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In the process of structural modal parameters identification under environmental excitation, the employed measured dynamic response signal is usually non-stationary and contains noise. As a novel signal analyzed method, symplectic geometry mode decomposition (SGMD) has been proven to be effective for dealing with non-stationary and noisy signals. However, the traditional SGMD may treat noise as modal information, which inevitably undermines the accuracy of modal identification. To overcome this problem, this paper proposes an optimized SGMD algorithm for structural modal parameter identification. First, the SGMD algorithm is refined with the Hankel matrix, Kurtosis theory, Pearson correlation coefficient, and energy entropy theory. Then, the natural frequencies and damping ratios are identified using the proposed method, which consists of the optimized SGMD algorithm, natural excitation technique (NExT), direct interpolating method, and curve-fitting function. Finally, the applicability of the proposed method under environmental excitation is investigated by two examples: a two-story frame structure and an 88-story office tower. The results demonstrate that the proposed method is effective for identifying the civil structural modal parameters from non-stationary dynamic responses. [ABSTRACT FROM AUTHOR]

Abstract In bridge structural health monitoring, typically the dynamic response of the system is used to assess the health condition of the bridge. However, the dynamic interaction between a bridge and a passing vehicle imposes non-stationarity on the system response, whereby the bridge modal parameters become time-dependent and detecting damage, for example, based on the bridge modal parameters, becomes challenging. Dynamic vehicle-bridge interaction (VBI) responses have mainly been investigated for damage detection through identifying signal singularities and abrupt changes. The singularities are usually associated with high-frequency components (relative to the bridge natural frequencies), and it is demanding to isolate the damage-induced singularities from those caused by either an operational condition, i.e., track irregularities, or noise. Unlike the high-frequency range, the influence of damage on the resonance frequency of the coupled system has not been fully explored. The present study proposes the shape of the bridge instantaneous frequency as a damage sensitive feature in which the influence of the vehicle dynamics can be excluded. This study demonstrates the feasibility of a damage detection approach based on the bridge instantaneous frequency by applying Wavelet Synchrosqueezed Transform (WSST). In this approach the bridge instantaneous frequency variation induced by damage is distinguished from the bridge instantaneous frequency variation induced by the vehicle. Several damage scenarios that are implemented numerically are analyzed to verify the method’s performance. The results demonstrate that a high resolution instantaneous frequency extracted from the VBI dynamic response outperforms the resonance frequency in determining the local disruption, leading to detecting the damage. A Damage Index (DI) is also proposed as an attempt to quantify the damage severity.

An alternating efficient approach for predicting non-stationary response of randomly excited nonlinear systems is proposed by a combination of radial basis function neural network (RBFNN) and stochastic averaging method (SAM). First, the n-degree-of-freedom quasi-non-integrable-Hamiltonian (QNIH) system is reduced to a one-dimensional averaged Itô differential equation within the framework of SAM for QNIH. Subsequently, the associated Fokker-Planck-Kolmogorov (FPK) equation is solved with the RBFNN. Specifically, the solution of the associated FPK equation is expressed in a linear combination of a series of basis functions with time-correlation weights. These time-depended weights are solved by minimizing a loss function, which involves the residual of the differential equations and the constraint conditions. Three typical nonlinear systems are studied to verify the applicability of the developed scheme. Comparisons to the data generated by simulation technique indicate that the approach yields reliable results with high efficiency. [ABSTRACT FROM AUTHOR]

From 2014 to 2016, several wind resistant field measurements were conducted to the high-rise building in Haikou. Based on these measurements, the present paper disclosed the characteristics of the time-history responses of axial acceleration on different floors during four typhoons, including the Rammasun, Kalmaegi, Mujigae and Sarika typhoons. The modal parameters of the measured building were identified by Morlet time-frequency wavelet transform methods, and the amplitude-dependent modal damping ratios and frequencies along translational directions were investigated. The results show that the variation trend of modal frequency with acceleration amplitude identified by the Morlet wavelet is the same as that recognized by time-domain method, while it is scattered with the interval bar (min-average-max) due to the nonstationary response of typhoon. Meanwhile, the larger the amplitude of acceleration response of high-rise buildings under strong wind, the greater the time-varying fluctuation of modal parameters identified by wavelet transform, and the bigger the difference between the interval bar (min-average-max). The full-scale study is expected to provide useful information on the wind-resistant design of high-rise buildings in typhoon-prone regions.

• A general non-stationary random vibration model for the SPCC is presented. • Propose a unified loading mechanism for multi-scenario loads. • Discuss the evolving PSD and time-varying RMS of the SPCC under various conditions. • Reveal the effects of geometric and load parameters on the system. In this work, a recursion reverberation-ray matrix method (RRRM) is presented to formulate an exact and unified solution for the non-stationary responses analysis of the sandwich panels with corrugated cores (SPCC) subjected to the moving random loads. The governing equations for the basic units are obtained by employing the simple first-order shear deformation theory (S-FSDT) and Hamilton's principle. Then, based on the traditional reverberation ray matrix method (MRRM), the RRRM is established by incorporating a bidirectional recursion technique to effectively calculate the exact solutions of the whole model. Thereinto, the kinematic relation matrix between the cell units can be constructed to facilitate the coupling of various desired numbers of elements by employing the virtual coupling spring. In addition, a unified loading mechanism for multi-scenario loads is proposed by integrating the pseudo-excitation method (PEM) with the load stage division technique. The applicability and accuracy of the current method to non-stationary response behaviors of the SPCC are clarified by carrying out sufficient comparative studies between the calculated results with reference solutions from FEM and Monte Carlo simulation method. Furthermore, several meaningful conclusions are drawn regarding the effects of structural and load parameters on the vibration characteristic, non-stationary displacement response, power spectrum density (PSD), and time-varying root mean square (RMS). [Display omitted] [ABSTRACT FROM AUTHOR]

In bridge structural health monitoring, typically the dynamic response of the system is used to assess the health condition of the bridge. However, the dynamic interaction between a bridge and a passing vehicle imposes non-stationarity on the system response, whereby the bridge modal parameters become time-dependent and detecting damage, for example, based on the bridge modal parameters, becomes challenging. Dynamic vehicle-bridge interaction (VBI) responses have mainly been investigated for damage detection through identifying signal singularities and abrupt changes. The singularities are usually associated with high-frequency components (relative to the bridge natural frequencies), and it is demanding to isolate the damage-induced singularities from those caused by either an operational condition, i.e., track irregularities, or noise. Unlike the high-frequency range, the influence of damage on the resonance frequency of the coupled system has not been fully explored. The present study proposes the shape of the bridge instantaneous frequency as a damage sensitive feature in which the influence of the vehicle dynamics can be excluded. This study demonstrates the feasibility of a damage detection approach based on the bridge instantaneous frequency by applying Wavelet Synchrosqueezed Transform (WSST). In this approach the bridge instantaneous frequency variation induced by damage is distinguished from the bridge instantaneous frequency variation induced by the vehicle. Several damage scenarios that are implemented numerically are analyzed to verify the method's performance. The results demonstrate that a high resolution instantaneous frequency extracted from the VBI dynamic response outperforms the resonance frequency in determining the local disruption, leading to detecting the damage. A Damage Index (DI) is also proposed as an attempt to quantify the damage severity. [ABSTRACT FROM AUTHOR]

Vibro-impact system (VI-S) have demonstrated their potential to contribute to engineering practice throughout the last few years. Nonetheless, their scope of application are still very limited. One of a primary reason is that dynamic behaviors of VI-S under the combination of deterministic period excitations (deterministic period excitation) and random noises (random noises) are not entirely understood. Toward this, the radial basis function neural network (rbfnn) is used to analyze dynamical behaviors evolution of VI-S under deterministic period excitation combined with random noises. To illustrate the potential of the proposed scheme, two classical examples of Mathieu–Duffing oscillator and Duffing–Rayleigh oscillator are considered. The evolutionary of dynamics behaviors and stochastic P-bifurcation phenomenon are examined through a qualitative change of the probability distribution, which indicates that system parameters and noise intensity, respectively, can be treated as bifurcation-induced parameters. Besides, numerical results are also carried out to confirm the accuracy of semi-analytical prediction. • Transient response prediction for VI-S under combined excitation with RBFNN. • Two examples are presented for illustrating the applicable of the proposed method. • Stochastic bifurcation with respect to the system parameters were discussed. [ABSTRACT FROM AUTHOR]

This paper expands the application of the RBFNN method to the prediction of non-stationary responses in strongly nonlinear systems subjected to wide-band noises (WBNs) excitation. Specifically, the SAM is initially employed to deduce the averaged Fokker–Planck–Kolmogorov (FPK) equation. The non-stationary responses of the energy of the system under WBNs are modeled as a one-dimensional Markov diffusion process. This yields a one-dimensional FPK equation that governs the NSRs of the system subject to WBNs. Subsequently, solving the corresponding FPK equation and obtaining the system's NSRs are accomplished with the RBFNN method. Furthermore, four indicative cases exposed to WBNs are studied to verify the proposed scheme. Comparisons with simulations demonstrate the accuracy and efficiency of the developed technique. • RBFNN method extended for solving nonlinear systems under wide band noises. • Numerical applications are provided, including smooth system and non-smooth system. • The proposed scheme verified by Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Abstract A block matrix analysis procedure of the generalized cell mapping (GCM) method is proposed in this paper. The proposed method solves the storage problem in the response analysis of nonlinear stochastic dynamical system with the GCM method, and makes it possible to compute the non-stationary and stationary probability density functions (PDFs) of multi-degree-of-freedom (MDOF) nonlinear systems without using supercomputing. Two examples of two-degree-of-freedom systems under external or parametric excitations of combined Gaussian and Poisson white noises are presented to demonstrate the efficiency of the proposed method. Monte Carlo (MC) simulations are used to verify the accuracy of the solutions obtained with the proposed method. Highlights • The generalized cell mapping method based on block matrix analysis is presented. • Probability density functions of response of MDOF dynamical system can be obtained. • Non-stationary response of systems under Gaussian and Poisson white noises is studied. • The accuracy of the solutions is verified by the Monte Carlo (MC) simulations. [ABSTRACT FROM AUTHOR]

Highlights • Design wind velocity and wind-induced damage are often related to thunderstorms. • Research on thunderstorm loading of structures is still fragmentary and uncertain. • Calibration and advance are provided of response spectrum technique and time-domain analysis. • The response spectrum technique is a suitable tool for engineering calculations. • Time-domain analysis is highly efficient with a limited computational burden. Abstract Thunderstorms are transient events. Design wind velocity and wind-induced damage are often related to them. Despite this, research on thunderstorm loading of structures is still fragmentary and uncertain due to their complexity, short duration and small size. These issues make it difficult to set physically realistic and simple models as well as to gather real data. This favoured the implementation of refined methods based on limited measurements. The European Projects "Wind and Ports" and "Wind, Ports and Sea" realised an extensive monitoring network from which many thunderstorm outflow records were extracted. They were analysed to inspect their characteristics and to formulate methods coherent with measurements. Firstly, the response spectrum technique conceived for earthquakes was extended to thunderstorms. Then, a hybrid simulation strategy was proposed and time-domain integrations of the structural response were applied. This paper provides a joint calibration and advancement of these two methods, leading to results that substantially agree, especially faced with their conceptual and operative diversities. This confirms the potential of the response spectrum technique to become a suitable tool for calculating the thunderstorm loading of structures and the efficiency of hybrid simulations and time-domain analyses to investigate, with a limited computational burden, advanced structural issues. [ABSTRACT FROM AUTHOR]

The impact of changeable operating conditions on the deceleration of progressive safety gears of PP 16 type and CHP 2000 new design is presented by the authors. The study was performed in the normal (dry friction) operation conditions (S) and also with the use of mineral oil lubricant (OM). The values of braking delays were recorded with the load of 4 kN and 10 kN applied. Statistical and wavelet analyses were performed to determine variability and waveforms of the system response. The authors reported the differences in dynamical characteristics of the examined safety gears designs in the frequency response. Furthermore, the asymmetry of the acceleration distribution is discussed in this research study. [ABSTRACT FROM AUTHOR]

To accurately detect an early transverse crack in the rotating machinery caused by fatigue or creep, various kinds of diagnosis systems utilizing the steady-state responses of a cracked rotor were developed. The paper focuses on the non-stationary response of a rotor system such as the startup, the shutdown or the variable running speeds of a rotating machinery to detect a transverse crack and to overcome the defects of the diagnosis system utilizing steady-state responses. Non-stationary characteristics during passages through the major resonance and various kinds of resonances are studied numerically and experimentally. The results demonstrate that the changes of vibration characteristics in a non-stationary response can detect a crack in a wide rational speed range and also prevent the dangerous operation for detecting a crack. [ABSTRACT FROM AUTHOR]

• An inverse problem strategy from phenomenon to knowledge to solution is conducted. • An automatic extraction method for non-stationary section of wind-induced vibration from time series signal is proposed based on the Gaussian mixture model of the data envelope. • A new process of the damping ratio identification is presented using the last descent of non-stationary data after bandpass filtering. • Implicit correlation between wind speed and vibration frequency is mined out and modeled based on data clustering results. Input-output characteristics in an event of the abnormal vibration of a kilometer-level railway-highway-combined cable-stayed bridge's cables under in-service winds are deeply investigated. The knowledge of commonality that cables' abnormal vibration exists multiple independent non-stationary sections in time series with high-amplitude and quasi-single-frequency is summarized. An automatic extraction of non-stationary section of abnormal vibration is conducted via Gaussian mixture modeling of the envelope of time series signal. A new process of modal parameter identification is presented using the data of non-stationary section after bandpass filtering and its last descent. It is demonstrated that the identified damping ratio of cables with abnormal vibration will be below 0.05%. Each abnormal non-stationary vibration's frequency, damping ratio, and wind speed are clustered into corresponding natural vibration modes. Correlation model of wind speed-vibration frequency is fitted by data centroid of clusters to predict the possible-occurrence frequency of an abnormal non-stationary vibration before it is fully completed. [ABSTRACT FROM AUTHOR]

Abstract: A method is presented to compute the stochastic response of single-degree-of-freedom (SDOF) structural systems with fractional derivative damping, subjected to stationary and non-stationary inputs. Based on a few manipulations involving an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion is reverted to a set of coupled linear equations involving additional degrees of freedom, the number of which depends on the discretization of the fractional derivative operator. As a result of the proposed variable transformation and discretization, the stochastic analysis becomes very straightforward and simple since, based on standard rules of stochastic calculus, it is possible to handle a system featuring Markov response processes of first order and not of infinite order like the original one. Specifically, for inputs of most relevant engineering interest, it is seen that the response second-order statistics can be readily obtained in a closed form, to be implemented in any symbolic package. The method applies for fractional damping of arbitrary order . The results are compared to Monte Carlo simulation data. [Copyright &y& Elsevier]

This paper concentrates on the results of responses of a multi-span continuous bridge isolated with double concave friction pendulum bearings subjected to non-stationary random seismic excitation characterized by the incoherence, the wave-passage, and the site-response effects. The earthquake excitation is modelled as a non-stationary random process as uniformly modulated broad-band excitation. To perform the seismic isolation procedure, the double concave friction pendulum bearings which are sliding devices that utilize two spherical concave surfaces are placed at each of the six support points of the deck. The non-stationary response of the isolated bridge is compared with the corresponding stationary response in order to study the effects of non-stationary characteristics of the earthquake input motion. Solutions obtained from the stationary and non-stationary stochastic analyses for the isolated bridge to spatially varying earthquake ground motions are compared for the special cases of the earthquake ground motion model. The spatially varying earthquake ground motions are described stochastically based on an empirical coherency loss function and a filtered power spectral density function. The site effect is considered by a transfer function derived from one dimensional wave propagation theory. It is observed that the stationary assumption is reasonable for the considered ground motion duration. [ABSTRACT FROM AUTHOR]

Abstract: Probability density function (PDF) of stochastic responses is a critical topic in uncertainty analysis. In this paper, orthogonal decomposition technique was extended to discuss non-stationary response of non-linear oscillator under random excitation. The PDF of stochastic reponses is represented by a set of standardized multivariable orthogonal polynomials. According to the Galerkin scheme, the original problem, which has to solve the Fokker–Planck–Kolmogorov (FPK) equation, was converted to a first-order linear ordinary differential equation, in terms of unknown time-dependent coefficients. Then, stationary and non-stationary PDFs of uncertainty responses were obtained. In numerical examples, first-order and second-order non-linear systems exposed to the Gaussian white noise were considered. Finally, the accuracy of the proposed method was demonstrated through appropriate comparisons to Monte-Carlo simulation and analytical results. [ABSTRACT FROM AUTHOR]

The recurrent approach constructed via the stochastic central difference (SCD) is a very fast method for analyzing non-stationary random responses. However, the computational results depend to a great extent upon the discrete time-step size. A new recurrent approach is proposed in this report. It is based on the theory of linear differential equations. Theoretical analysis shows that this algorithm is unconditionally stable for all damped systems. Two examples show that the proposed approach is not sensitive to the time-step. [ABSTRACT FROM AUTHOR]

The dynamics of two-degrees-of-freedom dynamical systems with weak quadratic nonlinearities is analyzed in the neighborhood of bifurcation points when the excitation frequency varies slowly through the region of primary resonance. The two modes of vibration are in 1 : 2 subharmonic internal resonance. The slowly evolving averaged equations are numerically studied for motions initiated in the vicinity of stationary responses, and observations are made about the nature of responses of the system near the transition from single-mode to coupled-mode solutions (pitchfork points), and near jump and Hopf bifurcations in the coupled-mode solutions. An analytical technique based on the dynamic bifurcation theory is developed to explain the numerical observations for passage through the bifurcations. A numerical study is carried out to determine the effects of system parameters on the dynamics near the pitchfork bifurcation points and results are compared with analytical and numerical descriptions of dynamics. [ABSTRACT FROM AUTHOR]

This paper aims to identify the natural frequencies and modal damping ratios of the Tsing Ma suspension bridge during Typhoon Victor using the newly emerged empirical mode decomposition (EMD) method in conjunction with the Hilbert-transform (HT) technique. Stationary tests on the acceleration responses of the bridge recorded at different locations and in different directions during Typhoon Victor are first carried out to classify the recorded response data. Natural frequencies and modal damping ratios identified by the EMD-HT method are then compared with those obtained by the traditional fast Fourier transform (FFT)-based method. The modal parameters identified by the EMD-HT method from the bridge responses recorded at different locations are compared with each other to check their consistency. Furthermore, the variations of natural frequency and total modal damping ratio with vibration amplitude and mean wind speed are examined. The results demonstrated that the EMD-HT method is applicable to modal parameter identification of large civil structures under typhoons. The EMD-HT method and the FFT-based method produced almost the same natural frequencies but the FFT-based method gave higher modal damping ratios than the EMD-HT method in general. [Copyright &y& Elsevier]

The GeoSHM project feasibility study for monitoring the Forth Road Bridge is briefly introduced and the instrumentation summarised. The events of January 9th, 2015 are described, when the bridge was struck by storm Elon, which caused widespread damage across Scotland and led to the temporary closure of the bridge when a van was blown over. During this storm an anomalous large amplitude response was observed. The data for January 9th, 2015 are analysed to show that the extreme response and the corresponding wind are non-stationary and non-Gaussian. Further analysis of the rainfall radar data for the same time shows a line of intense rainfall extending for over 100 ​km, which passes the site of the bridge at exactly the time of the peak response. The rainfall intensity was high enough to indicate that this feature was caused by convective activity and this observation was corroborated by records of lightning strikes. It is concluded that non-stationary wind events can give rise to large response of long span bridge structures and that this response can exceed that observed from the stationary wind field. Furthermore, historical data confirm that energetic squall lines are not uncommon in the UK. Therefore, the assumption of stationarity in predicting the wind induced response of long span bridges may be non-conservative and the climatology of large convective systems, such as squall lines, should be considered in assessing the wind hazard for these structures. • Presents evidence from field monitoring of the non-stationary response of a long span bridge to wind loading. • Presents evidence associating intense rainfall radar data with observed non-stationary large amplitude response. • Demonstrates the added value of using GNSS sensors to monitor the deflection of large structures under wind load. [ABSTRACT FROM AUTHOR]