Nonstationary Excitation Research Articles

An explicit time-domain approach for sensitivity analysis of non-stationary random vibration problems

This paper presents an explicit time-domain method for sensitivity analysis of structural responses under non-stationary random excitations. Based on time-domain explicit expressions of dynamic responses, a new and more concise time-domain explicit expression of response sensitivity is derived using the direct differentiation method (DDM). Then a more efficient algorithm for direct construction of the explicit expression of response sensitivity is developed based on the physical meanings of the coefficient matrices in the formulation. The adjoint variable method (AVM) is further used to establish the explicit expression of the sensitivity of an arbitrary response. Finally, based on the time-domain explicit expressions for both dynamic response and its sensitivity, an efficient time-domain approach is proposed to calculate the sensitivity of variance responses of a structure subjected to non-stationary random excitations. Numerical examples of different structural systems under non-stationary random excitations are presented to demonstrate the accuracy and efficiency of the proposed method.

Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

An approximate technique for assessing the reliability of nonlinear multi-degree-of-freedom (MDOF) systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) oscillators. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are determined. Overall, the developed technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF system exhibiting hysteresis following the Bouc-Wen model is included in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the accuracy of the technique.

Damage detection of framed structures subjected to earthquake excitation using discrete wavelet analysis

This paper describes an application of discrete wavelet analysis for damage detection of a framed structure subjected to strong earthquake excitation. The response simulation data on each floor were obtained by non-linear dynamic analysis. Damage to the frame was introduced due to the non-linear behaviour of the columns and beams. In order for the structural members to reach the yield point or go slightly beyond yielding, the earthquake excitation was scaled up with the appropriate factor. Since the dynamic behaviour of an inelastic structure during an earthquake is a non-stationary process, discrete wavelet analysis was performed in order to analyze the simulation response data for each floor. It was shown that structural damage on a floor, and the time when this occurred can be clearly detected by spikes in the wavelet details of the response, acquired from the corresponding floor. Damage can be detected by observing the spikes directly from the wavelet details or following a statistical procedure. An automatic numerical procedure that can clearly distinguish between the spikes associated with damage and the spikes due to non-stationary excitation is proposed. The effects of noise were taken into account by adding a white Gaussian noise to the simulation response data. Damage to the element can also be detected again from the noised signal, if the level of details and the order of wavelets in the wavelet analysis of the response signal are increased. Numerical results show the effectiveness of the discrete wavelet approach to damage detection of framed structures.

Modal damping ratio analysis of dynamical system with non-stationary responses

During the long term monitoring of the structure, the damping ratio reflects the characteristics of the structure from perspective of energy loss, and its changes can reflect the structural damages to some extent. But in the structural modal analysis based on the prototype measurement, the damping ratio identification results are difficult to identify, especially for the non-stationary structural responses, besides, ICA loses accuracy in the presence of higher-level damping. In allusion to these problems, a modal identification method based on the stationary filter-time frequency independent component analysis (filter-TFICA) is proposed. First a stationary filter using moving average is used to eliminate the non-stationary components. Then the modal identification of mooring system is incorporated into the blind source separation formulation where TFICA is introduced. The validity of the proposed method is confirmed through the identification of a multi degree of freedom numerical simulation system under non-stationary random excitations. Further, the prototype measurement data of the floating production, storage and offloading (FPSO) single point mooring system are analyzed. Compared with the traditional method, the differences of identified damping ratios at the same frequency range by the proposed method are smaller. The distribution of identified modal frequencies is more scattered and the mutually coupled modes are decoupled well. Each of the calculated motion tracks corresponding to the mode shapes presents single form of motion more prominently.

Fast Equivalent Linearization Method for Nonlinear Structures under Nonstationary Random Excitations

AbstractAn efficient analysis procedure has been developed for the random vibration analysis of nonlinear structures subjected to nonstationary random excitations based on the equivalent linearization method and the time-domain explicit formulation method. When the equivalent linearization method is used for the nonstationary random vibration analysis of a nonlinear structural system, equivalent linear systems are constructed for different time instants and the analysis problem is transformed to a series of analyses of these linear systems. Because a large number of linear analyses must be conducted to get reliable results for the original nonlinear system, efficiency of the analysis algorithm for the linear analysis is crucial for its successful application. The time-domain explicit formulation method, recently proposed for the nonstationary random vibration analysis of linear systems, has much higher computational efficiency than other methods owing to the use of explicit expressions of dynamic response...

Damage detection for shear structures based on wavelet spectral transmissibility matrices under nonstationary stochastic excitation

SUMMARY A new method of spectral transmissibility function extraction and damage detection for shear frame structures under nonstationary stochastic excitation is proposed. A new concept named wavelet spectral transmissibility function is proposed as damage feature. It is demonstrated that the wavelet spectral transmissibility function can characterize the structure while closing to the natural frequencies of the structure. Subsequence, the singular value decomposition of wavelet spectral transmissibility matrices with different references is proposed as an identification method of natural frequencies, and wavelet spectral transmissibility functions between two neighborhood measurement points at the natural frequencies under nonstationary stochastic excitation. At last, a new damage indicator is developed to locate and quantify the damage of shear frame structure, based on the wavelet spectral transmissibility functions and constraint linear least square method. A numerical model and a lab-scale frame structure successfully verify the validity of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.

Analysis of a high-pier railway bridge under spatial stochastic stationary and non-stationary earthquake excitations

Analysis of a high-pier railway bridge under spatial stochastic stationary and non-stationary earthquake excitations

Non-stationary random vibration analysis of multi degree systems using auto-covariance orthogonal decomposition

An algorithm that integrates Karhunen–Loeve expansion (KLE) and finite element method (FEM) is proposed to carry out random vibration analysis of complex dynamic systems excited by stationary or non-stationary random processes. In KLE, the auto-covariance function of random process is discretized using orthogonal basis functions. During the response calculations, the eigenvectors of KLE are applied as forcing functions. Three methods are proposed to carry out the random vibration analysis termed as, Method 1A, Method 1B and Method 2. In Method 1A and Method 1B, the basis functions are chosen such that they include multiples of complete or half-cosine and sine functions over the selected time. In Method 2, the basis functions are chosen to be simple piecewise constants. The proposed algorithm is applied to a 2DOF system, a cantilever beam and a stiffened panel for both stationary and non-stationary excitations. Results show that three methods can describe the statistics of the dynamic response with sufficient accuracy. However, Method 1A results have a relatively larger error than that for Method 1B and Method 2 during initial transient time. The Method 2 results have an excellent agreement with analytical results. Moreover, the runtime of Method 2 algorithm is significantly less than both Method 1A and Method 1B algorithms even though its usage results in an increase in the number of KLE terms. Furthermore, Method 2, unlike Method 1A and 1B, neither yields negative and/or infinite eigenvalues for the auto-covariance function nor large inaccuracies.

Adaptive photodetectors based on charge gratings in the problems of frequency-modulated optical signal detection

Nonstationary photovoltage excitation by frequency-modulated light in an adaptive photodetector based on GaAs is studied. To observe the effect, the crystal is exposed to light beams with the relative frequency shift Δf(t). Linear frequency modulation Δf(t) = At is used in the experiments. As a result of such illumination, a pulsed electrical signal is induced in the crystal. The pulse appears at the deceleration of the interference pattern motion, and its duration is controlled by the frequency variation rate A and the time of the charge grating formation. The possibility of using the effect in the systems for measuring velocities and accelerations of moving objects is shown.

Integration algorithm for covariance nonstationary dynamic analysis using equivalent stochastic linearization

Deterministic mechanical systems subject to stochastic dynamic actions, such as wind or earthquakes, have to be properly evaluated using a stochastic approach. For nonlinear mechanical systems it is necessary to approximate solutions using mathematical tools, as the stochastic equivalent linearization. It is a simple approach from the theoretical point of view, but needs numerical techniques whose computational complexity increases in case of nonstationary excitations. In this paper a procedure to solve covariance analysis of stochastic linearized systems in the case of nonstationary excitation is proposed. The nonstationary Lyapunov differential matrix covariance equation for the linearized system is solved using a numerical algorithm which updates linearized system coefficient matrix at each step. The technique used is a predictor–corrector procedure based on backward Euler method. Accuracy and computational costs are analysed showing the efficiency of the proposed procedure.

Transient sound radiation from an impulsively excited piezoelectric composite hollow sphere in a wedge-shaped acoustic domain

The exact 3D linear piezoelasticity theory, the linear acoustic wave equation, and the classical method of images are employed for the coupled acousto-elastodynamic time response analysis of an arbitrarily thick two-layered elasto-piezoelectric composite hollow sphere that is freely suspended in a perfect acoustic wedge with impenetrable (rigid/compliant) boundaries, while subjected to arbitrary (non-axisymmetric) non-stationary electro-mechanical excitations. Problem solution is attained by application of the method of eigen-function expansion, a revised form of translational addition theorems for modified spherical Bessel functions in Laplace transform domain, and Durbin’s numerical inversion algorithm with an advanced (modified Cesàro) convergence improvement scheme. Numerical simulations include selected radiated pressure time signatures of a water-submerged air-filled PZT4/aluminum spherical shell driven by a pair of external diametrical short duration mechanical pulses. The effects of sphere wall thickness, wedge opening (apex) angle (γ=π/6,π/4,π/2) and surface condition (hard or pressure-release) are examined. Also, some noteworthy features of the transient fluid/structure interaction are recognized through proper 2D visualizations of the internal and external sound fields. Lastly, accuracy of the proposed acousto-elastic model is confirmed with the help of a commercial FEA software in addition to comparison with the available data.

Non-resonant energy harvesting via an adaptive bistable potential

Narrow bandwidth and easy detuning, inefficiency in broadband and non-stationary excitations, and difficulties in matching a linear harvester’s resonance frequency to low-frequency excitations at small scales, have convinced researchers to investigate nonlinear, and in particular bistable, energy harvesters in recent years. However, bistable harvesters suffer from co-existing low and high energy orbits, and sensitivity to initial conditions, and have recently been proven inefficient when subjected to many real-world random and non-stationary excitations. Here, we propose a novel non-resonant buy-low-sell-high strategy that can significantly improve the harvester’s effectiveness at low frequencies in a much more robust fashion. This strategy could be realized by a passive adaptive bistable system. Simulation results confirm the high effectiveness of the adaptive bistable system following a buy-low-sell-high logic when subjected to harmonic and random non-stationary walking excitations compared to its conventional bistable and linear counterparts.

Non-stationary frequency domain system identification using time–frequency representations

System properties of buildings and bridges may vary with time due to temperature changes, aging or extreme loadings. To identify these time-varying system properties, this study proposes a new output-only non-stationary system identification (SI) framework based on instantaneous or marginal spectra derived from the time–frequency representation, e.g., short time Fourier or wavelet transform. Spectra derived from these time–frequency representations are very popular in tracking time-varying frequencies; however, they have seldom been used to identify the time-varying damping ratio because a short window needed to capture the time-varying information amplifies the bandwidth significantly, which may lead to considerably overestimating the damping ratio. To overcome this shortcoming, this study modifies the theoretical frequency response function (FRF) to explicitly account for the windowing effect, and therefore enables SI directly using instantaneous or marginal spectra derived from the wavelet or short time Fourier transform. The response spectrum estimated using the short time window and the modified FRF are both influenced by the same time window, thus the instantaneous or time-localized marginal spectrum of response can be fitted to the modified FRF to identify frequency and damping ratio at each time instant. This spectral-based SI framework can reliably identify damping in time-varying systems under non-stationary excitations. The efficacy of the proposed framework is demonstrated by both numerical and full-scale examples, and also compared to the time-domain SI method, stochastic subspace identification (SSI), since the time-domain SI approaches and their extensions are popular in identifying time-varying systems utilizing recursive algorithms or moving windows.

A study on semi-active Tuned Liquid Column Dampers (sTLCDs) for structural response reduction under random excitations

This paper proposes a new model for semi-active Tuned Liquid Column Damper (sTLCD) where the sTLCD is connected to the primary structure using an adaptive spring. Short time Fourier transformation (STFT) based control algorithms (feedforward and feedback) are developed to control the stiffness of the spring such that the sTLCD is tuned in real-time when the dominant excitation frequency varies or damage occurs to the primary structure. The effectiveness of the proposed sTLCD and the associated control algorithms is examined numerically under random excitations including stationary and non-stationary excitations. Root Mean Square (RMS) response is computed in three cases: with no TLCD, with a passive Tuned Liquid Column Damper (pTLCD) and with the sTLCD. Results indicate that the developed control algorithms are effective in tuning the frequency of the sTLCD in real-time. As a result, the sTLCD provides more robust reduction than the pTLCD because the pTLCD becomes off-tuned and loses its effectiveness when the properties of the excitations or the primary structure vary.

Harmonic wavelets based excitation–response relationships for linear systems: A critical perspective

An analytical approach based on generalized harmonic wavelets (GHWs) for determining the response evolutionary power spectral density (PSD) of single-degree-of-freedom linear structural systems subjected to non-stationary stochastic excitations is developed. Specifically, utilizing a periodized GHW transform, applying a Galerkin scheme, and relying on the orthogonality properties of the GHWs, an analytical relationship between wavelet coefficients of the system response and of the excitation is derived. It is shown that in comparison with a recently developed GHW based excitation–response relationship, which is based on a “locally stationary” stochastic process representation and employs localized in time monochromatic functions, the herein developed relationship exhibits enhanced accuracy for cases of relatively flexible systems and/or for systems with relatively low damping where the related impulse response function cannot be assumed to be short-lived. Pertinent numerical examples and Monte Carlo simulation data are included as well for demonstrating the reliability of the approach.

An efficient framework for the reliability-based design optimization of large-scale uncertain and stochastic linear systems

This paper is focused on the development of an efficient reliability-based design optimization algorithm for solving problems posed on uncertain linear dynamic systems characterized by large design variable vectors and driven by non-stationary stochastic excitation. The interest in such problems lies in the desire to define a new generation of tools that can efficiently solve practical problems, such as the design of high-rise buildings in seismic zones, characterized by numerous free parameters in a rigorously probabilistic setting. To this end a novel decoupling approach is developed based on defining and solving a limited sequence of deterministic optimization sub-problems. In particular, each sub-problem is formulated from information pertaining to a single simulation carried out exclusively in the current design point. This characteristic drastically limits the number of simulations necessary to find a solution to the original problem while making the proposed approach practically insensitive to the size of the design variable vector. To demonstrate the efficiency and strong convergence properties of the proposed approach, the structural system of a high-rise building defined by over three hundred free parameters is optimized under non-stationary stochastic earthquake excitation.

Wavelet-expansion-based stochastic response of chain-like MDOF structures

This paper presents a wavelet-expansion-based approach for response determination of a chain-like multi-degree-of-freedom (MDOF) structure subject to full non-stationary stochastic excitations. Specifically, the generalized harmonic wavelet (GHW) is first utilized as the expansion basis to solve the dynamic equation of structures via the Galerkin treatment. In this way, a linear matrix relationship between the deterministic response and excitation can be derived. Further, considering the GHW-based representation of the stochastic processes, a time-varying power spectrum density (PSD) relationship on a certain wavelet scale or frequency band between the excitation and response is derived. Finally, pertinent numerical simulations, including deterministic dynamic analysis and Monte Carlo simulations of both the response PSD and the story-drift-based reliability, are utilized to validate the proposed approach.

Fully Nonstationary Analysis of Linear Structural Systems Subjected to Multicorrelated Stochastic Excitations

AbstractThe stochastic analysis of structural systems subjected to seismic excitations requires the spectral characterization of both the excitation and the structural response. For large multisupported structures, the spatial variability of ground motion affects significantly the response so that in these cases the assumption of uniform ground motion is inappropriate and only the multicorrelated model of the ground motion acceleration is able to catch the actual effects of seismic waves on the structure. To reproduce the typical characteristics of real earthquakes ground-motion time history, such as the time and frequency varying content, the zero mean Gaussian evolutionary and the sigma-oscillatory stochastic processes have been proposed in literature for multicorrelated input too. In this study, a closed-form solution of the evolutionary power spectral density of the response of linear classically damped structural systems subjected to fully nonstationary multicorrelated excitations for both evolutiona...

Extended Blind Modal Identification Technique for Nonstationary Excitations and Its Verification and Validation

AbstractRecently the authors developed an output-only (or blind) identification technique for the modal identification of structures under ambient/free vibrations. In the present study, this method is extended to incorporate nonstationary unknown inputs—a feature that existing output-only methods are unable to replicate. The method employs a so-called PARAllel FACtor technique to decompose the third-order tensor that is built using the spatial time–frequency matrices of the response signals in order to find the mode shapes and modal coordinates’ auto time–frequency distribution (TFD). The proposed method is first verified using a synthetic data set and then used to extract the modal parameters from vibration data recorded during shaking table tests on the International Institute of Earthquake Engineering and Seismology (IIEES) test structure. The accuracy of the blind identification results is assessed through comparisons with a well-established input–output identification method, namely, a well-known com...

A stochastic simulation algorithm for evaluation of seismic pounding response of adjacent structures

This article proposes a comprehensive closed-form approach to determine the dynamic response of single-degree-of-freedom and multi-degree-of-freedom systems subjected to stationary and non-stationary Gaussian excitations. The proposed method presents the probabilistic seismic response of adjacent systems under different levels of seismic intensity, in terms of summarized incremental dynamic analysis curves, and has the ability to consider the seismic pounding effect based on the standard deviation of the response of adjacent systems. In comparison with the incremental dynamic analysis procedure, the proposed approach shows acceptable results with much less computational time and cost.