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

Highlights

• An improved, hybrid method for modal testing of full-scale structures.

• Combining ambient and artificial excitation using small shakers for modal identification.

• Increased confidence in finding accurate estimates of modal properties using hybrid excitation.

• Evaluation of output only modal identification algorithms on hybrid testing data.

Abstract

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.

Introduction

In recent decades, the evaluation of the actual behaviour of in-service bridges and their safety throughout life cycle via measurements of structural responses has been attracting increasing research efforts as an alternative to visual inspections or localised non-destructive tests [1], [2], [3], [4], [5], [6], [7], [8]. Particularly attractive are vibration measurements that can be processed for the estimation of the modal characteristics of bridges, as well as for the calibration of the finite element models (FEMs) used to simulate their behaviour. The information about the identified modal parameters and the updated FEMs can be used for design validation [9], [10], [11], [12], damage detection [13], [14], [15], [16] and structural health monitoring [17], [18], [19], [20], [21], [22].

The estimation of the modal characteristics often requires the application of system identification methods that process output-only, or ambient, vibrations, since for large-scale civil structures strong enough controlled input excitation cannot be directly imparted or measured in most practical situations. A variety of system identification techniques have been developed using only structural response data, which are typically referred to as operational modal analysis (OMA) or output-only modal analysis. The principal assumption made in the development of output-only identification techniques is that the input can be represented by a stationary white noise process. Stochastic techniques in the frequency domain, such as peak-picking [23], frequency domain decomposition [24] and maximum likelihood identification [25], have then been developed based on response auto and cross-spectral densities. However, due to limitations in frequency resolution as well as leakage errors, time domain methods are continuously being developed and enhanced. They arguably tend to provide better results, especially for large number of closely spaced modes hidden in the data. They usually can be subdivided into one-stage and two-stage methods. In the two stage approaches, firstly free vibration response is extracted from measurements based on random decrement functions or response correlation functions. Subsequently, modal parameters are identified using the classical system identification algorithms, e.g. the Ibrahim time domain method [26] or the least-squares complex exponential method [27], based on impulse or free response function estimates. In contrast to the two-stage approaches, one-stage system identification methods, such as the notable data-driven stochastic subspace identification (SSI-data) algorithm [28], [29], [30], can be used to identify modal parameters directly from the output-only measurements. Due to the advantage of state space representation of system dynamics in which the observation vector is separated from the system state vector, SSI-data has shown robustness in noise-contaminated testing environments and proved capable of yielding high quality modal identification results [31], [32], [33], [34], [35], [36]. However, its drawbacks are the computational effort and time required.

Amongst other state-of-the-art OMA techniques are the auto-regressive (AR) time series method [37], [38] and the eigensystem realization algorithm with observer/Kalman identification (ERA-OKID) [39], [40], which were originally developed for the identification of lightly damped linear structures in aerospace applications. They have shown good computational efficiency while preserving high identification accuracy. The parametric AR representations of measured responses capture the temporal covariances of the observed responses and can be converted into estimates of the natural frequencies, damping ratios and mode shapes of the structure. Recently, multivariate AR models have started to be applied to model the dynamic behaviour of vibrating structures and to infer their modal parameters when subjected to ambient vibration, such as industrial structures excited by hydro-electric generators or hydraulic pumps [41], [42], buildings [43] or cable stayed bridges [44].

In the ERA-OKID method, the observer/Kalman filter is used to remedy the lack of knowledge of initial conditions, extend the applicability of the ERA to general input-output systems, and create unique system Markov parameters. The ERA-OKID algorithm has proven to be very successful in several input–output cases [45], [46], [47]. In recent years, the ERA-OKID method has been extended to output-only measurements by splitting the state-space model into the deterministic and stochastic subsystems [48], [49], [50]. The strength of the ERA-OKID algorithm lies in the fact that the original state space equations are augmented with the observer gain for deriving the transformed state space model, which can eliminate the input and feedthrough matrices for large model orders, stabilize the system and increase its identification accuracy.

Although these two system identification algorithms can be found in civil engineering and SHM applications, their reliability and computational efficiency when confronted with full-scale, multiple span bridges have been poorly investigated, especially for comprehensive comparisons to the classical SSI-data method, which is better understood in these contexts. Such an application and comparisons are thus part of the focus of this paper.

The convenience of OMA continues to attract significant interest from both researchers and practitioners since bridge OMA tests will normally present none or only minimal disruption to the normal traffic. However, the natural excitation in ambient vibration testing (AVT) is always coloured noise, and thus the success of OMA techniques obviously depends on how close the excitation is to the principal white noise assumption. Notwithstanding, OMA has been invoked in testing of a wide range of short to medium-span bridges, including suspension structures [51], trusses [52] and arches [19]. However, AVT has shown some inherent drawbacks due to the variable nature of the actual excitation amplitude, direction, duration and frequency content which are, as per definition, not measured. For instance, the level of ambient excitation may be weak, or the frequency content may be narrow-band, and as a result only a limited number of modes can be extracted from the ambient data.

Missing modes have commonly been reported in AVT when compared to numerical structural models or alternative tests. Brownjohn et al. [53] reported difficulty in identifying the lateral modes of the Fatih Sultan Mehmet suspension bridge by utilising ambient traffic and wind excitation due to low vibrational levels. Alwash et al. [54] found that resonant response at the fundamental natural frequency could not be distinguished from background vibration, while higher modal responses could be identified in the case of environmental (wind and flowing water) excitation for testing of a three-span, 100.5 m long continuous reinforced concrete bridge. Chen et al. [36] pointed out that the fundamental lateral mode as well as several high order vertical modes failed to be extracted from the environmental excitation responses of a concrete motorway off-ramp bridge with 11 short to medium continuous spans. The uncertainty introduced by missing modes continues to challenge OMA, because it can have profound effects on the ultimate outcomes such as correct model updating or damage detection [55].

These challenges have seen an emergence and increased interest in hybrid vibration testing (HVT), where an artificial force is applied to the structure in addition to the ambient excitation, and a system model is identified using the response to such combined forcing [55], [56], [57], [58]. The main advantage of HVT is the ability to use excitation devices that are small and practical when compared to the exciters needed for the traditional experimental modal analysis (e.g. eccentric mass shakers), which are heavy and difficult to transport, since the amplitude of the artificial forces needed for HVT can be equal to, or even lower than, the amplitude of the ambient forces. HVT has been explored by Reynders et al. for the modal system identification of the Z24 bridge [57], a steel arch footbridge and a concrete stressed-ribbon footbridge [58]. In-depth comparisons with numerical models and other tests showed that the modal parameters obtained from the HVT are of good quality [58]. HVT-based FEM updating and bridge structural damage identification reported in [57] delivered improved well-posedness of the updating problem and allowed detecting inaccuracies in the FEM.

However, previous research efforts [57], [58] utilized either a drop weight system or a pneumatic artificial muscle to provide excitation for the implementation of HVT. Only in [56] a preliminary effort to use small electromagnetic shakers on a 13-storey reinforced concrete building was reported. Light-weight electrodynamic shakers [56], [59] can easily provide a specific, controllable excitation signal, such as a single or multiple concurrent sines, periodic, random, swept sine etc. We therefore propose herein, as our first contribution, that light electrodynamic shakers be utilized in HVT to provide the controlled artificial dynamic excitation to a multiple-span post-tensioned segmental concrete bridge to enable more robust and reliable dynamic analysis. To the best knowledge of the authors, small shakers with sweep or chirp excitation have not yet been used in HVT.

Furthermore, the previous work on HVT is restricted to only selected system identification methods, such as the reference-based combined deterministic-stochastic subspace identification [55]. The input artificial force needs be measured, which may not be favoured or convenient for the civil engineering practitioner working in challenging field conditions. Thus, there still exists a gap in exploring the HVT combined with output-only identification techniques popular for modal identification in the civil engineering community. The present study, on the other hand, explores output-only identification algorithms for extracting structural modal parameters from HVT, taking the advantages of both AVT (no requirement for input measurement) and increased excitation levels provided by HVT but using only small and practical actuators. Two different output-only time-domain system identification algorithms, i.e. AR and ERA-OKID, were employed to recover modal frequencies, damping ratios and mode shapes from the corresponding vibration response data. The SSI-data system identification algorithm was also applied to experimental data in order to compare the former algorithms’ performance in terms of mode identifiability, result quality and computational effort. Modal identification results are also obtained from pure AVT to highlight the improvements brought about by HVT. Furthermore, a detailed FEM was developed and used to calculate bridge vibration modes theoretically. The correlation analysis between experimentally and numerically derived modal parameters were conducted to obtain a further insight into the modal identifiability and identification reliability of the proposed HVT methodology. The application of OMA system identification techniques to HVT and thorough evaluation of their performance is our second contribution.

The following text is structured as follows. First, the bridge structural system and FE modelling are presented. Then, the choice of actuators and the proposed experimental program of the AVT and HVT are discussed. Next, the theory behind the modal system identification techniques adopted is briefly overviewed. The results of modal identification are then thoroughly discussed. The article ends with the conclusions drawn from the tests that summarise the key findings of the paper.