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Identifying the parameters of multispan rigid frames is challenging because of their complex structures and large computational workloads. This paper presents a stiffness separation method for the static response parameter identification of multispan rigid frames. The stiffness separation method segments the global stiffness matrix of the overall structure into the stiffness matrices of its substructures, which are to be computed, thereby reducing the computational workload and improving the efficiency of parameter identification. Loads can be applied individually to each separate substructure, thereby guaranteeing obvious local static responses. The veracity and efficacy of the proposed methodology are substantiated by applying it to three- and eight-span continuous rigid frame structures. The findings indicate that the proposed approach significantly enhances the efficiency of parameter identification for multispan rigid frames.

Quantifying vehicle-bridge interaction mechanism is critical for bridge safety design, transportation weight control, condition assessments in maintenance, and structural health monitoring. In this paper, the stochastic non-stationary characteristics of a bridge under vehicle-bridge interaction are investigated. The response of the bridge under the loading of vehicles is, respectively, depicted in Fourier spectrum, spectrogram, and Hilbert spectrum. Both Fourier spectrum and spectrogram exhibit some cluster bands. The Hilbert spectrum exhibits time-varying frequencies in the proximity of low bridge natural modes, which suggests possible non-linear and non-stationary characteristics. The stochastic and non-stationary properties are further characterized by using bispectrum and recurrence analysis, and the weak nonlinear properties are characterized by using nonlinear invariants. The free-decay response of bridge (vehicle left the bridge) exhibits linear properties, which is correlated with the natural modes of bridge, whereas the bridge vibrations under moving vehicle exhibit complicated stochastic non-stationary and non-linear properties. These provide the insights into the conventional modal analysis-based approaches for heavy vehicle-loaded bridge condition assessments and structural health monitoring.

The inversion of a high‐dimensional stiffness matrix with unknown parameters is time‐consuming. In this study, a stiffness separation method is used to solve the large‐scale matrix inversion problem. Substructures are isolated from the overall structure by mapping the substructure‐related matrix, and the solvable equilibrium equations for the substructures can be established. This method divides the entire stiffness matrix into the sub‐stiffness matrices, and the size of the matrix is reduced, thus greatly reducing the stiffness matrix inversion workload. Meanwhile, this paper refines the formulation of the stiffness separation method and presents the compatibility of forces and displacements with the stiffness matrix. A space‐truss structure with different damage cases is studied to validate the effectiveness of the proposed method. The division of the structure into single and multi‐region scenarios is considered, and the effect of the size and number of substructures on the damage identification is analyzed. These results demonstrate that the stiffness separation method can reduce the computational effort required for analyzing large‐scale truss structures. [ABSTRACT FROM AUTHOR]

This paper presents a method to identify the damages in frame structures with slender beams. This method adjusts the parameters of the structure to match the analytical and the measured displacements. The effect of transverse shear deformation on the nodal analytical displacement is analyzed, and the parameter identification of frame structures with slender beams is performed. The results demonstrate that parameter-identification accuracy can be considerably improved by considering the transverse shear deformation in the frame structure with slender beams. The proposed method can accurately identify the damages in frame structures with slender beams using displacement measurements.

Shear deformation plays an important role in certain structures, and neglecting shear deformation can affect the accuracy of structural response. This paper proposes a non-destructive damage evaluation method that considers shear deformation, based on static response, for identifying corrosion in beam-like structures. The influence of shear deformation on nodal displacement for simply supported beams with different cross-sections was analyzed. The results indicate that even small errors yield inaccurate identification results when neglecting shear deformation. To solve this problem, analytical displacements of the structure were determined based on the Timoshenko beam theory, and the objective function was established. Additionally, the damage identification results were obtained by minimizing the objective function using the interior point method. Several progressively complex examples were used to demonstrate the effectiveness of the proposed method in identifying damage in beam-like structures.

A damage identification methodology considering shear deformation was presented in this paper to identify damage to semi-rigid frames with slender beams. On the basis of the successful identification of structural joint damage, the combined joint and member damage of the structure was identified. The objective function was formulated to minimize the discrepancies between the analytical and measured nodal displacements. Damage identification was performed on semi-rigid frame structures with different cross-sectional shapes, and the results were compared with those of ignoring shear deformation. Several frame structures were employed to verify the advantages and efficiency of the proposed method. The results demonstrate that the present method could significantly improve the accuracy of damage identification for semi-rigid frames compared with the method ignoring shear deformation.

The viscoelastic property of pile-soil interactions is modeled by fractional derivative method and is used to characterize the structural dynamics of pile and rheological behavior of a thawing frozen soil. A study of the thawing frozen soil impacts on pile structure’s dynamic characteristic is carried out. The frequency spectrum analysis and empirical modal decomposition are used to identify the pile structure dynamic properties. The rocking mode vibration in which pile behaviors like rigid body supported by viscoelastic soil is extracted to capture the viscoelastic property of pile-soil interactions. The rocking mode exhibiting time-varying frequency features is modeled with fractional derivative model and the fractional derivative order is identified. This study proposes a quick and reliable method to identify the viscoelastic property of pile-soil interactions.

This paper presents a parameter-identification method for rod structures with different connections. In this method, the parameters of the structure are adjusted to match its analytical and measured displacements. The damage identification for truss structure and rigid frame were investigated. Previous studies often considered the cross-sectional area damage or joint damage; there are few studies on the simultaneous existence of these two types of damage. In this study, damage identification for a rigid frame with both cross-sectional and joint damage was performed. Based on the measured displacements, the proposed method can accurately identify the cross-sectional and joint damage for a rigid frame.

Technology that measures bridge responses when a vehicle is crossing over it for structural health monitoring has been under development for approximately a decade. Most of the proposed methods are based on identification of the dynamic characteristics of a bridge such as the natural frequency, the mode shapes, and the damping. Specifically, many time–frequency domain approaches have been used to extract complex spectrum signatures from the complicated vibrations of a bridge due to the interactions of a vehicle with the bridge, which usually involves nonlinear, nonstationary, stochastic, and impact vibrations. In this paper, a method known as complete ensemble empirical mode decomposition with adaptive noise is applied for the first time to analyze the acceleration response of a bridge to a moving vehicle, and the purpose is to extract the spectrum signature of the vehicle–bridge response for structural health monitoring. The time–frequency Hilbert-Huang transform (HHT) spectrum of the decomposed mode from complete ensemble empirical mode decomposition with adaptive noise is presented. The results are well-correlated with finite element analysis. The advantages of the complete ensemble empirical mode decomposition with adaptive noise method are demonstrated in comparing the data from conventional methods, including power spectra, spectrograms, scalograms, and empirical mode decomposition.

Health condition monitoring through comprehensive monitoring, incipient fault diagnosis, and the prediction of impending faults allows for the promotion of the long-term performance of wind turbines, particularly those in harsh environments such as cold regions. The condition monitoring of wind turbines is characterized by the difficulties associated with the lack of measured data and the nonstationary, stochastic, and complicated nature of vibration responses. This article presents a characterization of the vibrations of an operational wind turbine by spectrogram, scalogram, and bi-spectrum analyses. The results reveal varied nonstationary stochastic properties and mode-coupling instability in the vibrations of the tested wind turbine tower. The analysis illustrates that the wind turbine system vibrations exhibit certain non-Gaussian stochastic properties. An analytical model is used to evaluate the nonstationary, stochastic phenomena and mode-coupling phenomena observed in the experimental results. These results are of significance for the fault diagnosis of wind turbine system in operation as well as for improving fatigue designs beyond the wind turbulence spectral models recommended in the standards.

In this paper, we investigate vehicle–bridge interactions and propose a new method for assessing bridge conditions based on nonlinear vibration analysis. A vehicle model is presented, and the dynamic load on the bridge is quantified based on bridge road roughness. The vibration of a river bridge under a moving vehicle is recorded and analyzed. The Fourier spectrum of the bridge response due to vehicle loading exhibits complicated cluster bands in addition to multiple peaks, some of which are correlated with the bridge natural modes characterized by finite element method analysis and free decay testing, and some of which are correlated with the vehicle dynamic load spectrum. To characterize the unidentified narrow band in the bridge response spectrum, the Lyapunov exponent of the response is estimated, which is found to be a positive value indicating the nonlinear properties of the bridge’s large response under vehicle loading. This finding correlates with the bridge inspection, which shows that some supporting roller bearings do not properly contact the superstructure of the bridge. To elaborate this phenomenon, a model of beam with nonideal supporting condition is analyzed, and a narrow band spectrum is characterized using He’s variational-iteration method. This research offers insight to using the vehicle–bridge interaction to monitor the health status of a bridge by using nonlinear properties, as well as linear properties.

A novel technique to identify bridge damage using genetic algorithms and simulated annealing is proposed in this article. In the proposed method, the cross-sectional area of the damaged member is set as a variable that can be updated. An objective function was investigated to estimate the current condition of the damaged members. This function is the relationship between the measured strain and the analytical strain at the damage location. To obtain better agreement, the parameters were then identified using a genetic algorithm and simulated annealing to minimize the objective function. The proposed method was verified by a truss bridge and can directly estimate the damage based on strain measurements.

This paper investigates the creep groan of a vehicle’s brake experimentally, analytically, and numerically. Experimentally, the effects of acceleration on caliper and strut, noise, brake pressure, and tension are measured. The results show that the measured signals and their relevant spectra broadly capture the complex vibrations of creep groan. This includes the simple stick-slip, severe stick-slip vibrations/resonances, multiple harmonics, half-order harmonics; stick-slip-induced impulsive vibrations, steady/unstable vibrations, and their transitions. Analytically, a new mathematical model is presented to capture the unique features of half-order harmonics and the connections to fundamental stick-slip/resonant frequency and multiple harmonics. The analytical solution and the experimental results show that the vibro-impact of the brake pad-disc system can be triggered by severe stick-slip vibrations and is associated with instable, impulsive stick-slip vibration with wideband. The induced stick-slip vibro-impact can evolve into a steady and strong state with half-order, stick-slip fundamental, and multiple-order components. This new mechanism is different from all previously proposed mechanisms of creep groan in that we also view some type of creep groan as a stick-slip vibration-induced vibro-impact phenomenon in addition to conventional stick-slip phenomena. The new mechanism comprehensively explains the complex experimental phenomena reported in the literature. Numerically, the salient features of phase diagrams of instable stick-slip and vibro-impact are examined by using a seven-degree-of-freedom brake system model, which shows that the phase diagrams of the dynamics of creep groan with and without vibro-impact are substantially different. The phase diagram of the dynamics with vibro-impact is closer to the experimental results. In contrast to existing mechanisms, the proposed new mechanism encompasses the instable stick-slip nature of creep groan and elaborates the inherent connections and transition of the spectrogram. The new knowledge can be used to attain critical improvements to brake noise and vibration analysis and design. By applying the proposed new model in addition to existing models, all experimental phenomena in creep groan are elaborated and quantified.

As all bridges get deteriorated over time, structural health monitoring of these structures has become very important for the damage identification and maintenance work. Evaluating a bridge’s health condition requires the testing of a variety of physical quantities including bridge dynamic responses and the evaluation of the functions of varied bridge subsystems. In this study, both the acceleration of the deck and the dynamic rotational angle of the bearings in a long-span steel girder bridge were measured when the bridge system was excited by passing-by vehicles. The nonstationary dynamical phenomena including vibration mode interactions and coupling are observed in response spectrogram. To elaborate the phenomena, the linear vibration mode properties of the bridge are characterized by finite element analysis and are correlated with the specific modes in test. A theoretical model is presented showing the mechanism of the mode coupling and instability originated from the friction effects in bearing. This study offers some insights into the correlation between complex bridge vibrations and the bearing effects, which lays a foundation for the in situ health monitoring of bridge bearing by using dynamical testing.

This paper investigated dynamical interactions between pile and frozen ground by using the ensemble empirical mode decomposition (EEMD) method. Unlike the conventional empirical mode decomposition (EMD) method, EEMD is found to be able to separate the mode patterns of pile response signals of different scales without causing mode mixing. The identified dynamic properties using the EEMD method are more accurate than those obtained from conventional methods. EEMD-based results can be used to reliably and accurately characterize pile-frozen soil interactions and help designing infrastructure foundations under permafrost condition.

Shear deformation plays an important role in certain structures, and neglecting shear deformation can affect the accuracy of structural response. This paper proposes a non-destructive damage evaluation method that considers shear deformation, based on static response, for identifying corrosion in beam-like structures. The influence of shear deformation on nodal displacement for simply supported beams with different cross-sections was analyzed. The results indicate that even small errors yield inaccurate identification results when neglecting shear deformation. To solve this problem, analytical displacements of the structure were determined based on the Timoshenko beam theory, and the objective function was established. Additionally, the damage identification results were obtained by minimizing the objective function using the interior point method. Several progressively complex examples were used to demonstrate the effectiveness of the proposed method in identifying damage in beam-like structures. [ABSTRACT FROM AUTHOR]

A damage identification methodology considering shear deformation was presented in this paper to identify damage to semi-rigid frames with slender beams. On the basis of the successful identification of structural joint damage, the combined joint and member damage of the structure was identified. The objective function was formulated to minimize the discrepancies between the analytical and measured nodal displacements. Damage identification was performed on semi-rigid frame structures with different cross-sectional shapes, and the results were compared with those of ignoring shear deformation. Several frame structures were employed to verify the advantages and efficiency of the proposed method. The results demonstrate that the present method could significantly improve the accuracy of damage identification for semi-rigid frames compared with the method ignoring shear deformation. [ABSTRACT FROM AUTHOR]

Quantifying vehicle-bridge interaction mechanism is critical for bridge safety design, transportation weight control, condition assessments in maintenance, and structural health monitoring. In this paper, the stochastic non-stationary characteristics of a bridge under vehicle-bridge interaction are investigated. The response of the bridge under the loading of vehicles is, respectively, depicted in Fourier spectrum, spectrogram, and Hilbert spectrum. Both Fourier spectrum and spectrogram exhibit some cluster bands. The Hilbert spectrum exhibits time-varying frequencies in the proximity of low bridge natural modes, which suggests possible non-linear and non-stationary characteristics. The stochastic and non-stationary properties are further characterized by using bispectrum and recurrence analysis, and the weak nonlinear properties are characterized by using nonlinear invariants. The free-decay response of bridge (vehicle left the bridge) exhibits linear properties, which is correlated with the natural modes of bridge, whereas the bridge vibrations under moving vehicle exhibit complicated stochastic non-stationary and non-linear properties. These provide the insights into the conventional modal analysis-based approaches for heavy vehicle-loaded bridge condition assessments and structural health monitoring. [ABSTRACT FROM AUTHOR]

A method to identify optimal strain sensor placement for examining structural static responses is presented. The method is based on the use of numerical optimization. Based on an assumed set of applied static forces, the optimal sensor placement can be obtained, and the measured strains can be used to provide the information needed to describe the structural stiffness. For example, the cross-sectional area can be determined by minimizing the difference between the analytical and measured strains. This approach is used to identify the optimized sensor placement. The objective of this study is to identify the minimum number of static strain sensors and the optimal sensor layout needed to evaluate a bridge’s structural condition. This study includes an automatic model parameter identification method, optimal static strain sensor placement, damage detection, and application to an actual bridge.

Quantifying the non-stationary properties of bridge under passing vehicle has been an important topic in structural health monitoring of bridge. There are many methods of time–frequency representation used for the study of dynamics of bridge under passing vehicle, including spectrogram, wavelet, Hilbert–Huang transform, and so on. This article uses adaptive optimal kernel time–frequency representation to quantify the non-stationary properties of the response of bridge under passing vehicle and illustrates and discusses its advantages over conventional time–frequency methods.