A system and method for detecting structural damage is provided that utilizes a general order perturbation methodology involving multiple perturbation parameters. The perturbation methodology is used iteratively in conjunction with an optimization method to identify the stiffness parameters of structures using natural frequencies and/or mode shape information. The stiffness parameters are then used to determine the location and extent of damage in a structure. A novel stochastic model is developed to model the random impact series produced manually or to generate a random impact series in a random impact device. The random impact series method or the random impact device can be used to excite a structure and generate vibration information used to obtain the stiffness parameters of the structure. The method or the device can also just be used for modal testing purposes. The random impact device is a high energy, random, and high signal-to-noise ratio system.

System and method for detecting structural damage

A global, single-input-multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data

The DoD has various vehicle platforms powered by high performance gas turbine engines that would benefit greatly from predictive health management technologies that can detect, isolate and assess remaining useful life of critical line replaceable units (LRUs) or subsystems In order to meet these needs for next generation engines, dedicated prognostic algorithms must be developed that are capable of operating in an autonomous and real-time engine health management system software architecture that is distributed in nature This envisioned prognostic and health management system should allow engine-level reasoners to have visibility and insight into the results of local diagnostic and prognostic technologies implemented down at the LRU and subsystem levels To accomplish this effectively requires an integrated suite of prognostic technologies that can be applied to critical engine systems and can capture fault/failure mode propagation and interactions that occur in these systems, all the way up through the engine and eventually vehicle level In the paper, the authors will present a generic set of selected prognostic algorithm approaches that can be applied to gas turbine engines, as well as provide an overview of the required reasoning architecture needed to integrate the prognostic information across the engine

An Overview of Selected Prognostic Technologies With Application to Engine Health Management

https://personalpages.manchester.ac.uk/staff/tianjian.ji/research/papers/a4-beam-distributed%20mass-spring.pdf

Dynamic characteristics of a beam and distributed spring-mass system

In this paper we examine the conditions that influence the return time, the time it takes before energy returns from a set of satellite oscillators attached to a primary structure. Two methods are presented to estimate the return time. One estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators. The result gives a lower-bound estimate for the return time. A more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide. Such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves. The resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators, and of their number, on the return time as compared with the asymptotic case of a continuous set with infinite oscillators. In the paper we also introduce a new method based on a Hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators. The expressions developed for return time and damping factor show close agreement with direct numerical simulations. The paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities.

Transient energy exchange between a primary structure and a set of oscillators: return time and apparent damping.

Multiple degree of freedom (MDOF) algorithms are the dominant methods for extracting modal parameters from measured data These methods are founded on the notion that because the response of a linear dynamic system is the sum of many modal contributions, the extraction technique must deal with all of the modal parameters in a simultaneous fashion The Mode Isolation Algorithm (MIA) described here is a frequency domain formulation that takes an alternative viewpoint It extracts the modal parameters of each mode in an iterative search, and then refines the estimation of each mode by isolating its effect from the other modal contributions The first iteration estimates modes in a hierarchy of their dominance As each mode is estimated, its contribution is subtracted from the data set, until all that remains is noise The second and subsequent iterations subtract the current estimates for all other modes to identify the properties of the mode under consideration The various operations are described in detail, and then illustrated using data from a four-degree-of-freedom system that was previously used to assess the Eigensystem Realization Algorithm (ERA) and Enhanced ERA Eigenvalues and mode shapes are compared for each algorithm Another example analyzes simulated data for a cantilever beam with three suspended one-degree-of-freedom subsystems, in which the parameters are adjusted to bring two natural frequencies into close proximity The results suggest that MIA is more accurate, and more robust in the treatment of noisy data, than either ERA version, and that it is able to identify modes whose bandwidth is comparable to the difference of adjacent natural frequencies

Mode isolation: A new algorithm for modal parameter identification

This work was prompted by a study performed by Strasberg [7] in which numerous small spring-mass-damper systems are attached to a large suspended mass representing the master structure. The isolated natural frequency of each attached system was selected to match in average the natural frequency of the isolated master structure, Strasberg found that the critical issue when an impulse excitation is applied to the master structure is the bandwidth of the isolated attached systems in comparison to the spacing between the natural frequencies of the system. Modal overlap, which corresponds to bandwidths that exceed the spacing of those frequencies, was shown to greatly influence the response of the master structure. Light damping, for which there is little or no modal overlap, corresponds to an impulse response that consists of a sequence of nearly periodic exponentially decaying pulses, and the transfer function for harmonic excitation of the master structure indicates that the substructure acts as a vibration absorber for the master structure. Increased damping leads to modal overlap, with the result that the impulse response consists of a single decaying pulse. The frequency domain transfer function indicates that the vibration absorber effect is enhanced. The present work explores these issues for continuous systems by replacing the one degree of freedom master structure with a cantilever beam. The system parameters are selected to match Strasberg's model, with the suspended oscillators placed randomly along the beam. The beam displacement is represented as a Ritz series whose basis functions are the cantilever beam modes. The coupled equations are solved by a state-space eigenmode analysis that yields a closed form representation of the response in terms of the complex eigenmode properties. The continuous fuzzy structure is shown not to display the transfer of energy between the master structure and the substructure that was exhibited by the discrete fuzzy structure, apparently because of the asynchronous motion of the attachment points resulting from the spatial variability of the beam's motion. The vibration absorber effect for harmonic excitation is only obtained for the heavy damping in the case of a beam.

Modal Overlap and Dissipation Effects of a Cantilever Beam with Multiple Attached Oscillators

The Algorithm of Mode Isolation (AMI) extracts modal properties from complex frequency response data. Previous work used classic undamped modes as the analytical framework for the algorithm. The present work extends the algorithm to implement damped modal analysis, in which the eigenvalues and eigenvectors are complex. In order to assess how well this reformulation performs when natural frequencies are close and drive point mobilities are low, a prototypical system consisting of a cantilever beam with attached subsystems is introduced. One of these subsystems is selected to be a tuned vibration absorber for the isolated beam, so the system features a combination of modes whose natural frequencies are close and modes whose drive point mobility is low. The time domain response of this system is evaluated, contaminated with substantial white noise, and then FFT processed in order to obtain synthetic complex frequency response data. The performance of AMI is evaluated by comparing extracted values for natural frequency, modal damping ratio, and complex normal mode vectors to the analytical values. The results reveal that the pair of modes having proximite natural frequencies are accurately identified. Natural frequencies and damping ratios for those modes whose drive mobility is low are identified by processing the ensemble of frequency response functions, but identification of normal mode coefficients for such modes remains problematic.

State Space Implementation of the Algorithm of Mode Isolation

Several experimental modal analysis techniques fit resonance peaks to the response curves of a single degree of freedom system in order to identify the natural frequencies and modal damping ratios. The present study identifies a fundamental property of frequency response curves that allows the natural frequency to be identified from a simple characteristic of the curve, independently of the damping ratio. After the natural frequency has been determined, the damping ratio can be computed directly. The fundamental property holds for all values of damping, which eliminates the need to approximate either the natural frequency or damping ratio.

Exact evaluation of natural frequency and damping ratio from a frequency response curve

Multiple degree of freedom (MDOF) methods for modal parameter extraction in current use deal with all of the modal parameters in a simultaneous fashion in the process of matching measured data to analytical forms. In contrast, the mode isolation algorithm exploits the fact that each mode has unique characteristics that can be used to isolate it from the contribution of other modes. The present work extends the algorithm to use state-space modes as the analytical foundation. The paper describes how modal parameters are identified and then refined in a recursive manner. One of the issues of primary importance for a modal identification is the number of modes that significantly contribute to the measured response. Most MDOF algorithms require an a priori guess of the number of significant modes, or degrees of freedom, of the system. Several MDOF methods address this matter by utilizing peak counting of amplitude-frequency plots to identify the number of modes. However, such estimation becomes problematic for systems that exhibit modal coupling. In contrast, the mode isolation method offers a simple and consistent modal extraction methodology that is inherently automatic in nature. A prototypical system is used to demonstrate that it is not limited by the presence of modal coupling. A cantilever beam with three attached spring-mass-damper systems is tuned such that the bandwidths of two resonances are commensurate with the natural frequency separation. Differing levels of noise are imposed on the simulated time-domain response, which is then transformed to the frequency domain. The simulated data is used to illustrate the results of the algorithmic steps. The natural frequencies and damping ratios that result from the procedure are found to match the analytical system properties, with an error that is less than the noise level that was added.

Michael V. Drexel

Papers

Mode isolation: A new algorithm for modal parameter identification

Modal Overlap and Dissipation Effects of a Cantilever Beam with Multiple Attached Oscillators

State Space Implementation of the Algorithm of Mode Isolation

Exact evaluation of natural frequency and damping ratio from a frequency response curve

Modal parameter identification using state space mode isolation