Chulho Yang

An embedded sensitivity approach for diagnosing system-level vibration problems

Abstract In diagnosing a system-level vibration problem, the goals are to identify which component or components(s) are most responsible for the phenomenon and which changes to the system are most likely to mitigate the problem. The use of sensitivity analysis in diagnosing system-level vibration phenomena is examined in this work. It is shown that even if only a small subset of measured system input–output functions is available, an appropriate analytical parameterization of these functions leads to simple relationships between the measured data and the desired embedded sensitivity functions. These functions are then reformulated in terms of transmissibility functions with respect to a single input using a novel modal deflection chain technique in order to accommodate system-level operating response data in the absence of input measurements. The embedded sensitivity approach is used to examine two competing design modifications for reducing a structure-borne noise problem in an exhaust system. The sensitivity analysis shows that although both modifications mitigate the resonant vibration problem of interest, one of the modifications is more effective than the other because it introduces less overall change in the forced response characteristics at other frequencies.

Embedded sensitivity functions for characterizing structural damage

The use of embedded sensitivities in vibration-based damage identification for structural health monitoring is discussed. Embedded sensitivity functions are algebraic combinations of measured frequency response function data that determine how the forced responses of structural systems change with perturbations in mass, damping, or stiffness. After the theory of embedded sensitivity functions is reviewed, they are applied to characterize damage in an analytical three-degree-of-freedom system, a bench top two-degree-of-freedom system, and a full-scale exhaust system. By comparing embedded sensitivity functions with finite difference functions using undamaged and damaged frequency response functions, damage is shown to be properly detected, located, and quantified in theory and practice assuming that structures are only damaged in one location. Demonstrations on the bench top system and exhaust system indicate that the technique is most effective when certain frequency ranges in the data are analyzed to avoid ranges of low signal-to-noise ratios and when changes to frequency response functions are not excessive to avoid distortions in the estimated perturbations.

System Identification of Nonlinear Mechanical Systems Using Embedded Sensitivity Functions

A novel method of experimental sensitivity analysis for nonlinear system identification of mechanical systems is examined here. It has been shown previously that embedded sensitivity functions, which are quadratic algebraic products of frequency response function data, can be used to identify structural design modifications for reducing vibration levels. It is shown here that embedded sensitivity functions can also be used to characterize and identify mechanical nonlinearities. Embedded sensitivity functions represent the rate of change of the response with variation in input amplitude, and yield estimates of system parameters without being explicitly dependent on them. Frequency, response junctions are measured at multiple input amplitudes and combined using embedded sensitivity analysis to extract spectral patterns for characterizing systems with stiffness and damping nonlinearities. By comparing embedded sensitivity functions with finite difference frequency response sensitivities, which incorporate the amplitude-dependent behavior of mechanical nonlinearities, models can be determined using an inverse problem that uses system sensitivity to estimate parameters. Expressions for estimating nonlinear parameters are derived using Taylor series expansions of frequency response functions in conjunction with the method of harmonic balance for periodic signals. Using both simulated and experimental data, this procedure is applied to estimate the nonlinear parameters of a two degree-of-freedom model and a vehicle exhaust system to verify the approach.

Structural Damage Identification in a Mechanically Attached Metallic Panel Using Embedded Sensitivity Functions

A vibration-based structural damage identification method is discussed using experimental embedded sensitivity functions, which are algebraic combinations of measured frequency response functions (FRFs) that reflect changes in the response of mechanical systems when mass, damping, or stiffness parameters are changed. The theory of embedded sensitivity functions is reviewed and applied to identify damage in simulations with a six degree-of-freedom model of a metallic panel and in experiments on the actual panel. Measured FRFs, before and after simulated damage is imposed, are compared to an experimental sensitivity function. By matching the spectral shapes of these two sets of functions, damage is first located and classified as changes in stiffness, damping, or mass. Then the damage is quantified directly in engineering units as changes in stiffness or mass using only the measured data.

Predicting Changes in Vibration Behavior With Respect to Multiple Variables Using Empirical Sensitivity Functions

Engineers must routinely predict how structural systems will vibrate after design modifications are made to the mass, damping, or stiffness properties of the components. To reduce the cost of product development, sensitivity prediction methods are desired that can be applied using only empirical data from an initial prototype. Embedded sensitivity functions derived solely from empirical data have previously been applied (a) to identify optimal design modifications for reducing linear vibration resonance problems and (b) to predict the change in frequency response. In this previous work, predictive methods were developed that assumed that only one design parameter in the system was modified. In many applications, it is necessary to extend this approach to all major parameters for a more accurate prediction of the structural dynamic response. This paper utilizes a multivariable Taylor series to take into account multiple parameter changes that affect a broadband frequency range. The method is applied to a single degree of freedom analytical model to determine the accuracy of the predictions. Finite element analyses are then conducted on a three-story structure and an automotive vehicle component with modifications to the stiffness and mass distributions to demonstrate the feasibility of these predictions in applications to more complicated structural systems.

Identification of Multiple Damages in a Structure Using Embedded Sensitivity Functions and Optimization Techniques

A new method for identifying multiple damages in a structure using embedded sensitivity functions and optimization algorithms is presented in this work. Optimization techniques are used to minimize the difference between the measured frequency response functions from a damaged structure and the predicted FRFs from the baseline structure. The predicted FRF functions are calculated directly from the undamaged system response data using the embedded sensitivity functions and their Taylor series expansions. The optimal damage parameters are identified in engineering units as changes in stiffness, damping, or mass through the optimization process for minimizing the difference between those two FRFs. The method is applied to a two degree of freedom analytical model to determine the accuracy of the diagnostic results. Finite element analyses are then conducted on a three-story structure with damages in the form of stiffness and mass perturbations to demonstrate the applicability of this method to more complicated structural systems. It is shown that the suggested technique can detect and quantify multiple damages in a structure with high numerical accuracy in the level of the estimated damages.Copyright

Structural Damage Detection for Metal Panel Using Embedded Sensitivity Functions

Vibration-based damage identification method using embedded sensitivity functions is discussed. The theory of embedded sensitivity functions is reviewed and applied to identify damage in a three degree-of-freedom system and a metallic panel. Embedded sensitivity functions are algebraic combinations of measured frequency response functions that reflect changes in the response of mechanical systems when mass, damping or stiffness parameters are changed. By comparing the embedded sensitivity functions with finite difference functions using undamaged and damaged frequency response functions, damage is shown to be properly detected, located and quantified in theory and practice assuming that structures of interest are only damaged in one location. Simulated and experimental results indicate that the technique is most effective when changes to frequency response functions are small to avoid distorsions in the estimated perturbations due to variations in the sensitivity functions.

Embedded Sensitivity Functions for Experimentally Diagnosing Vibration Problems and Identifying Nonlinear Models of Automotive Components

In the development and manufacture of vehicle components and systems, it is often necessary to quickly identify optimal design modifications for mitigating noise and vibration problems to meet the production schedule. To address this need, experimental techniques for determining the sensitivity of forced vibration response to changes in mass, damping or stiffness properties are of great use. In order to distinguish physical changes in the system from nonlinear input-output distortion, experimental techniques for identifying nonlinear input-output models in mechanical systems are also needed. The use of experimental sensitivity measurements and analyses for studying linear and nonlinear forced vibration data is examined in this work. Embedded sensitivity functions are first used to identify design modifications for reducing a vibration resonant problem. These sensitivity functions are then applied to characterize and identify a nonlinear mechanical system and the accuracy of estimated nonlinear parameters with respect to several factors is examined. A vehicle exhaust system is used to experimentally demonstrate the results achieved using the diagnostic and system identification methods.

Structural damage identification using embedded sensitivity functions

Vibration-based damage identification using embedded sensitivity functions is discussed. These sensitivity functions are computed directly from experimental frequency response functions and reflect changes in the forced response of structural systems when mass, damping or stiffness parameters are changed. The theory of embedded sensitivity functions is reviewed and applied to characterize damage in a simulated three degree-of-freedom system and a full-scale exhaust system with nonlinear characteristics. Linear damage is shown to be properly detected, located and quantified in theory and practice for structures with one damage mechanism by comparing embedded sensitivity functions with finite difference frequency response functions in undamaged and damaged test data. It is also shown using the exhaust system that false indications of damage due to nonlinear amplitude dependence can be avoided by developing nonlinear baseline models. Experimental results indicate that the technique is most effective when changes to frequency response functions are no larger than 10% to avoid distortions in the estimated perturbations due to variations in the sensitivity functions.

Enhancement of an Optimization-Based Damage Detection Technique

Various structural health monitoring (SHM) techniques utilizing vibration signals have been developed for identification of damages in a structure. Many of these studies are based on sensitivity analysis, finite element model (FEM) updating, and optimization techniques. FEM updating technique is one of the major techniques that iteratively minimizes the difference between the modal parameters measured from the real structure and the corresponding analytical predictions. This method would be more beneficial for typical continuous systems such as beams, plates, and shells which cannot be reasonably discretized. One of the drawbacks of these techniques is the large number of unknowns to be estimated. These techniques in the literature that use FEM updating to estimate perturbed parameters for all elements in the model can be time-consuming and ill-conditioned, even for relatively simple structures. The technique also requires a full and accurate finite element model for each monitored structure.A new method to identify damages in a structure using embedded sensitivity functions and optimization algorithms is described and its performance is demonstrated in this paper. The perturbed frequency response function (FRF) is calculated using Taylor series expansion in terms of the baseline system and the embedded sensitivity functions. The optimization process minimizes the difference between the measured FRFs of the damaged structure and the perturbed FRFs calculated from the baseline structure. Structural damages are often characterized by changes in mechanical parameters such as stiffness, mass, and damping. Embedded sensitivity functions offer a means of determining the path that is followed from the baseline to the perturbed FRF of the structure.The robustness and efficiency of suggested structural health monitoring method are discussed in this paper. The accuracy of damage estimation is investigated with respect to various types and values of damages, objective functions, frequency ranges, scale factors, procedures, and noise levels. Precise measurement and monitoring of vibration signals are critical for accurate detection of the location, type, and level of damage. However, in most practical mechanical systems, vibration tests may result in noise on the input or output measurements. Noise on the measurement affects the accuracy of the FRFs and identification of damages in a structure. Based on the results of the study, several parameters and factors in the optimization process and structural dynamics are suggested to enhance the efficiency and robustness of damage identification process.It is shown that the iteration number of the optimization process is significantly reduced. Accurate estimate of damages can be obtained within the range of 2∼5% error with various enhancements applied to the technique.Copyright