Non-stationary Response Signals Research Articles

Multi-shaker time-varying root mean square non-stationary random vibration environmental control test

The current multi-shaker random control methods concentrate on the simulation of stationary vibrations. This work presents an innovative technique for multi-shaker non-stationary random vibration environmental control test. Firstly, an amplitude modulation method is introduced to generate multi-input non-stationary random signals with time-varying root mean square values, whose kurtoses and moving RMS values are specified by amplitude modulation functions. Then, the generated signals are applied as excitation signals for the non-stationary random vibration environmental control test. The response signals of a linear vibration system under non-stationary excitations are derived in the frequency domain. The derived formulas for kurtoses and moving RMS values are also applicable to non-stationary response signals. Meanwhile, the stationary power spectral densities of response signals are put forward. When the amplitude modulation functions are zero mean Gaussian distributions, the power spectral densities of the response signals can be directly calculated. Ultimately, the control of kurtoses, moving RMS values and stationary power spectral densities of response non-stationary random signals is realized. Simulation and experimental examples both adopt a two-input two-output beam vibration system and the results prove the correctness and practicability of the proposed method. The presented control procedure is concise and efficient in simulating multi-shaker non-stationary random vibration environments.

An improved time-frequency analysis method for structural instantaneous frequency identification based on generalized S-transform and synchroextracting transform

In this paper, an improved time-frequency analysis (TFA) method based on generalized S-transform (GST) and synchroextracting transform (SET), named improved synchroextracting generalized S-transform (ISEGST) is proposed to improve the accuracy of structural instantaneous frequency (IF) identification. Namely improved generalized S-transform (IGST), a new transform is first put forwarded by optimizing the window function of GST. The parameters of window function in IGST are obtained by the energy concentration measure (CM) and the optimization methodology. Applying IGST in association with SET, the ISEGST is then derived. Compared with the TFA methods in the literature, the performance of ISEGST in numerical signals has been significantly improved, especially in the presence of noise. In simulation, a nonlinear Duffing system and a two-layer shear frame model are used respectively to verify the effectiveness of the proposed method. Moreover, a time-varying cable test is conducted. Acceleration responses of the structure under linear and sinusoidal varying tension force are collected respectively. Then, the ISEGST is used for IF identification. Numerical simulation and experimental results show that the ISEGST can effectively identify IF of structures with non-stationary response signals, and it has high accuracy and good stability.

A New Online Operational Modal Analysis Method for Vibration Control for Linear Time-Varying Structure

From the viewpoint of vibration control, if the amplitude of the main frequencies of the vibration response can be reduced, the vibration energy of the structure is greatly reduced. Modal parameters, including modal shapes, natural frequencies, and damping ratios, can reflect the dynamics of the structure and can be used to control the vibration. This paper integrates the idea of “forgetting factor weighting” into eigenvector recursive principal component analysis, and then proposes an operational modal analysis (OMA) method that uses eigenvector recursive PCA with a forgetting factor (ERPCAWF). The proposed method can identify the transient natural frequencies and transient modal shapes online and realtime using only nonstationary vibration response signals. The identified modal parameters are also suitable for online, real-time health monitoring and fault diagnosis. Finally, the modal identification results from a three-degree-of-freedom weakly damped linear time-varying structure shows that the ERPCAWF-based OMA method can effectively identify transient modal parameters online using only nonstationary response signals. The results also show that the ERPCAWF-based approach is faster, requires less memory space, and achieves higher identification accuracy and greater stability than autocorrelation matrix recursive PCA with a forgetting factor-based OMA.

A new instantaneous frequency extraction method for nonstationary response signals in civil engineering structures

Civil engineering structures in essence belong to time-varying and nonlinear structures and the resultant dynamic responses are usually nonstationary signals. A new method is proposed to extract instantaneous frequency of such nonstationary signals. The new method combines the extended analytical mode decomposition, normalization scheme, and improved arccosine function algorithm. In this method, a multicomponent response signal is first decomposed into several mono-components signals by the extended analytical mode decomposition theorem, and then the extracted mono-components are demodulated into purely frequency modulated signals by a repeated normalization scheme. After that, the improved arccosine function is presented to compute the instantaneous phase and instantaneous frequency. A numerical example and an experimental study of a cable with time-varying tension force are provided to illustrate the working of the method. The results demonstrate that the proposed method can extract instantaneous frequencies from multicomponent signals more accurately than Hilbert–Huang transform.

A New Approach of evaluating the damage in simply-supported reinforced concrete beam by Local mean decomposition (LMD)

How to analyze the nonstationary response signals and obtain vibration characters is extremely important in the vibration-based structural diagnosis methods. In this work, we introduce a more reasonable time-frequency decomposition method termed local mean decomposition (LMD) to instead the widely-used empirical mode decomposition (EMD). By employing the LMD method, one can derive a group of component signals, each of which is more stationary, and then analyze the vibration state and make the assessment of structural damage of a construction or building. We illustrated the effectiveness of LMD by a synthetic data and an experimental data recorded in a simply-supported reinforced concrete beam. Then based on the decomposition results, an elementary method of damage diagnosis was proposed.

Operational modal analysis for linear time-varying continuous dynamic structure based on LMPCA

Based on the theory of time-frozen, this paper proposes a novel operational modal analysis (OMA) for linear time-varying structure using limited memory principal component analysis (LMPCA). Compared with modal coordinate de- composition of non-stationary response signals for linear time-varying continuous beam structure, it is found that PCA can be decomposed to extract time-varying instantaneous modal parameters, which reveal structure characteristics in limited memory window length L. Numerical simulations results on a cantilever beam with slow time-varying mass are presented to verify the TV instantaneous natural frequencies and modal shapes identification capability of the LMPCA.

Damage detection using transient trajectories in phase-space with extended random decrement technique under non-stationary excitations

This paper proposes a damage detection method based on the geometrical variation of transient trajectories in phase-space, and the proposed methodology is compatible with non-stationary excitations (e.g., earthquake-induced ground motion). The work presented assumes zero-mean non-stationary excitation, and extends the random decrement technique to convert non-stationary response signals of the structure into free-vibration data. Transient trajectories of the structure are reconstructed via the embedding theorem from the converted free-vibration data, and trajectories are mapped successively into phase-space to enhance statistical analysis. Based upon the characterized system dynamics in terms of phase-space, the time prediction error is adopted as the damage index. To identify the presence and severity of damage in a statistically rigorous way, receiver operating characteristic curves and the Bhattacharyya distance are employed. The results from both numerical simulations and experiments validate the proposed framework, when the test structures are subject to non-stationary excitations. The extension achieved in this paper enables the phase-space damage detection approach to be compatible with non-stationary scenarios, such as traffic, wind, and earthquake loadings. Moreover, the results indicate that this phase-state-based method is able to identify damage-induced nonlinearity in response, which is an intrinsic characteristic associated with most structural damage types.

Ambient modal identification using non-stationary correlation technique

The topic of this paper is the modal identification from non-stationary ambient response data by applying correlation technique. It is shown theoretically that by assuming the ambient excitation to be non-stationary white noise in the form of a product model, the non-stationary response signals can be converted into free vibration data via the correlation technique. Previous studies have showed that the practical problem of insufficient data samples available for evaluating non-stationary correlation can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the non-stationary responses into stationary ones. However, the errors involved in the approximate free-decay response would generally lead to a distortion in the modal identification. In the present paper, we propose that, if the ambient excitation can be represented by a product model with slowly time-varying function, without any additional treatment of transforming the original nonstationary responses, the non-stationary responses of the system can be treated approximately as a stationary random process; then, the nonstationary cross correlation functions of structural response evaluated at an arbitrary, fixed time instants of structural response are of the same mathematical form as that of free vibration of a structure, from which modal parameters of the original system can thus be identified. Numerical simulations, including one example of using the practical earthquake data served as the excitation input acting on a linear two-dimensional model of one-half of a railway vehicle, confirm the validity of the proposed method for identification of modal parameters from non-stationary ambient response data only.

A modified random decrement technique for modal identification from nonstationary ambient response data only

Modal identification is considered from response data of structural system under nonstationary ambient vibration. In a previous paper, we showed that by assuming the ambient excitation to be nonstationary white noise in the form of a product model, the nonstationary response signals can be converted into free-vibration data via the correlation technique. In the present paper, if the ambient excitation can be modeled as a nonstationary white noise in the form of a product model, then the nonstationary cross random decrement signatures of structural response evaluated at any fixed time instant are shown theoretically to be proportional to the nonstationary cross-correlation functions. The practical problem of insufficient data samples available for evaluating nonstationary random decrement signatures can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. Modal-parameter identification can then be performed using the Ibrahim time-domain technique, which is effective at identifying closely spaced modes. The theory proposed can be further extended by using the filtering concept to cover the case of nonstationary color excitations. Numerical simulations confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data.

Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.

Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.For this study, some reinforced concrete beams have been tested in the framework of a vast project: these beams show a clear softening nonlinear behaviour, well detectable when the excitation is produced by a hammer (free response). If the passage of a carriage is considered, moreover, the variation of natural frequencies is always larger than expected because of this softening nonlinearity.The article first analyzes theoretically the two effects on the natural frequencies of a simply supported beam, then a numerical and an experimental tests are presented. The identification procedure is conducted with a linear algorithm called ST-SSI, which has been demonstrated to be appropriate for the analysis of non-stationary signals, in particular in presence of moving masses. The article shows that the nonlinear contribution can be well estimated by using this linear tool but, on the contrary, when also moving masses are present, it is difficult to separate the nonlinear effects from the time varying ones.

Identification of Modal Parameters from Nonstationary Ambient Vibration Data Using Correlation Technique

Identification of modal parameters is considered from response data of structural systems under nonstationary ambient vibration. It is shown theoretically that by assuming the ambient excitation to be nonstationary white noise in the form of a product model, the nonstationary response signals can be converted into free-vibration data via the correlation technique. The practical problem of insufficient data samples available for evaluating nonstationary correlation can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. Modal-parameter identification can then be performed using the Ibrahim time-domain technique, which is effective at identifying closely spaced modes. The theory proposed can be further extended by using the filtering concept to cover the case of nonstationary color excitations. Numerical simulations confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data.