Ting Kau Research Articles

Bayesian dynamic linear model framework for structural health monitoring data forecasting and missing data imputation during typhoon events

A Bayesian dynamic linear model (BDLM) framework for data modeling and forecasting is proposed to evaluate the performance of an operational cable-stayed bridge, that is, Ting Kau Bridge in Hong Kong, by using SHM strain field data acquired. One of the major challenges in dealing with the existing in-service bridge under extreme typhoon loads is to forecast structural behavior using the typhoon response exhibiting non-stationarity, large data fluctuations and strong randomness. The first attempt for SHM data modeling during extreme events, that is, typhoons, using BDLM framework, was conducted in this study. The data from multiple sensors are analyzed for one-step, multi-step ahead forecasting and missing data imputation. The overall bridge behavior is incorporated into a forecasting model by superposition of forecasting results of trend (representing the structural baseline response), periodic component (response component evolving regularly over time), and autoregressive component (time-dependent error) through BDLM algorithm. The results demonstrate that the BDLM framework yielded more accurate calculations compared with Gaussian process and Variational Heteroscedasticity Gaussian Process methods with respect to one-step ahead forecasting for strain data under typhoons. Multi-step ahead forecasting was successfully carried out both for non-typhoon and typhoon responses within an acceptable precision range. The correlation between periodic component and temperature was also investigated. Regarding missing data imputation, BLDM algorithm can generate robust results due to making full use of the monitoring data both before and after the missing segments.

Practical model updating of the Ting Kau Bridge through the MCMC-based Bayesian algorithm utilizing measured modal parameters

Bayesian model updating framework provides a reliable method for building high-fidelity finite element models (FEMs). To realize the efficient model updating of large-scale civil engineering structures, a practical Bayesian inference framework based on software interaction is proposed. The newly developed framework was applied to update the FEM of a long-span cable-stayed bridge, Ting Kau Bridge in Hong Kong, utilizing measured modal parameters from the literature. The model updating results are found to be highly sensitive to the selection of model classes. Furthermore, the area of the main girder of the bridge deck is a key parameter influencing the lower modes of the cable-stayed bridge. A full-scale vehicular load test is conducted on the Ting Kau Bridge to obtain the displacement influence line through the data recorded by GPS sensors on the bridge. The set of measured influence lines is employed to verify the accuracy of the updated FEM. The results demonstrate that the characteristics of the FEM updated using the proposed Bayesian model updating framework based on measured dynamic properties are consistent with the structural characteristics of the bridge. The proposed framework can facilitate the structural health monitoring of large-scale civil engineering structures.

Engineering performance of two analytical methodologies for estimating modal parameter uncertainty for structures

Stochastic subspace identification (SSI) and Bayesian methods are now the main representative approaches for high-performance system identification and uncertainty quantification. Both methods have been extensively used in engineering applications for the last 10 years despite them having quite different views in principle. However, no comparison has been carried out to inform which method is actually better for engineering applications in terms of modal identification accuracy, uncertainty quantification, and so forth. This paper therefore investigates the differences between these two quantifications of parameter uncertainty in system identification. Synthetic data for a six-degree-of-freedom spring–mass numerical system are first studied to compare their identification accuracy and applicable conditions. The investigation is then extended to field data from actual structures, which involves ambient modal testing of Heritage Court Tower in Canada, Canton Tower in China, and Ting Kau Bridge in Hong Kong. Results from the synthetic data show that, under white-noise excitation, identified modal parameters and quantified uncertainty for both methods are highly consistent with the values of frequentist statistics. However, when the excitation is not white noise, there may be some spurious modes identified via SSI, and the uncertainty quantified under colored-noise excitation via SSI is almost always larger than those under white noise, while the Bayesian method is not disturbed. Results for the structural field data indicate that in general applications under environmental excitation the identified modal parameters from both methods are almost identical; the quantified uncertainty of the SSI method is slightly larger than that of the Bayesian method, but they are of the same order of magnitude and can meet engineering requirements.

Automatic identification of modal parameters for structures based on an uncertainty diagram and a convolutional neural network

A novel method for automatic identification of structural modal parameters is proposed, based on new developments in both uncertainty quantification for stochastic subspace identification and deep learning. An uncertainty diagram is first constructed to visualize uncertainty estimates, for clearly distinguishing spurious modes. Because the uncertainty of spurious modes is significantly larger than that of the real ones, a convolutional neural network (CNN) is adopted to automatically analyse the uncertainty diagram and efficiently determine the physical structural modes. The method is then applied to identify modal parameters for a six-degree-of-freedom spring–mass model, the Heritage Court Tower building in Canada, and the Ting Kau Bridge in Hong Kong. Results indicate for all three structures that the constructed CNN is effective for analysing the uncertainty diagram and can automatically and accurately obtain the real modes.

Automatic operational modal analysis of structures based on image recognition of stabilization diagrams with uncertainty quantification

A novel automatic operational modal analysis method is proposed based on the image recognition of stabilization diagrams with uncertainty quantification. The method not only enriches the contents of the stabilization diagrams to make them much clearer—it can also avoid heavy manual analysis of the stabilization diagrams by automatically obtaining operational modal parameters. In order to increase the efficiency in identifying modal parameters of structures, a traditional stabilization diagram is re-constructed to convey the uncertainty estimates. These stabilization diagrams are then resolved into single mode stabilization diagrams (SMSDs) with a specified frequency interval, for image recognition. Subsequently, a convolutional neural network (CNN) is adopted to automatically analyze the SMSDs. In this study, the CNN is trained by the SMSDs derived from the stabilization diagrams of two numerical examples and three engineering structures. The trained CNN is then validated with a 6 degree-of-freedom model, the Heritage Court Tower building, and the Ting Kau Bridge. The robust learning and prediction results establish that the constructed CNN is effective for analyzing the stabilization diagrams of different structures. It can automatically and accurately identify the physical modes on the stabilization diagrams, without extracting any characteristic parameters.

A new fatigue reliability analysis method for steel bridges based on peridynamic theory

A fatigue reliability model based on the peridynamic (PD) theory was proposed to analyze the fatigue performance of steel bridges in this study. Different from previous methods based on classical continuum mechanics, the PD model does not require additional criteria to guide the growth of crack or damage. In particular, the influence of fatigue threshold value was considered in a systematic formula, and the response surface method was utilized to analyze fatigue failure probability. The proposed model was applied to complex fatigue phenomena such as spontaneous crack nucleation, crack branching, and fatigue failure under biaxial cyclic loadings where fatigue crack paths interact in complicated ways. The fatigue crack growth pattern, fatigue life, and fatigue reliability of specimens considering the biaxial or uniaxial fatigue loadings were analyzed. The accuracy of the fatigue model was verified through a series of comparisons with the experimental, analytical, and FEM results. The effectiveness of the proposed method was also demonstrated in the application to the fatigue reliability analysis of the Ting Kau Bridge.

Optimal sensor placement for damage detection of bridges subject to ship collision

Ship collisions threaten the safety of bridges over navigable waterways in modern times. Postcollision damage and condition assessment is thus of significant importance for decision making on whether closure of bridge to traffic is necessary and for planning the consequent bridge strengthening or retrofitting. Online structural health monitoring systems provide a unique approach to monitor bridge responses during ship collisions and detect the structural damage. The damage information contained in the monitoring data, which is critical for damage detection, however, is largely dependent on the sensor layout. In this paper, an optimal sensor placement method targeting postcollision damage detection of bridges is proposed for selecting the optimal sensor set so that the measured data are most informative for damage detection. The sensor configuration is optimized by a multi-objective optimization algorithm, which simultaneously minimizes the information entropy index for each possible ship-bridge collision scenario. One advantage of the proposed method is that it can handle the uncertainty of ship collision position. It also guarantees a redundancy of sensors for the most informative regions and leaves a certain freedom to determine the critical elements for monitoring. The proposed method is applicable in practice to determine the sensor placement, prior to field testing, with the intention of identifying postcollision damage. The cable-stayed Ting Kau bridge in Hong Kong is employed to demonstrate the feasibility and effectiveness of the proposed method.

Fatigue reliability assessment considering traffic flow variation based on weigh-in-motion data

The remaining service life of a bridge is an important criterion for the bridge master to make decisions of maintenance and rehabilitation. In the assessment of fatigue problems of steel and composite bridges, a crucial step is to determine the fatigue stress spectra, which are usually obtained through field measurements. In this study, the standard fatigue vehicle spectrum of Ting Kau Bridge in Hong Kong is obtained from the dynamic weigh-in-motion system that monitors the traffic flow and volume and axle and gross vehicle weights. An advanced probabilistic loading model is proposed to simulate the vehicles running along the bridge based on measurements from the weigh-in-motion system considering not only the diurnal variations of traffic flow within different time intervals but also the rate of change of the annual traffic. The statistical fatigue reliability assessment at critical locations can then be carried out to estimate the remaining service life of the bridge.

Optimal reduction from an initial sensor deployment along the deck of a cable-stayed bridge

The ambient vibration measurement is an output-data-only dynamic testing where natural excitations are represented, for instance, by winds and typhoons. The modal identification involving output-only measurements requires the use of specific modal identification techniques. This paper presents the application of a reliable method (the Stochastic Subspace Identification - SSI) implemented in a general purpose software. As a criterion toward the robustness of identified modes, a bio-inspired optimization algorithm, with a highly nonlinear objective function, is introduced in order to find the optimal deployment of a reduced number of sensors across a large civil engineering structure for the validation of its modal identification. The Ting Kau Bridge (TKB), one of the longest cable-stayed bridges situated in Hong Kong, is chosen as a case study. The results show that the proposed method catches eigenvalues and eigenvectors even for a reduced number of sensors, without any significant loss of accuracy.

Investigation of modal identification and modal identifiability of a cable-stayed bridge with Bayesian framework

In this study, the Bayesian probabilistic framework is investigated for modal identification and modal identifiability based on the field measurements provided in the structural health monitoring benchmark problem of an instrumented cable-stayed bridge named Ting Kau Bridge (TKB). The comprehensive structural health monitoring system on the cable-stayed TKB has been operated for more than ten years and it is recognized as one of the best test-beds with readily available field measurements. The benchmark problem of the cable-stayed bridge is established to stimulate investigations on modal identifiability and the present paper addresses this benchmark problem from the Bayesian prospective. In contrast to deterministic approaches, an appealing feature of the Bayesian approach is that not only the optimal values of the modal parameters can be obtained but also the associated estimation uncertainty can be quantified in the form of probability distribution. The uncertainty quantification provides necessary information to evaluate the reliability of parametric identification results as well as modal identifiability. Herein, the Bayesian spectral density approach is conducted for output-only modal identification and the Bayesian model class selection approach is used to evaluate the significance of different modes in modal identification. Detailed analysis on the modal identification and modal identifiability based on the measurements of the bridge will be presented. Moreover, the advantages and potentials of Bayesian probabilistic framework on structural health monitoring will be discussed.

Structural damage alarming and localization of cable-supported bridges using multi-novelty indices: a feasibility study

This paper presents a feasibility study on structural damage alarming and localization of long-span cable-supported bridges using multi-novelty indices formulated by monitoring-derived modal parameters. The proposed method which requires neither structural model nor damage model is applicable to structures of arbitrary complexity. With the intention to enhance the tolerance to measurement noise/uncertainty and the sensitivity to structural damage, an improved novelty index is formulated in terms of auto-associative neural networks (ANNs) where the output vector is designated to differ from the input vector while the training of the ANNs needs only the measured modal properties of the intact structure under in-service conditions. After validating the enhanced capability of the improved novelty index for structural damage alarming over the commonly configured novelty index, the performance of the improved novelty index for damage occurrence detection of large-scale bridges is examined through numerical simulation studies of the suspension Tsing Ma Bridge (TMB) and the cable-stayed Ting Kau Bridge (TKB) incurred with different types of structural damage. Then the improved novelty index is extended to formulate multi-novelty indices in terms of the measured modal frequencies and incomplete modeshape components for damage region identification. The capability of the formulated multi-novelty indices for damage region identification is also examined through numerical simulations of the TMB and TKB.

Investigation of mode identifiability of a cable-stayed bridge: comparison from ambient vibration responses and from typhoon-induced dynamic responses

Modal identification of civil engineering structures based on ambient vibration measurement has been widely investigated in the past decades, and a variety of output-only operational modal identification methods have been proposed. However, vibration modes, even fundamental low-order modes, are not always identifiable for large-scale structures under ambient vibration excitation. The identifiability of vibration modes, deficiency in modal identification, and criteria to evaluate robustness of the identified modes when applying output-only modal identification techniques to ambient vibration responses were scarcely studied. In this study, the mode identifiability of the cable-stayed Ting Kau Bridge using ambient vibration measurements and the influence of the excitation intensity on the deficiency and robustness in modal identification are investigated with long-term monitoring data of acceleration responses acquired from the bridge under different excitation conditions. It is observed that a few low-order modes, including the second global mode, are not identifiable by common output-only modal identification algorithms under normal ambient excitations due to traffic and monsoon. The deficient modes can be activated and identified only when the excitation intensity attains a certain level (e.g., during strong typhoons). The reason why a few low-order modes fail to be reliably identified under weak ambient vibration excitations and the relation between the mode identifiability and the excitation intensity are addressed through comparing the frequency-domain responses under normal ambient vibration excitations and under typhoon excitations and analyzing the wind speeds corresponding to different response data samples used in modal identification. The threshold value of wind speed (generalized excitation intensity) that makes the deficient modes identifiable is determined.

Damage Localization of Cable-Supported Bridges Using Modal Frequency Data and Probabilistic Neural Network

This paper presents an investigation on using the probabilistic neural network (PNN) for damage localization in the suspension Tsing Ma Bridge (TMB) and the cable-stayed Ting Kau Bridge (TKB) from simulated noisy modal data. Because the PNN approach describes measurement data in a Bayesian probabilistic framework, it is promising for structural damage detection in noisy conditions. For locating damage on the TMB deck, the main span of the TMB is divided into a number of segments, and damage to the deck members in a segment is classified as one pattern class. The characteristic ensembles (training samples) for each pattern class are obtained by computing the modal frequency change ratios from a 3D finite element model (FEM) when incurring damage at different members of the same segment and then corrupting the analytical results with random noise. The testing samples for damage localization are obtained in a similar way except that damage is generated at locations different from the training samples. For damage region/type identification of the TKB, a series of pattern classes are defined to depict different scenarios with damage occurring at different portions/components. Research efforts have been focused on evaluating the influence of measurement noise level on the identification accuracy.

Effect of baseline calibration on assessment of long-term performance of cable-stayed bridges

To enable the long-term health monitoring and condition assessment of a long-span cable-stayed bridge, a reasonable baseline finite element model to reflect the current structural behaviour is indispensable. With proper calibration, the model provides realistic predictions of the static and dynamic behaviour. This paper describes the development of baseline model of Ting Kau Bridge in Hong Kong using the cable forces as the basic parameters, with the measured frequencies and the initial equilibrium configuration of the bridge as the reference. Methods to estimate the fatigue lives of structural components are reviewed with special attention paid to the mean stress effect. The short-term performance and long-term performance of Ting Kau Bridge are studied based on both the initial model without baseline calibration and the baseline model. While the stress amplitudes due to moving loads do not change much, the mean stresses do change at many critical locations. As the mean stress effect is significant in the estimation of fatigue lives, baseline calibration of cable-stayed bridges is considered essential.

Major bridge development in Hong Kong, China-past, present and future

The first “modern” type of vehicular bridge was built in Hong Kong China in the 1920s. The need for an efficient transportation system to cope with population growth and enable economic development has demanded the construction of more and more bridges since the middle of the 20th century. By 2007, Hong Kong had a total of about 1300 vehicular bridges. Four of these bridges, including the Tsing Ma Bridge, Kap Shui Mun Bridge, Ting Kau Bridge, and the cable-stayed bridge on the Hong Kong-Shenzhen Western Corridor, are considered to be major bridges supported by cables. Currently, the Stonecutters Bridge on Route No. 8 is under construction and is expected to be completed in late 2009. At the same time, the Hong Kong-Zhuhai-Macao Bridge will be in its detailed design stage soon. While efforts have been made by bridge builders to construct these giant structures, the upkeeping of these valuable assets at a high standard and ensuring their continuous functioning and performance during their intended lifespans will be another important task for bridge engineers. Wind and structural health monitoring system (WASHMS) will play a key role in this respect.

Simulation of vibrations of Ting Kau Bridge due to vehicular loading from measurements

The Ting Kau Bridge in Hong Kong is a cable-stayed bridge comprising two main spans and two side spans. The bridge deck is supported by three towers, an end pier and an abutment. Each of the three towers consists of a single reinforced concrete mast strengthened by transverse cables and struts. The bridge deck is supported by four inclined planes of cables emanating from anchorages at the tower tops. In view of the heavy traffic on the bridge, and threats from typhoons and earthquakes originated in areas nearby, the dynamic behaviour of long-span cable-supported bridges in the region is always an important consideration in their design. Baseline finite element models of various levels of sophistication have been built not only to match the bridge geometry and cable forces specified on the as-constructed drawings but also to be calibrated using the vibration measurement data captured by the Wind and Structural Health Monitoring System. This paper further describes the analysis of axle loading data, as well as the generation of random axle loads and simulation of vibrations of the bridge using the finite element models. Various factors affecting the vehicular loading on the bridge will also be examined.

Eliminating Temperature Effect in Vibration-Based Structural Damage Detection

False-positive or false-negative damage may be signaled by vibration-based structural damage detection methods when the environmental effects on the changes of dynamic characteristics of a structure are not accounted for appropriately. In this paper, a parametric approach for eliminating the temperature effect in vibration-based structural damage detection is proposed that is applicable to structures where dynamic properties and temperature are measured. First, a correlation model between damage-sensitive modal features and temperature is formulated with the back-propagation neural network (BPNN) technique. With the correlation model, the modal features measured under different temperature conditions are normalized to an identical reference status of temperature to eliminate the temperature effect. The normalized modal features are then applied for structural damage identification. The proposed approach is examined in the instrumented Ting Kau Bridge in Hong Kong. Using the long-term monitoring data of both modal frequencies and temperatures, a BPNN correlation model with validated generalization capability is formulated, and the normalized modal frequencies before and after damage are derived and applied for the structural damage alarm using the autoassociative neural network (AANN)–based novelty detection technique. The proposed approach is competent for eliminating the temperature effect and eschewing the false-positive damage alarm that originally occurred when using the measured modal frequencies directly. Case studies assuming damage at different structural components of the bridge are carried out to verify the proposed approach and the detectability of damage using the AANN-based novelty detection technique. The results show that the approach can detect damage when the damage-induced frequency change is as small as 1%. Nevertheless, it is worth mentioning that the frequency-based approach is most effective for detecting damage of a certain severity rather than detecting the onset of damage.

The Finite Element Models for the Built Ting Kau Bridge

The Ting Kau Bridge in Hong Kong is a cable-stayed bridge comprising two main spans and two side spans. The bridge deck is supported by three towers, an end pier and an abutment. Each of the three towers consists of a single reinforced concrete mast which reduces its section in steps, and it is strengthened by transverse cables and struts in the transverse vertical plane. The bridge deck is supported by four inclined planes of cables emanating from anchorages at the tower tops. In view of the heavy traffic on the bridge, and threats from typhoons and earthquakes originated in areas nearby, the dynamic behaviour of long-span cable-supported bridges in the region is always an important consideration both in their design and health monitoring. This paper describes the development of the 3D grid model for the structural health monitoring of the bridge. The 3D grid model is intended to form the backbone of subsequent multi-scale finite element models for bridge rating. The baseline model is built up and calibrated to match the bridge geometry and cable forces specified on the as-built drawings. The modelling of the concrete deck in the simplified grid model is an important issue as it has great effect on the lateral and torsional vibrations of the bridge. This paper examines in particular the shear lag effect on the modelling strategy.

Structural damage alarming using auto-associative neural network technique: Exploration of environment-tolerant capacity and setup of alarming threshold

With the intention of avoiding false-positive and false-negative alarms in structural damage alarming using the auto-associative neural network (AANN) technique, two issues pertaining to this technique are addressed in this study. The first issue explored is the environment-tolerant capacity of the AANN. Efforts have been made to seek a generalization technique to enhance the environment-tolerant capacity. First, a baseline AANN model is formulated using the conventional training algorithm. Generalization techniques including AIC and FPE, early stopping, and Bayesian regularization are then investigated, resulting in three new AANN models. Their environment-tolerant capacity is evaluated as per their capability to avoid false-positive and false-negative alarms. The other issue addressed is the setup of alarming threshold, with intent to reduce the uncertainty in AANN-based structural damage alarming. A procedure based on the probability analysis of the novelty index is proposed for this purpose. First, the novelty index characterizing the intact structure is analyzed by the Kolmogorov–Smirnov goodness-of-fit test to obtain its best-fit continuous probability distribution. A confidence interval is then defined in consideration of the compromise between type I and type II errors. The alarming threshold of the novelty index is consequently set at the upper limit of the confidence interval. The above explorations are examined by using the long-term monitoring data on modal properties of the cable-stayed Ting Kau Bridge. The capability to eliminate false-positive alarm is verified by using unseen testing data which were not used in formulating the AANN models, while the capability to alleviate false-negative alarm is examined by using simulated data from the ‘damaged’ bridge with the help of a precise finite element model. The study indicates that the early stopping technique performs best in improving the environment-tolerant capacity of the AANN, and the alarming threshold set by the proposed procedure helps to reduce the uncertainty in AANN-based structural damage alarming.

Constructing input to neural networks for modeling temperature-caused modal variability: Mean temperatures, effective temperatures, and principal components of temperatures

In this study, the construction of appropriate input to neural networks for modeling the temperature-caused modal variability is addressed with intent to enhance the reproduction and prediction capabilities of the formulated correlation models. Available for this study are 770 h modal frequency and temperature data that were obtained from the instrumented cable-stayed Ting Kau Bridge in Hong Kong. With the temperature data measured at different portions of the bridge, three kinds of input, i.e., mean temperatures, effective temperatures, and principal components (PCs) of temperatures, are constructed as input to neural networks for modeling the correlation between the modal frequencies and environmental temperatures. By dividing the 770 h modal frequency and temperature data into training data set, validation data set and testing data set, an optimally configured back-propagation neural network (BPNN) is formulated for each kind of input, in which the validation data are utilized to determine the optimal number of hidden nodes while the early stopping technique is applied to optimize the BPNN parameters. Then the reproduction and prediction performance of the BPNNs configured with the three kinds of input is examined and compared in respect of the seen training data set and the unseen testing data set, respectively. It is revealed that the temperature profile characterized by the effective temperatures is insufficient for formulating a good correlation model between the modal frequencies and temperatures. When a sufficient number of PCs are used, the BPNN with input of the PCs of temperatures performs better than the BPNN with input of the mean temperatures in both reproduction and prediction capabilities.