Modal parameter identification of a long-span footbridge by forced vibration experiments

A database of dynamic characteristics of woodframe buildings was developed through analysis of recorded earthquake response and by forced vibration and shake-table testing. Modal identification was performed on eight sets of strong-motion records obtained from five buildings, and forced vibration tests were performed on five other buildings. The periods identified were sensitive to the amplitude of shaking, due to the reduction in lateral stiffness at stronger shaking levels. The equivalent viscous damping ratios were usually more than 10% of critical during earthquake shaking. A regression analysis was performed on the earthquake and forced vibration test data to obtain a simple, but reasonably accurate, period formula for woodframe buildings at low drift levels (less than 0.1%). Data obtained from the UC San Diego and UC Berkeley full-scale shake-table tests illustrate the shift in periods due to increasing shaking amplitude. Forced vibration tests of the UC Berkeley 3-story building before and after the shake-table tests showed how the periods and modeshapes shift due to damage. A simple analytical model of masses and springs was used to model the UC Berkeley test structure. The effects of diaphragm stiffness and mass distribution assumptions were evaluated and found to have a significant effect on the model torsional response. This model was used to find the equivalent wall stiffnesses giving frequency-response curves that best-fit the experimental data. These spring values were used to quantify the stiffness loss resulting from severe shaking of the structure, and the observed damage corresponded to stiffness losses of over 75%. The correlation between stiffness loss and damage to woodframe buildings has potential structural health monitoring implications.

This chapter is focused on the experimental investigations that can be carried out to dy‐ namically characterize open-ended pipe piles in marine environment. Different test ty‐ pologies, such as impact load test, free vibration test, forced vibration test, and ambient vibration test, are presented and described with the purpose to provide the right tools to analyze the dynamic behavior, at both small and large strains, of single piles or a system of piles. The appropriate instrumentation, with the suitable protection from marine envi‐ ronment and pile driving installation procedure, is also illustrated. Furthermore, the most common signal processing techniques useful for handling the experimental raw data are addressed together with the analysis techniques for the evaluation of the modal parame‐ ters: natural frequencies, damping ratios, and mode shapes. Finally, a part of the experi‐ mental campaign carried out by the authors on near-shore open-ended pipe piles is reported as a case study.

Operational modal analysis of a high-rise multi-function building with dampers by a Bayesian approach

Ambient and forced vibration tests were recently conducted on an offshore steel template platform in the Ekofisk complex of the North Sea. Valuable information about the dynamic characteristics of the structure was obtained. This paper focuses on the measurement and analysis of damping data for the platform. Modal damping values are very important in the dynamic analysis of offshore structures. Correct values of modal damping need to be utilized for the dynamic analysis to accurately predict the response of the structure. Little experimentally verified information of the modal damping characteristics of the fundamental and higher order modes of offshore structures is currently available. Damping values were calculated for the fundamental and higher order jacket modes which included natural frequencies up to approximately 5 Hz. Damping values are compared for forced and ambient vibration data, for bandwidth and response techniques, and for different excitation levels. The general results indicated that the fundamental modes important in fatigue had damping values of 1 to 3 percent of critical and the higher order modes had damping values of 2 to 3 percent of critical. Emphasis is placed on the apparent merits and limitations of the data presented. Response comparisons are also presented using an analytic model of the platform with various values of critical damping. INTRODUCTION Accurately predicting the dynamic behavior of offshore oil and gas production platforms to withstand the effects of earthquakes and environmental fatigue due to wind and wave loading is an essential part of the design of such structures. Research and development work currently being undertaken to apply integrity monitoring techniques to these platforms also requires an accurate interpretation of the structural dynamic behavior. These applications of vibration technology translate directly into cost effective design and increased reliability and safety of offshore structures. The complexity of these structures requires a high level of theoretical analysis in developing models which duplicate the dynamic behavior under design loading conditions. Current state-of-the-art modeling methods usually apply finite element techniques which discretize the structure into an assemblage of mass and stiffness matrices which mathematically define the structure. The complexity of these structures also implies the need for confirmation and improvement of the structural models by experimental techniques. Using system identification methods, both analytic and experimental results can be used to accurately define the dynamic behavior of structures. Structural damping is one of the least understood yet most vital design characteristics of dynamically loaded structures. An analytical model of a structure in which low critical damping values are used will respond much differently to environmental loads than one in which higher damping values are used. This paper presents values of critical damping obtained experimentally on an offshore platform and comparisons are made to an analytic model of the structure. The vibration tests were conducted on an offshore steel template platform in the Ekofisk complex of the North Sea. Both ambient and forced vibration test procedures were utilized.

The responses to forced vibrations, ambient vibrations, and large explosives were measured for Masjed Soleiman Dam, the highest embankment dam in Iran. Based on the results of these tests, the first 23 modal frequencies of the dam were measured and the related mode shapes for the first 16 modes were identified. A modal analysis of the dam body was also performed. The effects of reservoir water level variation, the rigidity and flexibility of the foundation and abutments and their depths and inertial properties, and the effect of material properties on the dynamic characteristics of the dam body were investigated, and the first eight modes of the dam body were identified. A comparison of the results of the numerical analysis with those from the tests indicates the best fit in lower modes occurs when the complete mass foundation is considered, whereas in higher modes the massless foundation model is a better fit.Key words: embankment dam, forced vibration test, ambient vibration test, explosion, modal properties.

This paper presents the experimental investigation of the Fei-Tsui arch dam using the forced vibration test and its seismic response data. A forced vibration test was conducted on Fei-Tsui dam, this study presents the identified dynamic properties of the dam from these test data. For the identification of dam properties from seismic response data, in order to consider the nonuniform excitation of the seismic input and to describe the global behavior of the dam, the multiple input/multiple output discrete-time ARX model with least square estimation is applied to identify the dynamic characteristics of the dam. The system modal frequency, damping ratio and frequency response function are identified from both the forced vibration and seismic response data. To verify the accuracy of the identification result, comparison between discrete-time ARX model and a frequency domain conditioned spectral analysis was made. Finally, the spatial variation of ground motion across the free-field canyon surface is also studied.

Accounting for amplitude of excitation in model updating through a hierarchical Bayesian approach: Application to a two-story reinforced concrete building

Ambient and forced vibration testing and finite element model updating of a full-scale post-tensioned laminated veneer lumber building

Vibration analysis of the civic tower in Rieti

This article investigates the performance of finite element model updating to identify the induced damage in a two-story reinforced concrete masonry-infilled building using vibration data as well as lidar (light detection and ranging) scans. The building, located in El Centro, California, was severely damaged due to the 2010 El Mayor–Cucapah (Baja California, Mexico) Earthquake, and it was planned to be demolished following a number of ambient and forced vibration tests. The forced vibration tests were performed using an eccentric mass shaker. During the testing sequence, damage was induced to the building by removing four exterior walls. The modal parameters of the structure are estimated using the ambient vibration and forced vibration measurements at the reference state and damaged state. Lidar data are also used to detect surface defects and quantify the temporal changes of surface defects caused by the wall removal and forced vibration tests. Based on site inspections, geometry measurements, and material test data, two initial finite element models are built, namely the un-tuned initial model and the tuned initial model. The tuned initial model implements stiffness reduction factors to account for the observed damage in the building at its reference state while the un-tuned model does not. Two sets of reference models are calibrated to represent the structure at the reference state using the un-tuned and tuned initial models. The reference models are then updated to fit the measured data at the damaged state of the building with damage being estimated as the loss of stiffness in updating substructures. The estimated damage is compared to the nominal value of induced damage and surface defects detected by lidar scans. The analysis of the results indicates that the un-tuned and tuned initial models provide similar updated models and damage identification results which are in good agreement with the nominal values of damage and lidar detection results.

The service behavior and real performance of engineering materials and systems are best evaluated using data obtained from prototype or full-scale testing, or both. For large engineering structures composed of materials such as concrete, with variable properties, data from such tests are invaluable. Full-scale forced vibration testing is a useful tool for obtaining information on the condition of structural systems. As compared to ambient vibration testing, forced vibration testing can provide more accurate estimates of damping capacity and yield data from which better system identification of structural parameters is possible. However, full-scale forced vibration field testing is much more difficult to achieve when compared with laboratory tests on prototypes. The (large) size of the structure usually means special excitation systems are required. The development and performance characteristics of such an excitation system is described in the article. The system consists of an hydraulic actuator, mounted within a purpose built frame, two pumps, an electronic control unit, and a personal computer. It can be used to induce vertical excitation of highway bridges, long-span floor slabs, and similar structures.

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.

As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts.

Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes

Identification of modal parameters of unmeasured modes using multiple FRF modal analysis method