Modal Parameter Identification and Numerical Simulation for Self-anchored Suspension Bridges Based on Ambient Vibration

Modal parameter identification via ambient vibration is popular but faces challenges from uncertainties due to unknown inputs and low signal‐to‐noise ratio. Bayesian methods are gaining increasing attention for operational modal identification due to their ability to quantify uncertainties. However, improvements in computational efficiency are needed, particularly when addressing numerous modes and degrees of freedom. To address this challenge, this study proposes an innovative approach, termed the “Bayesian spectral decomposition” method (BSD), employing the decompose‐and‐conquer strategy. This novel method, operating within the frequency domain, identifies each mode individually by exploiting their inherent separated modal characteristics. For each mode, the response spectrum matrix undergoes an eigenvalue decomposition, yielding crucial eigenvalues (incorporating frequency and damping information) and eigenvectors (containing mode shape information). Subsequently, statistical properties of the eigenvalues and eigenvectors are utilized to establish likelihood functions for Bayesian parameter identification. By combining prior information, the posterior probability distribution functions of modal parameters are derived. The optimal solution is then obtained by resolving the maximum posterior probability distribution function problem. To further quantify the uncertainty of modal parameters, Gaussian distributions are employed to approximate the posterior probability distribution functions. The adoption of the decomposition approach circumvents the joint identification of all modal parameters, substantially reducing the parameter dimensions for optimization. Consequently, this strategy leads to decreased computational complexity and significantly improved computational stability. The effectiveness of the BSD is confirmed through simulated data generated from an 8‐story shear building as well as measured data collected from both an experimental shear frame and the Canton Tower. The results demonstrate that the proposed method achieves high accuracy in identifying modal parameters, greatly improves computational efficiency, and effectively quantifies the uncertainties in modal parameters.

Self-anchored cable-stayed suspension bridge has highly competitive in large-span bridge scheme selection due to it combines both stress characteristics and structural characteristics of cable-stayed bridge and self-anchored suspension bridge. This paper focuses on the development of self-anchored and earth-anchored cable-stayed suspension bridge in China, lists the bidding scheme and the actual project of this type bridges.

As a new type of bridge, self-anchored cable-stayed suspension bridge has the advantages of both cable-stayed suspension bridge and self-anchored suspension bridge. It enjoys good structural performances, as well as remarkable technical and economical benefits, therefore has been adopted by the engineering field so far. However, there is little research on the dynamic behavior of this type of bridge. With the engineering background of Zhuanghe Construction Bridge, this article studies the dynamic characteristics and seismic responses of this new structural system, and the main research work covers the following aspects: Natural vibration frequencies and principal modes of the bridge. The standard seismic response spectrum is input from longitudinal, transverse and vertical directions respectively. With structural geometric nonlinear factors considered, the artificial earthquake wave is input from longitudinal, transverse and vertical directions respectively to get the response time histories of internal force and displacement of control-section such as main beam and tower. The effect regulation is discussed in detail. Three structural restriction patterns are analyzed and compared, from which the one with the best aseismatic qualities is sorted out, namely the elastic restriction structural system composed of towers and beams. This paper also analyzes the influence of longitudinal elastic restriction on dynamic character and seismic response.

Modal parameter identification is an important content for the research on dynamic behavior of civil engineering structures. For the conventional modal parameter identification techniques, excitation signal and response signal are necessary. But excitations can not be measured for structures under natural loading conditions, or excited by random forces. So, the operational modal parameter identification approaches are developing to identify structural modal parameters by using vibration response signal directly. In this paper, a new method for modal parameter identification depending on ambient excitation response signal is proposed based on independent component analysis (ICA). For modal coordinates independent of each other, ICA can extract modal coordinates of structure and estimate mode shape matrix using vibration response signal directly. The free vibration responses can be obtained by random decrement technique (RDT) from modal coordinates which are random processes, and then the natural frequencies and damping ratios are calculated by Hilbert transform. Numerical simulation results indicate that this method is effective and suitable for output-only structural modal parameter identification.

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.

In this research, a finite element model is established to investigate effective seismic control schemes for a self-anchored suspension bridge (SASB) with three towers. Nonlinear dynamic analyses are conducted to evaluate the seismic performance of SASB with different layout schemes of viscous dampers and buffers, which were installed in longitudinal direction and transversal direction, respectively. The responses of the SASB designed with 10 seismic control schemes are compared to ascertain suitable seismic schemes for SASBs. The results show that the number and location of lateral buffers have an important impact on the dynamic characterization of the SASB, especially for the first lateral mode and lateral fundamental frequency. To effectively increase the seismic performance of SASBs with three towers, mounting buffers between the side towers and the main girder of SASBs is an appropriate scheme. The viscous dampers can effectively decrease the dynamic reaction of the towers and longitudinal deformation of the girder under earthquake excitations. The plan involves the installation of dampers between the main concrete stiffening girder and the side towers as the optimal longitudinal seismic scheme for the SASB. The study offers important insights into the seismic design of SASBs with three towers.

The integrity of offshore structures is prone to the threat of drifting sea ice. By exciting the natural frequencies of the ice–structure interaction system, severe vibrations may occur. For a better understanding of how dynamic ice–structure interaction affects the system properties, a stochastic subspace system identification technique, SSI-cov is introduced to identify modal parameters during dynamic ice–structure interactions. Due to the uncertain input variables of SSI-cov, the identified modal parameters suffer from the quantitative judgment of the analyst. To address this problem, this study proposes an uncertainty analysis (UA) framework to obtain estimates of modal parameters. This framework constitutes both a sensitivity analysis (SA) and a UA. First, SA is applied to pick up the input variables that contribute the most to the identified modal parameters. Next, the important variables are left free to vary over their range of existence to obtain the modal parameters’ uncertainties. The framework is applied to full-scale tests from Norströmsgrund lighthouse and model tests carried out in Hamburg Ship Model Basin (HSVA). The comparison with traditional automated modal parameter identification shows its superiority in terms of the accuracy of modal parameters.

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

Ultimate bearing capacity analysis of self-anchored suspension bridge with steel box girders considering local buckling

An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the modal parameters from output-only data. This article presents the results of modal parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of modal parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical modal parameters in the case where the block Hankel matrix has full row rank. The time-domain modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in modal parameter identification using response data only.

The paper presents the results of the ambient vibration survey and the finite element analysis of the Bosporus Suspension Bridge in Istanbul. In each of the experiment series several measurements of the ambient vibration of the deck were obtained at different locations and orientations at different traffic conditions. Most of the frequencies of the vibrations assessed from experimental data is between 0.07 and 1.0 Hz. The substantial amount of vibration energy on the bridge deck is contained between 2 and 3 Hz. The results of these experiments have been analyzed in terms of the modal shapes, frequencies as well as damping ratios. A comparison is given between experimentally obtained mode shapes and theoreticaly calculated ones. Structural symmetry and the absence of the suspended side spans allow us to consider the main span along with the complete structure. Main span is modeled as a box beam in the finite element model as it was constructed. Good correlation between experimental and theoretical results have been observed.

Traditional modal parameter identification methods have many disadvantages, especially when used for processing nonlinear and non-stationary signals. In addition, they are usually not able to accurately identify the damping ratio and damage. In this study, methods based on the Hilbert-Huang transform (HHT) are investigated for structural modal parameter identification and damage diagnosis. First, mirror extension and prediction via a radial basis function (RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition (EMD), which is a crucial part of HHT. Then, the approaches based on HHT combined with other techniques, such as the random decrement technique (RDT), natural excitation technique (NExT) and stochastic subspace identification (SSI), are proposed to identify modal parameters of structures. Furthermore, a damage diagnosis method based on the HHT is also proposed. Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure. The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure. Finally, acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches. The results show that the proposed approaches based on HHT for modal parameter identification and damage diagnosis are reliable and practical.

Automated identification and long-term tracking of modal parameters for a super high-rise building

Modal analysis, which provides modal parameters including frequencies, damping ratios, and mode shapes, is essential for assessing structural safety in structural health monitoring. Automated operational modal analysis (AOMA) offers a promising alternative to traditional methods that depend heavily on human intervention and engineering judgment. However, estimating structural dynamic properties and managing spurious modes remain challenging due to uncertainties in practical application conditions. To address this issue, we propose an automated modal identification approach comprising three key aspects: (1) identification of modal parameters using covariance-driven stochastic subspace identification; (2) automated interpretation of the stabilization diagram; (3) an improved self-adaptive algorithm for grouping physical modes based on ordering points to identify the clustering structure (OPTICS) combined with k-nearest neighbors (KNN). The proposed approach can play a crucial role in enabling real-time structural health monitoring without human intervention. A simulated 10-story shear frame was used to verify the methodology. Identification results from a cable-stayed bridge demonstrate the practicality of the proposed method for conducting AOMA in engineering practice. The proposed approach can automatically identify modal parameters with high accuracy, making it suitable for a real-time structural health monitoring framework.