Mechanical and Aerospace Engineering

This paper presents improvements of a multivariable autoregressive (AR) model for applications in operational modal analysis considering simultaneously the temporal response data of multi-channel measurements. The parameters are estimated by using the least squares method via the implementation of the QR factorization. A new noise rate-based factor called the Noise rate Order Factor (NOF) is introduced for use in the effective selection of model order and noise rate estimation. For the selection of structural modes, an orderwise criterion called the Order Modal Assurance Criterion (OMAC) is used, based on the correlation of mode shapes computed from two successive orders. Specifically, the algorithm is updated with respect to model order from a small value to produce a cost-effective computation. Furthermore, the confidence intervals of each natural frequency, damping ratio and mode shapes are also computed and evaluated with respect to model order and noise rate. This method is thus very effective for identifying the modal parameters in case of ambient vibrations dealing with modern output-only modal analysis. Simulations and discussions on a steel plate structure are presented, and the experimental results show good agreement with the finite element analysis.

In this paper, a method is developed for the modal analysis of vibrating structures whose properties may vary with time; it is based on an autoregressive model in a short-time scheme, and is called Short-Time Auto Regressive (STAR). This new method allows the successful modeling and identification of an output-only modal analysis of non-stationary systems. The originality of the proposed method lies in its specific handling of non-stationary vibrations, which allows the tracking of modal parameter changes in time. The paper presents an update of the model used with respect to order as well as a new criterion for the selection of an optimal model order, based on the noise-to-signal ratio. It is shown that this criterion works stably with respect to block data length. As for the block size itself, a length equal to four times the period of the lowest natural frequency has been found to be efficient. To validate the proposed method, a system with three degrees of freedom is first numerically simulated under a random excitation, and both linear and non-stationary vibrations are considered. In both cases, only a time-invariant autoregressive model is used in each sliding window, and the model parameters are estimated using least squares implemented via a QR factorization of the data matrix. The method is finally experimentally applied on the real multichannel data measured on a steel plate emerging from water, and compared to the conventional Short-Time Fourier Transform (STFT) method. It is shown that the proposed method outperforms in terms of frequency identification, whatever the non-stationary behaviour (either slow or abrupt change) due to the added mass effect of the fluid.

Cet article présente une technique pour analyser et évaluer la capacité portante des ponts dans des conditions d'opération normale. Elle est basée sur l'analyse de vibration de la structure sous l'excitation des surcharges passées sur le pont. Nous aborderons d'abord les principes et leur réalisation, les techniques de mesure et des méthodes de traitement des données. Finalement, nous présenterons les corrélations avec normes en vigueur. Le travail tente à jeter une base pour des manuels techniques d'ouvrages d'art durables.

In this paper, a method is developed for the modal analysis of vibrating structures whose properties may vary with time; it is based on an autoregressive model in a short-time scheme, and is called Short-Time Auto Regressive (STAR). This new method allows the successful modeling and identification of an output-only modal analysis of non-stationary systems. The originality of the proposed method lies in its specific handling of non-stationary vibrations, which allows the tracking of modal parameter changes in time. The paper presents an update of the model used with respect to order as well as a new criterion for the selection of an optimal model order, based on the noise-to-signal ratio. It is shown that this criterion works stably with respect to block data length. As for the block size itself, a length equal to four times the period of the lowest natural frequency has been found to be efficient. To validate the proposed method, a system with three degrees of freedom is first numerically simulated under a random excitation, and both linear and non-stationary vibrations are considered. In both cases, only a time-invariant autoregressive model is used in each sliding window, and the model parameters are estimated using least squares implemented via a QR factorization of the data matrix. The method is finally experimentally applied on the real multichannel data measured on a steel plate emerging from water, and compared to the conventional Short-Time Fourier Transform (STFT) method. It is shown that the proposed method outperforms in terms of frequency identification, whatever the non-stationary behaviour (either slow or abrupt change) due to the added mass effect of the fluid.

Since its first application to structural vibration in the late 1970's, the autoregressive moving average (ARMA) model has been considered one of the most appropriate mathematical models for dynamic modeling of structures. This paper presents the development of a multivariable autoregressive (AR) model along with a critical assessment of its application for structural modal analysis. The model parameters are estimated using QR factorization which is fast and provides a conditioned estimate. This model is very effective for the identification of modal parameters in cases of ambient responses when carrying out modern modal analysis using only output data. A system with two degrees of freedom (2DOF) is presented and the model is assessed by evaluating the following criteria; accuracy of the identified frequencies, damping ratio and mode shape of each mode at different noise-to-signal ratios and model orders. As a further evaluation the method is applied to dynamic testing data from a steel plate and found to be in close agreement with results of finite element analysis.

This paper presents a study on the identification of modal parameters by experimental operational modal analysis for the assessment of bridge rehabilitation. Modal parameters of the bridge before and after rehabilitation are estimated. Normal traffic flow over the bridge provided the excitation source. A single 3D accelerometer, located at mid-span of the bridge was used to obtain natural frequencies and damping ratios of the vibration modes. Identification of modal parameters was conducted using four methods including the Peak Picking method (PP), the Least Square Complex Exponential method (LSCE), the Autoregressive method (AR) and the Autoregressive Moving Average method (ARMA). During the study, the concrete deck of the bridge was replaced by orthotropic steel in order to increase its load capacity. The effect of this rehabilitation can be clearly observed through estimated vibration parameters in the stability diagrams.

A method is developed for the automatic identification of the spectrum and modal parameters of an operational modal analysis using multi sensors. A multivariate autoregressive model is presented, and its parameters are estimated by least squares via the implementation of QR factorization. A noise-independent minimum model order, from which all available physical modes may be identified, is developed. This so-called optimal model order is selected from the convergence of a global order-wise signal-to-noise ratio index. At this model order or higher, the modes are classified based on a decreasing damped modal signal-to-noise (DMSN) criterion. This decreasing order classification allows for easy identification of all the physical modes. A significant change in the DMSN index enables the determination of the number of physical modes in a specific frequency range, and thus, an automatic procedure for identifying the modal parameters can be developed to discriminate harmonic and natural frequencies from spurious ones. Furthermore, a multispectral matrix can be constructed from selected frequencies by introducing a powered amplification factor, which provides a smooth, balanced, noise-free spectrum with all main peaks. The proposed method has been performed on simulated multi-degree-of-freedom systems, on a laboratory test bench, and on an industrial operating high power hydro-electric generator offering the potential for automatic operational modal analysis and structural health monitoring.

Since its first application to structural vibration in the late 1970's, the autoregressive moving average (ARMA) model has been considered one of the most appropriate mathematical models for dynamic modeling of structures. This paper presents the development of a multivariable autoregressive (AR) model along with a critical assessment of its application for structural modal analysis. The model parameters are estimated using QR factorization which is fast and provides a conditioned estimate. This model is very effective for the identification of modal parameters in cases of ambient responses when carrying out modern modal analysis using only output data. A system with two degrees of freedom (2DOF) is presented and the model is assessed by evaluating the following criteria; accuracy of the identified frequencies, damping ratio and mode shape of each mode at different noise-to-signal ratios and model orders. As a further evaluation the method is applied to dynamic testing data from a steel plate and found to be in close agreement with results of finite element analysis.