Shu-Hsien Chao

Application of singular spectrum analysis to structural monitoring and damage diagnosis of bridges

Singular spectrum analysis (SSA) is a novel technique and has proven to be a powerful tool for time series data analysis. Through singular value decomposition of Hankel matrix data, the time series of data can be decomposed into several simple, independent and identifiable components from singular values and singular vectors. It has already been widely applied to process climatic, meteorological, geophysical and economic data. In this paper, we demonstrate that the coupling degree of the 1st and 2nd singular values in SSA contains useful indications on the feature and composition of the analysed signal. The proposed method is successfully applied to the monitoring of structure, such as damage detection of the simulated dynamic system, experimental steel frame, bridge foundation scouring and pier settlement in the laboratory and on-site bridge monitoring during typhoon strike. The proposed algorithm is simple and suitable for structural health monitoring in the field.

Structural damage assessment using output-only measurement: Localization and quantification

In this article, a systematic way of structural damage assessment algorithm, including identification of damage location and damage quantification, is proposed using output-only measurement. First, the null-space-based and subspace-based damage detection methods are used to confirm the damage severity of a structure. Then, the stochastic subspace identification technique is adopted to identify the time-varying system natural frequencies from the global response measurement. Finally, the novelty index, defined as the Euclidean norm of the time–frequency Hilbert amplitude spectrum of measurement between the intact and the damaged structures, is applied to locate the damage. To quantify the damage, the complete system realization is obtained from the identified modal properties through stochastic subspace identification method. From which, the inter-story stiffness reduction ratio can be identified using the normalized stiffness matrix. For case of limited measurement, the multi-setup operational modal analysis is applied to construct the complete system matrix. Verification of the proposed damage assessment algorithm using response data from a series of shaking table test of a six-story steel structure with the cut in column member to simulate the damage is demonstrated.

Uncertainty calculation for modal parameters used with stochastic subspace identification: an application to a bridge structure

Stochastic subspace identification method (SSI) has been proven to be an efficient algorithm for the identification of liner-time-invariant system using multivariate measurements. Generally, the estimated modal parameters through SSI may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, finite number of data samples etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the stabilization diagram can help users to identify the correct model, i.e. through removing the spurious modes. Modal parameters are estimated at successive model orders where the physical modes of the system are extracted and separated from the spurious modes. Besides, an uncertainty computation scheme was derived for the calculation of uncertainty bounds for modal parameters at some given model order. The uncertainty bounds of damping ratios are particularly interesting, as the estimation of damping ratios are difficult to obtain. In this paper, an automated stochastic subspace identification algorithm is addressed. First, the identification of modal parameters through covariance-driven stochastic subspace identification from the output-only measurements is used for discussion. A systematic way of investigation on the criteria for the stabilization diagram is presented. Secondly, an automated algorithm of post-processing on stabilization diagram is demonstrated. Finally, the computation of uncertainty bounds for each mode with all model order in the stabilization diagram is utilized to determine system natural frequencies and damping ratios. Demonstration of this study on the system identification of a three-span steel bridge under operation condition is presented. It is shown that the proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance the robustness and reliability in structural health monitoring.

Structural Damage Assessment Using Output-Only Measurement: Localization and Quantification

One of the important issues to conduct the damage detection of a structure using vibration-based damage detection (VBDD) is not only to detect the damage but also to locate and quantify the damage. In this paper a systematic way of damage assessment, including identification of damage location and damage quantification, is proposed by using output-only measurement. Four level of damage identification algorithms are proposed. First, to identify the damage occurrence, null-space and subspace damage index are used. The eigenvalue difference ratio is also discussed for detecting the damage. Second, to locate the damage, the change of mode shape slope ratio and the prediction error from response using singular spectrum analysis are used. Finally, to quantify the damage the RSSI-COV algorithm is used to identify the change of dynamic characteristics together with the model updating technique, the loss of stiffness can be identified. Experimental data collected from the bridge foundation scouring in hydraulic lab was used to demonstrate the applicability of the proposed methods. The computation efficiency of each method is also discussed so as to accommodate the online damage detection.Copyright

Vibration-based damage identification of reinforced concrete member using optical sensor array data

Detect and locate the structural damage from direct measurements can be done only when the sensors are very closely located to the damage initiating point, which is generally impossible to predict, particularly for the reinforced concrete structures. With the availability of high resolution distributed sensing, using optical tracker on light targets, the damage location as well as the level of damage can be identified. The objective of this paper is to conduct structural system identification of reinforced concrete frame by using the proposed structural integrity index (identify element curvature and null-space damage index) and the estimation of finite element strain. Finally, discussion on the identified time-varying system natural frequency and stiffness/strength degradation of the reinforced concrete structure from global measurement in relating to the calculated structural integrity index using optical sensing array data and element strain on the identification of damage location and damage severity are presented.

Application of Singular Spectrum Analysis to Bridge Structure Health Monitoring and Damage Detection

Singular Spectrum Analysis (SSA) is a novel technique and has proven to be a powerful tool for time data series analysis. It takes singular value decomposition (SVD) of Hankel matrix embedded by analyzed time data series and decomposes the data into several simple, independent and identifiable components. In this paper, first, the coupling degree of the 1st and 2nd singular values through the composition of the analyzed signal in SSA is used as two important values to detect damage. Besides, based on the extracted sub-space or null-space from SVD of analytic matrix, damage detection algorithm is developed by considering the orthonormality between the sub-space and null-space. The proposed algorithms are verified using non-stationary response data of a model bridge (data from scouring test of a bridge) and field experiment of a bridge during abnormal weather condition. Discussion on the proposed methods with different assessment method to identify the occurrence of damage using SSI-DATA and SSI-COV to identified the system dynamic characteristics are also made.Copyright

Application of higher order SVD to vibration-based system identification and damage detection

Singular value decomposition (SVD) is a powerful linear algebra tool. It is widely used in many different signal processing methods, such principal component analysis (PCA), singular spectrum analysis (SSA), frequency domain decomposition (FDD), subspace identification and stochastic subspace identification method ( SI and SSI ). In each case, the data is arranged appropriately in matrix form and SVD is used to extract the feature of the data set. In this study three different algorithms on signal processing and system identification are proposed: SSA, SSI-COV and SSI-DATA. Based on the extracted subspace and null-space from SVD of data matrix, damage detection algorithms can be developed. The proposed algorithm is used to process the shaking table test data of the 6-story steel frame. Features contained in the vibration data are extracted by the proposed method. Damage detection can then be investigated from the test data of the frame structure through subspace-based and nullspace-based damage indices.

Stochastic subspace identification for operational modal analysis of an arch bridge

In this paer the application of output-only system identification technique, known as Stochastic Subspace Identification (SSI) algorithms, for civil infrastructures is carried out. The ability of covariance driven stochastic subspace identification (SSI-COV) was proved through the analysis of the ambient data of an arch bridge under operational condition. A newly developed signal processing technique, Singular Spectrum analysis (SSA), capable to smooth noisy signals, is adopted for pre-processing the recorded data before the SSI. The conjunction of SSA and SSICOV provides a useful criterion for the system order determination. With the aim of estimating accurate modal parameters of the structure in off-line analysis, a stabilization diagram is constructed by plotting the identified poles of the system with increasing the size of data Hankel matrix. Identification task of a real structure, Guandu Bridge, is carried out to identify the system natural frequencies and mode shapes. The uncertainty of the identified model parameters from output-only measurement of the bridge under operation condition, such as temperature and traffic loading conditions, is discussed.

Finite element-based damage identification of RC frames

The objective of this study is the application of finite-element based damage detection techniques to identify the damage severity of reinforced concrete structures subject to different intensity level of earthquake excitation. The damage detection procedure consists of two parts: (1) identify the system dynamic characteristics using the system identification technique (subspace identification, SI) from direct input/output measurements, (2) develop damage assessment of structural members (joints) based on the progressive finite element model and large-scale optimization with nonlinear least-square technique. To verify the proposed method, first, four specimens of two-bay one-story reinforced concrete frame and one two-story reinforced frame structure, with the same design detail and same construction material properties, are tested on the shaking table with different intensity level of earthquake excitations. Integrate the Subspace Identification method and the Finite-element based model updating, damage identification of the structures are investigated. The proposed finite-element based damage identification method were found to be a very effective method for damage assessment of frame structure.

Reference-based damage diagnosis of structure using embedded statistical model

This paper presents a damage assessment method using the measurement data of restoring force from a sub-structural system. A normalized hysteretic energy (NHE) for bi-linear model is developed as a function structural period and system ductility, which serves as a reference-based model for damage assessment. The stiffness degradation, strength deterioration and pinching effect in the inelastic hysteretic model are then determined from a series of nonlinear time history analysis of an inelastic SDOF system. Next, modification factors on the NHE for sensitivities of the inelastic model parameters are developed. Based on the identified model parameters by measuring the inelastic hysteretic behavior of the restoring force incorporated with the reference-based NHE model and the modification factor, the percentage of structural damage in relating to strength and stiffness degradation can be evaluated. Verification of the proposed method by simulation and experimental data of the cyclic loading and shaking table tests of the RC frame are conducted.