David C. Zimmerman

Structural damage detection using a subspace rotation algorithm

A computationally inexpensive algorithm is developed to provide an insight to the location of structural damage, using the original finite element model and a subset of measured eigenvalues and eigenvectors. The computational requirements of the algorithm may make the technique suitable for real-time implementation. With damage location determined, a second algorithm is developed to determine the extent of damage. The algorithms are demonstrated using two classes of structural models. The effects of eigenvector measurement error is demonstrated and techniques to overcome the effects of noise are discussed.

Model validation and verification of large and complex space structures

In this paper two case studies of model validation and verification of large and complex space structures are presented. The first case study focuses on experience gained in performing model validation and verification of the mated Russian Mir Space Station and United States Space Shuttle. This study makes use of dynamic test data taken during the STS-81 flight associated with the Mir Structural Dynamics Experiment. The second case study involves the International Space Station P6 truss segment tested in the launch configuration. In both cases, a newly developed capability within UAI/NASTRAN is used to perform the model validation and verification. Key technical issues raised in these studies provide useful insight for future pretest planning and model validation and verification efforts.

Assessment of Damage Affecting All Structural Properties Using Experimental Modal Parameters

Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped and damped structures assuming damage results in a localized change in a subset (not full set) of the property matrices (mass, stiffness and damping matrices). The algorithms make use of a finite element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite element model. In this work, the concept of the Minimum Rank Perturbation Theory (MRPT) is adopted to simultaneously determine the damage extent of all property matrices of undamped and proportionally damped structures. Note that the property matrices are the mass, stiffness and damping matrices. Illustrative examples are presented to show the performance of the proposed theory.

The effects of finite element grid density on model correlation and damage detection of a bridge

Variation of model size as determined by grid density is studied for both model refinement and damage detection. In model refinement 3 it is found that a large model with a fine grid is preferable in order to achieve a reasonable correlation between the experimental response and the finite element model. A smaller model falls victim to the inaccuracies of the finite element method. As the grid become increasing finer, the FE method approaches an accurate representation. In damage detection the FE method is only a starting point. The model is refined with a matrix method which doesn`t retain the FE approximation, therefore a smaller model that captures most of the dynamics of the structure can be used and is preferable.

DAMAGE DETECTION USING EXPANDED DYNAMIC RESIDUALS

In this work, an algorithm for detecting the location of damage in a structure using a finite element model and pre- and post-damage measured modal properties is presented. In particular, an algorithm which addresses one aspect of the incomplete measurement problem, namely the measurement of mode shape information at fewer spatial degrees of freedom than that modeled in the finite element model, is presented. The performance of the algorithm is evaluated using the NASA 8-bay experimental test bed. The results indicate that the proposed approach holds great promise for identifying damage when structural instrumentation is limited. The same approach can also be used in model correlation efforts to aid in the selection of physical parameters to be estimated.

Analysis-test correlation and model updating of dynamic systems using MDO software tools

The requirements of analysis-test correlation and model updating of dynamic structural systems, often called system identification, are strongly related to those of Multidisciplinary Design Optimization (MDO). This paper describes how MDO tools have been used to form an integrated environment for performing these tasks. Specifically, it describes how these tools are used to modify modeling parameters in order to make the response of a finite element model better match test results. The techniques shown allow the simultaneous correlation of dynamic structural responses including natural frequencies, normal mode shapes and frequency response functions (FRFs). This methodology forms the basis for an important emerging technology being termed Model Validation and Verification (V&V).

Improved Experimental Ritz Vector Extraction With Application to Damage Detection

Load-dependent Ritz vectors, or Lanczos vectors, are alternatives to mode shapes as a set of orthogonal vectors used to describe the dynamic behavior of a structure. Experimental Ritz vectors are extracted recursively from a state-space system realization, and they are orthogonalized using the Gram-Schmidt process. In addition to the Ritz vectors themselves, the associated nonorthogonalized vectors are required for application to damage detection. First, this paper presents an improved experimental Ritz vector extraction algorithm to correctly extract the nonorthogonalized Ritz vectors. Second, this paper introduces a Ritz vector accuracy indicator for use with noisy data. This accuracy indicator is applied as a tool to guide the deflation of a state-space system realization identified from simulated noisy data. The improved experimental Ritz vector extraction algorithm produces experimental nonorthogonalized Ritz vectors that match the analytically computed vectors. The use of the accuracy indicator with simulated noisy data enables the identification of a state-space realization for Ritz vector extraction from which damage location and extent are correctly estimated. The improved Ritz vector extraction algorithm improves the application of Ritz vectors to damage detection, more accurately estimating damage location and extent. The accuracy indicator extends the application of Ritz vectors to damage detection in noisy systems as well.

Development of Pretest Planning Methodologies for Load Dependent Ritz Vectors

Load dependent Ritz vectors have been found to be suitable alternatives to mode shape vectors for structural vibration analysis. While much research has focused on how to best set-up and perform modal property identification, there has been no investigation on such pretest planning for Ritz vectors. Pre-test planning is a vital part of successful vibration tests, especially when dealing with large complex structures. In such cases, it is common that a limited number of sensors and actuators must be placed in a configuration to obtain the most important dynamic information. In this study, previously developed modal sensor placement techniques were utilized to determine Ritz vector sensor sets for the NASA eight-bay truss structure. The techniques used were the eigenvector product, kinetic energy product, and effective independence. The Modal Assurance Criteria was employed to determine how well each technique performed. Since Ritz vectors are subject to change due to the excitation locations, the paper also investigated the effect of various loading configurations on the Ritz vector sensor placement results. Finally, Ritz vectors and mode shapes were combined in an effort to verify that a single sensor set could be used to identify both sets of basis vectors.

Nonlinear damage detection using a time-domain minimum rank perturbation theory

Modal Minimum Rank Perturbation Theory (MRPT) computes perturbation matrices approximating structural changes from one linear state to another due to damage. The number of measured flexible modes determines the rank of the computed perturbation and is usually low in comparison with model dimension. This work extends a time-domain MRPT (TD-MRPT) for detection of state-dependent stiffness damage. TD-MRPT computes an instantaneous stiffness perturbation with the force balance residual arising in successive time steps. Recursive rank-1 updating of the current stiffness estimate results in a cumulating stiffness matrix that converges to the unknown stiffness regardless of the rank difference between the nominal and perturbed matrices. As a result, damage is detected at onset and is exactly tracked in the case of a rank-1 nonlinearity. Time variation of higher-rank nonlinearities will be approximated provided the rate of change is slow compared with the algorithmic convergence rate. Numerical integration is used to render dependency solely on acceleration response measurement and a time-dependent elemental subspace recognition procedure was employed for detecting damage location and extent in the case of incomplete spatial measurements. The algorithm is evaluated with a nonlinear three degree-of-freedom oscillator and virtual experimental data from a 96-degree-of-freedom structure corrupted with artificial measurement noise.

Structural Health Monitoring Using Vibration Measurements and Engineering Insight

Several system identification algorithms have been proposed that make use of analytical models and measured modal data to determine the location and/or extent of structural damage. In particular, the authors have proposed a computationally attractive Minimum Rank Perturbation Theory (MRPT) which determines perturbation matrices to the mass, damping, and/or stiffness matrices. Inspection of these perturbation matrices provides insight to both the location and extent of structural damage. This paper documents our practical experience in applying MRPT theory to a variety of structures. The ability to incorporate engineering insight and judgment into the algorithm is shown to enhance the performance of the MRPT technique when faced with real-world issues.