Novel structural flexibility identification in narrow frequency bands

SummaryFlexibility is an important parameter reflecting bridge load‐carrying capacity. Dynamic testing is a fast and effective method to obtain the structural modal flexibility of small‐ and medium‐span bridges. The Deterministic‐stochastic subspace identification (DSI) algorithm is a well‐established structure identification method in the time domain. However, the estimation of damping, especially the modal scaling factor, is not always reliable due to inevitable measurement noise, which directly affects the identification accuracy of flexibility. This paper proposes a maximum likelihood estimation method in subbands (SMLE), which can be regarded as an add‐on method of the DSI algorithm because the initial parameters are obtained from the DSI algorithm. The processing of frequency band division is implemented first, and the frequency response function curve in each subband of the whole frequency range is fit separately. Then, subband cyclic iteration is proposed to improve the identification accuracy in a closely spaced mode system. The proposed SMLE method maintains the advantages of the DSI algorithm while improving the accuracy of parameter estimation and flexibility identification. Two lumped mass models are used to verify that the proposed method can effectively improve estimates to obtain a precise flexibility matrix and predict the displacement of the structure under static loading. Experimental example of a continuous girder bridge is considered to verify the availability and effectiveness of the proposed method in practice.

Vibration characteristics of a powerplant, an important parameter to evaluate the booming noise and the durability of each parts of an automobile is a major field of simulation analysis using the finite element method (FEM). Overall vibration characteristics, however, depend heavily on the joint properties when it comes to the analysis of complicated structures like a powerplant where a number of parts are incorporated. Among other characteristics, it is extremely difficult to conduct accurate identification of the damping characteristics of the joint area, which had been the result of inaccurate analyses. This paper reports a newly established method to solve these problems through the application of frequency response function (FRF) data and FEM models. Also described is the result of application of the method to the evaluation of a transversely-mounted in-line four-cylinder engine in a front-wheel drive layout. The application revealed that the joint properties can be identified fairly accurately, which in turn allows reliable prediction of vibration level.

The evaluation of the structural performance and durability using only measurement data without any baseline data is practical. One measurement data type is the frequency response function (FRF) data set, which does not provide enough information about the health state because of the noise included in the data. Proper orthogonal modes (POMs) extracted from the FRF data in a prescribed frequency range are utilized as an index to recognize the existence of damage. The POMs represent the principal axes of inertia formed by the distribution of data on the modal coordinate curve. This work proposes a damage detection method to trace damage based on the POM energy curvature at the element of the finite element model. The validity of the proposed method is illustrated by a numerical experiment and an experimental test.

In experimental modal analysis, the use of characterized excitation and the choice of window functions are fundamental to the estimation of system frequency response function (FRF) data. It greatly influences the quality of the resulting FRF measurements. Discussed are combination methods of several commonly-used excitation signals with window function, which is relative to lightly damped systems. Study shows that burst random signal with Rectangular works well for lightly damped structures, and pure random with Hanning will bring about higher error. A modal testing of white car body was done. Experimental parameters analysis are given to demonstrate the study result presented above. So it poses a practicable method for improving the accuracy of frequency response function (FRF) measurements of lightly damped structure by using proper excitation signal with appropriate window function.

Linear systems are good approximations of the input-output relationship for many real systems. In practice, ensembles of nominally identical systems can seldom be adequately represented by a single linear system. Some accommodation needs to be made for representing inherent ensemble randomness. One approach would be to use a parameterized model of the system, with the random nature captured in discrete parameters of the parameterized model. Another approach is to use data measured from each system in the ensemble to represent the random nature of the ensemble in a non-parametric form. This is the approach described in this paper. There are several different types of data that could be collected from each system in the ensemble, each type capable of capturing the input-output behavior of the linear system: input-output time domain data, perhaps with specific excitation sequences; Markov parameters; and Frequency Response Functions (FRFs) to name a few. We choose to work with FRF data because many system attributes can be easily interpreted by inspection of the FRF. FRF data can also be used directly for control design. This paper develops a Karhunen-Loeve expansion representation for linear system behavior based on FRF data to develop a compact representation of the uncertainty inherent in an ensemble of systems. This non-parametric, compact, representation of the distribution of linear systems can then be used to characterize the performance and stability of a given feedback control law, as well as for control law design.

Frequency response function estimation techniques and the corresponding coherence functions: A review and update

Summary An efficient approach to identify multiple cracks in a slender beam using the frequency response function data is presented. It is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a slender beam. The cracks are modeled by rotational springs and the frequency response function is computed based on a spectral element model by the spectral finite element. The procedure gives a linear relationship explicitly between the changes of the measured frequency response function and crack parameters. The inverse problem is solved iteratively for the depths and locations of the cracks through the sensitivity-based model updating. Some numerically simulated tests on beam examples are provided for validating the feasibility of the method to identify the cracks. The results are generally agreement with the target values. Finally, the effect of noise on the damage identification is discussed in the numerical examples.

Uncertainty quantification of an inflatable/rigidizable torus

As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts.

Identification of modal parameters of unmeasured modes using multiple FRF modal analysis method

A DUAL FITTING ALGORITHM FOR MODAL PARAMETERS IDENTIFICATION

Damage detection in an offshore platform using incomplete noisy FRF data by a novel Bayesian model updating method

Traditional multi-reference impact testing (MRIT) has the merit to identify not only the structural modal parameters but also structural flexibility, however, it requires a large number of sensors mounted on the entire structure which leads to expensive experiment cost. A new mobile impact testing method is proposed in this article for a more efficient flexibility identification of bridges. In the proposed method, the structure under investigation is subdivided into smaller substructures which are tested independently. Then the experimental data collected from all sub-structures are integrated by taking the interface measurement as a reference for flexibility identification of the entire structure. The new impact testing method only requires limited instrumentation, thus it can be performed rapidly and efficiently. Especially, the signal processing procedure developed in the proposed method is able to identify the full flexibility matrix of the entire structure from the sparse FRF matrices of the sub-structures. Numerical and experimental examples studied successfully verify the effectiveness of the proposed method by comparing its results with those from the traditional MRIT method for structural flexibility identification and deflection prediction.

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

Traditional Frequency Response Function (FRF) estimation techniques used for analysis of Human Controller (HC) dynamics in tracking tasks assume HC dynamics to be linear, but generally do not quantify or compensate for the effects of human nonlinearities. The robust and fast Best Linear Approximation (BLA) techniques for estimating an FRF do provide such quantification of nonlinear distortions caused by Period-In-Same-Period-Out (PISPO) nonlinearities and can reduce the effect of PISPO nonlinear operations on the FRF estimate. This paper investigates the application of these BLA techniques to both measured and simulated HC data. For the simulated data, a linear HC model was deliberately extended with a symmetric PISPO deadzone nonlinear operator and a realistic level of HC noise. Overall, both the measured and the simulated data indicate that due to the high levels of remnant noise inherent to HC data, no consistent estimate of PISPO nonlinear contributions could be made. This also means that the improvement of using BLA techniques and averaging over multiple forcing function realizations does not result in a substantial improvement over the current practice of estimating HC FRFs from repeated measurements of a single forcing function.