The real-time identification of time-varying cable force is critical for accurately evaluating the fatigue damage of cables and assessing the safety condition of bridges. In the context of unknown wind excitations and only one available accelerometer, this paper proposes a novel cable force identification method based on an improved adaptive extended Kalman filter (IAEKF). Firstly, the governing equation of the stay cable motion, which includes the cable force variation coefficient, is expressed in the modal domain. It is transformed into a state equation by defining an augmented Kalman state vector with the cable force variation coefficient concerned. The cable force variation coefficient is then recursively estimated and closely tracked in real time by the proposed IAEKF. The contribution of this paper is that an updated fading-factor matrix is considered in the IAEKF, and the adaptive noise error covariance matrices are determined via an optimization procedure rather than by experience. The effectiveness of the proposed method is demonstrated by the numerical model of a real-world cable-supported bridge and an experimental scaled steel stay cable. Results indicate that the proposed method can identify the time-varying cable force in real time when the cable acceleration of only one measurement point is available.

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Real-Time Identification of Time-Varying Cable Force Using an Improved Adaptive Extended Kalman Filter

Data-driven methods for structural condition assessment have been extensively investigated using deep learning (DL). However, studies on quasi-static response data-based structural health diagnoses are relatively insufficient. The difficulty is that quasi-static response data contain coupled effects of structural parameters and external loads. Considering that the correlation between quasi-static responses subjected to identical external loads is only a function of structural parameters and independent from the external loads, the correlation can therefore be employed as an indicator of the structural condition. This study proposes a condition assessment approach for cable-stayed bridges based on correlation modeling between the deflection of girders and tension in cables. The correlation is modeled by an unsupervised DL network comprising two variational autoencoders (AE) and two generative adversarial networks (GANs). The input and output are marginal probability density functions (PDFs). The DL network is trained as the reconstruction and translation processes to model the intra-class and inter-class correlations. Assumptions of shared latent space and cycle consistency are taken to ensure mutual modeling capacity. The Wasserstein distance between the predicted and ground-truth PDFs of tension in cables is used as an indicator of the structural condition. Using probabilistic correlation of quasi-static responses only requires the PDF of external loads to be identical and does not need the external loads to be precisely identical at any moment, thus relieving time-synchronization restrictions for different sensors. The results show that the predicted PDFs agree well with the ground-truth values under normal conditions. Furthermore, the Wasserstein distance is sensitive to damage and shows noticeable variations when the damage of the stay cable occurs.

Unsupervised deep learning method for bridge condition assessment based on intra-and inter-class probabilistic correlations of quasi-static responses

On-board monitoring of track irregularities and bridge dynamic characteristics based on vehicle vibration responses provides basic data for the condition assessment of high speed railway bridges. However, the identification process inevitably introduces estimation uncertainty because of measurement noise and system parameter uncertainty. Here, in a probability framework, we propose a recursive Bayesian Kalman filtering (RBKF) algorithm for quantifying the identification uncertainty of the track irregularities and bridge natural frequencies. A nonlinear state-space model with measurement noise and process noise was first established for vehicle-bridge (VB) systems. Then the RBKF algorithm was formulated using a nonlinear state-space model, and the identification uncertainty was quantified in terms of estimation variances. A numerical study of two high speed railway bridges validated the RBKF algorithm. This study may help develop new approaches for on-board monitoring and condition assessment of high speed railway bridges. 

Identification of Frequencies and Track Irregularities of Railway Bridges Using Vehicle Responses: A Recursive Bayesian Kalman Filter Algorithm

Indirect method to identify dynamic properties of bridge by a passing vehicle is attractive recently since it does not require pre-installed sensors on bridge. However, the extracted dynamic properties are not accurate enough to identify local damages due to road surface roughness. To overcome this issue, a method to identify mode shapes and detect local damages in a simply supported bridge by movable sensory system is proposed in this study. Instead of using passing vehicles, two stationary vehicles are adopted in this study to perform as movable sensory system. They stay stationary at two different locations on the bridge subject to ambient environmental excitation, and their vertical accelerations are collected to calculate the vertical displacement of the two contact points between vehicles and bridge. Then they move to another two locations and the same procedures are repeated. After all locations along the bridge are tested, a matrix similar to frequency response matrix can be constructed and SVD method is used to extract the mode shapes. The element stiffness is thereafter evaluated by the fundamental mode shape, which can be then used to detect local stiffness reduction in the bridge. Numerical study has been conducted to validate the proposed method, and the effect of bridge damping, vehicle damping, measurement noise, and traffic flow is investigated. Moreover, field testing was conducted on Li-Zi-Wan Bridge and the results showed that the proposed method can re-construct the mode shapes and evaluate element bending stiffness as accurately as conventional direct approach. The proposed method is convenient and easy to implement in practice; and it is more robust because it is not affected by road surface roughness. 

Mode Shape Identification and Damage Detection of Bridge by Movable Sensory System

Indirect method to identify dynamic properties of bridge by a passing vehicle is attractive recently since it does not require pre-installed sensors on bridge. However, the extracted dynamic properties are not accurate enough to identify local damages due to road surface roughness. To overcome this issue, a method to identify mode shapes and detect local damages in a simply supported bridge by movable sensory system is proposed in this study. Instead of using passing vehicles, two stationary vehicles are adopted in this study to perform as movable sensory system. They stay stationary at two different locations on the bridge subject to ambient environmental excitation, and their vertical accelerations are collected to calculate the vertical displacement of the two contact points between vehicles and bridge. Then they move to another two locations and the same procedures are repeated. After all locations along the bridge are tested, a matrix similar to frequency response matrix can be constructed and SVD method is used to extract the mode shapes. The element stiffness is thereafter evaluated by the fundamental mode shape, which can be then used to detect local stiffness reduction in the bridge. Numerical study has been conducted to validate the proposed method, and the effect of bridge damping, vehicle damping, measurement noise, and traffic flow is investigated. Moreover, field testing was conducted on Li-Zi-Wan Bridge and the results showed that the proposed method can re-construct the mode shapes and evaluate element bending stiffness as accurately as conventional direct approach. The proposed method is convenient and easy to implement in practice; and it is more robust because it is not affected by road surface roughness.

The identification of time-varying physical parameters of nonlinear systems is still a challenging task. Limited studies based on the wavelet multiresolution analysis (WMA) have been attempted, which requires full measurements of structural displacement, velocity and acceleration responses of all degrees of freedom and exact information of external excitations. This limits the engineering application of these methods. This paper proposes approaches to identify the time-varying physical parameters of nonlinear structures in three cases using only partially measured structural responses. Firstly, the identification of time-varying nonlinear structures with a small number of elements under known excitations is discussed. The fading-factor unscented Kalman filter (FUKF) method is applied to locate the time-varying parameters, and the WMA integrated with UKF method is employed using partially measured acceleration responses. Secondly, it is further extended to the identification of time-varying nonlinear structures with a small number of elements but under unknown excitations. An improved fading-factor unscented Kalman filter under unknown input (FUKF-UI) method is proposed to locate the time-varying parameters, and WMA integrated with UKF-UI method is utilized with partially observed acceleration and displacement responses. Thirdly, for practical engineering applications, the identification of time-varying nonlinear structure with more elements under unknown excitations is conducted. The proposed FUKF-UI method is employed to locate the time-varying parameters of the whole structure. Then, the whole structure is divided into several substructures and the unknown interaction forces are regarded as the fictitious unknown inputs to the substructure. Thus, physical parameters of each substructure can be identified in parallel by the combination of WMA and UKF-UI. Three numerical studies corresponding to these three cases are conducted, respectively, to demonstrate the effectiveness and accuracy of the proposed methods.

Ning Yang

Papers

Identification of time-varying nonlinear structural physical parameters by integrated WMA and UKF/UKF-UI