S.V. Modak

Comparative study of model updating methods using simulated experimental data

The inverse eigensensitivity method and the response function method of analytical model updating have become relatively more popular among other methods and have been successfully applied to the practice of analytical model improvement. This paper gives a detailed comparison of these two approaches of model updating on the basis of computer simulated experimental data with the objective of studying the convergence of the two methods and the accuracy with which they predict the corrections required in a finite element model. The effect of the amount of experimental data used in the process of model improvement on the quality of an updated model is also studied. The test cases of complete, incomplete and noisy experimental data are considered. The updated models are compared on the basis of some error indices constructed to quantify error in the predicted natural frequencies, mode shapes and response functions.

Active structural-acoustic control of interior noise in a vibro-acoustic cavity incorporating system identification

Linear quadratic Gaussian optimal control is one of the techniques used for active noise control. In practical implementation of this technique, one of the key difficulties faced is the estimation of the states of the plant. A state observer that accurately estimates these states can be used in this regard. Studies reported make use of analytically or experimentally derived models to build observers. This paper proposes a method for active noise control in the framework of active structural-acoustic control incorporating system identification for the development of the linear quadratic Gaussian controller. Kalman filter is used as a stochastic state observer of the plant states. System identification is carried out using modal testing and finite element model updating to obtain an accurate model of the plant for building up the Kalman filter. The objective of the proposed method is to actively reduce the noise inside the cavity due to disturbances acting on the cavity structure. The active control is achieved by controlling the structural vibrations by taking into account the degree of coupling between the various structural and the acoustic modes. The effectiveness of the proposed method is evaluated experimentally on a 3D rectangular box cavity with a flexible plate.

A variable step-size filtered-x least mean square algorithm for continuously varying noise

The filtered-x least mean square algorithm (FxLMS) is a widely used technique in active noise control. In a conventional FxLMS algorithm, the value of convergence coefficient is kept constant which may not yield optimum performance if frequency of the primary noise changes. For some frequencies, this may result into a slower convergence and for some other frequencies, it may lead to instability. To deal with this situation, a normalized FxLMS algorithm, in which the convergence coefficient is normalized with the power of the filtered reference signal, is proposed. In the eigenvalue equalization method, the magnitude of secondary path transfer function is equalized such that the power of filtered reference signal remains equal at all the frequencies. The method proposed in this paper attempts to optimally adapt the convergence coefficient of the FxLMS algorithm for continuously varying noise. It is based on estimating how frequency of noise is varying using fast Fourier transforms of the reference signal and then, using this information to optimally adapt the convergence coefficient. The optimum value of the convergence coefficient is decided based upon the power and delay of the filtered reference signal and sampling frequency. A numerical study in a 3D acoustic cavity is presented to test the effectiveness of the proposed method and the results are also compared with the conventional FxLMS and the frequency-domain FxLMS algorithm. It is found that the proposed method leads to a faster convergence which results in higher noise reduction especially when the frequency of noise varies continuously. Simulation results show that the noise reduction obtained depends upon the rate at which the frequency of the primary noise varies. The higher the rate of variation and the duration for which the variation exist, the better the performance of the proposed method is over the conventional FxLMS algorithm in terms of noise reduction. The frequency-domain FxLMS algorithm is not found to be effective if the frequency of primary noise varies continuously.

Active Structural-Acoustic Control of Interior Noise using Direct Output Feedback- an Experimental Study

An important problem in systems such as automobile passenger compartments, aerospace interiors, helicopters, marine vehicles, launch vehicles and other enclosed spaces and cavities is the control of low frequency interior noise. In many of these systems the elastic structure surrounding the cavity vibrates under the action of mechanical and/or acoustic disturbances. These vibrations couple with the enclosed medium leading to generation of interior noise. Passive and active noise control methods can be used to reduce the interior noise. Active structural-acoustic control (ASAC) is a technique of active noise control (ANC) in which secondary sources of excitation are used on the structure itself with the objective of reducing the sound. In this paper, direct output feedback control strategy is experimentally evaluated on a 3-D rectangular box cavity. The modal analysis of the rectangular plate is carried out. The direct output feedback controller gain is calculated based on the pole-zero map. It is found that the actuation voltage adds damping at the resonance; also add stiffness, due to that the peaks are shifting towards right direction. It is observed that the noise inside the cavity has been reduced when direct output feedback control strategy is used.

A Method for Vibro-Acoustic FE Model Updating of Cavities Using Frequency Response

Interior noise due to structure-borne sources has always been a cause of concern in the cavities encountered in aerospace, automotive and other applications. In the design of such cavities, the coupled vibro-acoustic model is the key to evaluate its structural and acoustic design. It can also be used as a diagnostic tool to identify the potential noise sources and to assess the effectiveness of the proposed design modifications. However effectiveness of this model greatly depends on the accuracy of predictions made by these models. It is however seen that often there are inaccuracies in the modeling of structural and acoustic domain of a cavity. Methods to deal with structural and acoustic modeling inaccuracies have been developed in the past through FE model updating for uncoupled FE model, while the same have not been addressed in the context of a coupled vibro-acoustic FE model. This issue forms the topic of this paper. This paper proposes a method for updating vibro-acoustic FE model using frequency response function with the aim of identifying the material property of flexible surface of cavity. The updating problem is formed as constrained optimization. The method requires measured vibro-acoustic frequency responses of the system. Updating parameters related to the material property and the stiffness of joint between the plate and rectangular cavity are used. The effectiveness of the proposed method is validated through numerical studies on a 3D rectangular box cavity. The robustness of the method under presence of noise is also investigated. The proposed method is found to work satisfactorily to correctly estimate the updating parameters and yield an updated model that correlates well with the measured frequency response.

Multi Speed Model Updating of Rotor Systems

Accurate Finite Element (FE) models of rotor systems are required for predicting its dynamic behavior, in dynamic design and fault identification purposes. In inverse eigen-sensitivity method of finite element model updating, the limited number of measured eigenvalues available at any spin speed restricts the maximum number of parameters that can be updated. This paper proposes a multi speed model updating method based on inverse eigenvalue sensitivities to update parameters of a rotor system. The method uses eigenvalues obtained at more than one spin speed to update the model. Such an approach allows not only to update more number of parameters but also helps in obtaining a more consistent estimate of updating parameters.

Uncorrelated Modes Driven Inverse Eigensensitivity Method for Finite Element Model Updating

The inverse eigensensitivity method is one of the most widely used approaches for finite element model updating. One of the requirements for updating using this approach is that the correspondence between the experimental and the analytical modes must be known. However, at times, it may not always be possible to establish with certainty, for some analytical modes, to which experimental modes they correlate or correspond. Eigenvalues and eigenvectors of such modes cannot be used in the updating process, and this represents a drawback of the inverse eigensensitivity method and other iterative methods based on the modal data. If a finite element model has an excessive modeling error, then the correlated mode pairs may not remain stable during the updating process and may undergo changes. This situation also cannot be handled effectively using the current techniques that implicitly assume stability of the mode pairs. This paper presents a new method, the uncorrelated-modes-driven inverse eigensensitivity meth...

A Method for FE Model Updating of Coupled Vibro-Acoustic Systems Using Constrained Optimization

Finite element (FE) model updating is now recognized as an effective approach to reduce modeling inaccuracies present in an FE model. FE model updating has been researched and studied well for updating FE models of purely structural dynamic systems. However there exists another class of systems known as vibro-acoustics in which acoustic response is generated in a medium due to the vibration of enclosing structure. Such systems are commonly found in aerospace, automotive and other transportation applications. Vibro-acoustic FE modeling is essential for sound acoustic design of these systems. Vibro-acoustic system, in contrast to purely structural system, has not received sufficient attention from FE model updating perspective and hence forms the topic of present paper.In the present paper, a method for finite element model updating of coupled structural acoustic model, constituted as a problem of constrained optimization, is proposed. An objective function quantifying error in the coupled natural frequencies and mode shapes is minimized to estimate the chosen uncertain parameters of the system. The effectiveness of the proposed method is validated through a numerical study on a 3D rectangular cavity attached to a flexible panel. The material property and the stiffness of joints between the panel and rectangular cavity are used as updating parameters. Robustness of the proposed method under presence of noise is investigated. It is seen that the method is not only able to obtain a close match between FE model and corresponding ‘measured’ vibro-acoustic characteristics but is also able to estimate the correction factors to the updating parameters with reasonable accuracy.© 2013 ASME

A Review of Damping Matrix Identification Methods in Structural Dynamics

Damping matrix modeling and identification has important applications in many engineering fields such as vibration analysis and control, modal analysis, condition monitoring and structural dynamic modifications. A damping model should represent both the mechanism and spatial distribution of the energy loss in the system. In contrast to the mass and stiffness matrices, formulation of the damping matrix still stands as a big challenge in modeling a linear dynamic system. Several methods have been proposed in the literature to identify the damping and the parameters of a damping matrix from measurements on a vibrating system. It is felt that a review of the various approaches developed would help to compare their main features and their relative advantages or limitations to allow for choosing the most suitable method for a particular application. In view of this, this paper presents a review of the methods of damping identification in general, but with more emphasis on the methods developed in the framework of finite element model updating.Copyright

Finite Element Model Updating and Dynamic Design of Spot Welded Structures

Spot welds are used extensively in the automotive industry to join panels and for construction of other subassemblies that contains several thousands of spot-welds, so it is not practical in structural analysis to model each and every spot weld joint in detail. So a simple Finite element (FE) model of spot-welds needs to be used. There is not much work reported on dynamic testing, correlation and updating of the spot welded structures. This work explores the use of FE model updating to improve the dynamic characteristics of the spot welded structures. A hat like structure, used in earlier studies, is built and experimental modal analysis done on the spot welded structure. An FE model for the hat structure is built and correlated mode pairs are identified and attempts are made to update the FE model. Structural dynamic modification studies have been carried out to evaluate the effectiveness of the updated FE model of the spot welded structure for dynamic design. It is found that the updated FE model predicts more accurately the changes in dynamic characteristics as compared to the original FE model. Effect of spot welds on natural frequencies and damping of the spot welded structures is also studied.