realization algorithm with observer/Kalman identification (ERA-OKID), with the traditional data-driven stochastic subspace identification method (SSI-data) providing a comparative benchmark. The accuracy and efficiency of both system identification algorithms when used on hybrid testing data are investigated and compared to the results from purely ambient vibration testing data. The study demonstrates that using both output-only identification algorithms the collected vibration responses induced by the proposed hybrid vibration testing methodology can be used for extracting modal parameters with enhanced accuracy and reliability (i.e. more identified modes) for the large-scale post-tensioned concrete bridge due to the increase in the excitation strength and better coverage of the relevant frequency bands. Compared to the classical SSI-data, the AR and ERA-OKID techniques were able to identify more modes at reduced computational cost when applied to voluminous data from multi-channel measurements.

Analysis of vibration monitoring data of an onshore wind turbine under different operational conditions

A wind turbine structure works under the complicated environment and its operational state is complex. In this study, the operational state of a 1.5 MW wind turbine and the vibration response of the tower have been monitored for a long time. The vibration characteristic of the wind turbine under different operational conditions is discussed in detail, and it was observed that the rated rotation speed condition has the highest vibration level. The Campbell diagrams of wind turbine both in the FA direction and SS direction are drawn based on the natural frequencies results, which are identified by data-driven stochastic subspace identification method. It was observed from the Campbell diagrams that when the rotation speed is close to the grid-connected rotation speed, the blade-passing frequency 3f (0.43 Hz) is equal to the fundamental frequency of wind turbine which will easily lead to the resonance. This phenomenon is confirmed by the time history diagrams of the operational condition and vibration speed of a certain startup process. Lastly, the relationship between first-order, second-order modal parameters and operational conditions of the wind turbine are discussed in detail respectively. The mean value of first-order natural frequency is affected slightly by the different operational conditions while the value of second-order natural frequency increases significantly with the increase of rotation speed. The work in this paper can help us to better understand the response of the wind turbine under different operational conditions, which can also lay the foundation for the structure design, modal validation and damage diagnosis of wind turbine.

Automated long-term dynamic monitoring using hierarchical clustering and adaptive modal tracking: validation and applications

Historical buildings demand constant surveying because anthropogenic (e.g., use, pollution or traffic vibration) and natural or environmental hazards (e.g., environmental changes or earthquakes) can endanger their existence and safety. Particularly, in the Andean region of South America, earthen historical constructions require special attention and investigation due to the high seismic hazard of the area next to the Pacific coast. Structural Health Monitoring (SHM) can provide useful, real-time information on the condition of these buildings. In SHM, the implementation of automatic tools for feature extraction of modal parameters is a crucial step. This paper proposes a methodology for the automatic identification of the structural modal parameters. An innovative and multi-stage approach for the automatic dynamic monitoring is presented. This approach uses the Data-Driven Stochastic Subspace Identification method complemented by hierarchical clustering for automatic detection of the modal parameters, as well as an adaptive modal tracking procedure for providing a clear visualization of long-term monitoring results. The proposed methodology is first validated in data acquired in an emblematic sixteenth century historical building: the monastery of Jeronimos in Portugal. After proving its efficiency, the algorithm is used to process almost 5000 events containing data acquired in the church of Andahuaylillas, a sixteenth century adobe building located in Cusco, Peru. The results in these cases demonstrate that accurate estimation of predominant modal parameters is possible in those complex structures even if relatively few sensors are installed.

Laboratory evaluation of a fully automatic modal identification algorithm using automatic hierarchical clustering approach

Earth has been a traditional building material to construct structures in many different continents. In particular, adobe buildings are widely diffused in South America, and in Peru where form part of the cultural identity of the nation. Nowadays, the knowledge of existing adobe buildings is far from a complete understanding of the constructive system and a structural health monitoring (SHM) can quantify and reduce uncertainties regarding their structural performance without causing damage to the buildings. In this process, the implementation of automatic tools for feature extraction of modal parameters is desirable. In particular, the automation is important because, during a long-term monitoring, a huge amount of data is recorded and the direct check of the data of the user is not possible. The present work is focused on the development of an automated procedure for managing the results obtained from the parametric identification method, in particular from the Data-Driven Stochastic Subspace Identification method, which requires an automatic interpretation of stabilization diagrams. The work presents a fully automated modal identification methodology based on the following steps: (i) digital signal pre-processing of the recorded data; (ii) modal parameter identification using models with varying dimensions; (iii) automatic analysis of the stabilization diagram with the application of soft and hard validation criteria and the use of hierarchical clustering approach to eliminate the spurious modes; and (iv) automatic choice of the most representative values of the estimated parameters of each clustered mode: natural frequency, damping and mode shape. The developed algorithm was firstly tested with an inverted steel pendulum to check the accuracy and sensitivity, and subsequently, an earthen wall built in PUCP Structure Laboratory was analysed to determine its dynamic behaviour. The developed algorithm shows high percentages of detected frequencies and high sensitivity to the environmental and structural changes.

Finite-element model calibration of a railway vehicle based on experimental modal parameters

This article describes the experimental calibration of a three-dimensional numerical model of an Alfa Pendular train vehicle based on modal parameters. The dynamic tests of the carbody and bogie of the vehicle allowed the determination of the frequencies and modal configurations of 13 vibration modes, by applying the data-driven stochastic subspace identification method. In addition, a dynamic characterisation test of the passenger-seat system was also conducted. The calibration of the model was performed using a submodelling/multistep approach involving two phases, the first one focused on the calibration of the model of the bogie under test conditions and the second one focused on the calibration of the complete model of the vehicle. The calibration was performed through an iterative method based on a genetic algorithm and allowed to obtain optimal values of 17 parameters of the numerical model. For the pairing of the vibration modes, real and complex, a recent technique was used based on the calculation of the modal strain energy. The stability of a significant number of parameters considering different initial populations demonstrated the robustness of the algorithm. The comparison of experimental and numerical responses before and after calibration revealed significant improvements in the numerical model and a very good correlation between the responses obtained with the calibrated model and the experimental responses.

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.

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.