Minimum Rank Perturbation Theory Research Articles

Singular spectrum analysis based structural damage detection from nonlinear vibration measurements containing noise

Singular spectrum analysis is developed for the processing of nonlinear vibration measurements containing noise in structural damage detection. The method uses system augmentation to make the nonlinear system into an augmented linear system. The measured response of the system is decomposed and the corresponding decomposition subspace of the components which contains the least interference is reconstructed. Direct system parameter identification technique is then used to solve the model properties of the augmented system. Minimum rank perturbation theory is generalized so that it can be applied to detect local damage of the augmented system. Excellent identification results are obtained when Singular Spectrum Analysis (SSA) is applied, while identification result that without applying SSA shows large errors. The enhanced method is shown to be capable of yielding accurate identified results with noisy measurement in nonlinear systems.

Damage detection of offshore jacket structures using frequency domain selective measurements

The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitoring. In efforts to fulfill this task, concept of the minimum rank perturbation theory has been utilized. The present article introduces a promising methodology to select frequency points effectively. To achieve this goal, modal strain energy ratio of each member was evaluated at different natural frequencies of structure in order to identify the sensitive frequency domain for damage detection. The proposed methodology opens up the possibility of much greater detection efficiency. In addition, the performance of the proposed method was evaluated in relation to multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform, and the results proved to be satisfactory utilizing the proposed methodology.

Sensor Placement for Damage Detection in Nonlinear Systems Using System Augmentations

Currently, most sensor placement methodologies are focused on maximizing the controllability and observability of the monitored structure. Recently there have been several sensor placement techniques proposed for damage detection. The work herein provides an integrated sensor placement and reduced order health assessment approach that can be applied to both linear and nonlinear structures. The method uses the idea that often the damageable regions (hot spots) of the system are known in advance and therefore the modes that are sensitive to changes in these hot spots should be the ones exploited for damage detection. Generally,the sensors are placed near the hot spots. However if that is not possible, or if additional sensors are being used, then a generalized eectiv e independence distribution vector method is applied for the remaining sensors. The partial eigenvector information is expanded to the full space using the knowledge that damage is limited to the hot spots of the system. Modal based damage detection methods such as minimum rank perturbation theory (MRPT) can then be used to solve for the damage in a linear system. Also, an alternative damage identication by hot spot projection (DIHSP) method is a novel additional option for the damage detection presented herein. Nonlinear systems are handled by forming (higher dimensional) augmented linear systems that follow the same trajectory of the nonlinear system when projected onto the physical (lower dimensional) space. The sensor placement methodology for nonlinear systems is similar, but it requires that sensors be placed at the location of all nonlinearities as well as the hot spots. The damage can be detected using the multiple augmentations generalized MRPT approach previously developed by the authors or by DIHSP. Numerical simulations of the methodology are presented for linear and nonlinear 5-bay frame structures.

Multiple augmentations of nonlinear systems and generalized minimum rank perturbations for damage detection

A generalized minimum rank perturbation theory for identifying damage location and extent in nonlinear systems using a model-based approach is presented. This model updating method is able to handle changes in the mass, damping and stiffness parameters arising from the damage. The method uses a nonlinear discrete model of the system and the functional form of the nonlinearities to create an augmented linear model of the system. A modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the augmented linear system after the onset of damage. The methodology has been demonstrated for cubic spring nonlinearities. In this work, the class of nonlinearities is expanded to include Coulomb friction. Several new algorithms are presented, including an iterative generalized minimum rank perturbation theory and a technique based on multiple augmentations to determine damages in linear and nonlinear parameters when there is an incomplete set of eigenvectors. Finally, two eigenvector filtering algorithms, which reduce the effects of measurement noise, are presented.

Model Correlation and System Health Monitoring using Frequency Domain Measurements

In this paper, algorithmic approaches to enhance model correlation and system health monitoring capability are developed in which direct frequency response function (FRF) data are utilized. The algorithmic approaches utilizes the concept of minimum rank perturbation theory. The use of direct FRFs, as opposed to measured modal parameters, is shown to be one method to address a part of the incomplete measurement problem common to model correlation and system health monitoring; namely the mismatch in the number of measured vibration modes in the measured frequency band in comparison to the number of modes included in the analytical finite element model. Key points made in the development are highlighted using numerical and experimental studies.

Statistical confidence using minimum rank perturbation theory

In this paper, the effect of measurement noise on damage detection performance of the minimum rank perturbation theory is investigated. Closed-form solutions for the sensitivity of the minimum rank perturbation theory damage vectors and calculated stiffness perturbations with respect to errors in the measured modes shapes or frequency response functions are developed. This sensitivity allows one to establish confidence in damage existence, location and extent assessment. The use of this information in interpreting damage detection results is discussed in the context of an experimental study.

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. [S0739-3717(00)01904-8]

Development of a Coupled Approach for Structural Damage Detection with Incomplete Measurements

A procedure has been developed that couples model order reduction, damage location, dynamic residual and mode shape expansion, and damage extent estimation to overcome the incomplete measurements problem by using an appropriate undamaged structural model. The first significant contribution of this work is in the development of a process to estimate the full dynamic residuals using the columns of a spring connectivity matrix obtained by disassembling the structural stiffness matrix. The second significant contribution is the extension of an eigenvector filtering procedure to produce full-order mode shapes that more closely match the measured active partition of the mode shapes using a series of modified Ritz vectors. The full dynamic residuals and full mode shapes are used as inputs to the minimum rank perturbation theory to provide an estimate of damage location and extent. An analytical model of the NASA eight-hay truss and an experimental data set are used to exercise this process and to study the sensitivity to various parameters.

An Experimental Study of Structural Health Monitoring Using Incomplete Measurements

In this paper, algorithmic approaches to enhance structural health monitoring capability when faced with incomplete measurements are addressed. The incomplete measurement problem has two aspects: (i) experimental measurement of a lesser number of modes of vibration than that of the analytical model and (ii) experimental measurement of a lesser number of degrees of freedom than that of the analytical model. Studies comparing model reduction, eigenvector expansion, and a hybrid model reduction/eigenvector expansion to address the second contribution are performed using experimental data. These approaches to the incomplete measurement problem are evaluated within the frameworks of multiple-constraint matrix adjustment (both sparsity and nonsparsity preserving algorithms) and minimum rank perturbation theory, which are both applicable for model refinement as well as damage location. Experimental evaluation of the proposed approaches utilize data from the NASA Langley Research Center 8-bay truss and McDonnell Douglas Aerospace 10-bay truss facilities.

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.

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.

Structural damage assessment using a generalized minimum rank perturbation theory

Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties. 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 determine the damage extent on the mass properties of an undamped structure. In addition, the MRPT is extended to the case of proportionall y damped structures. For proportionally damped structures, the MRPT is used to find the damage extent in any two of the three structural property matrices (mass, damping, or stiffness). Finally, illustrative case studies using both numerical and actual experimental data are presented. HE advent of the Space Shuttle has prompted considerable attention to the design and control of large space structures. Due to the large size and complexity of envisioned structures, as well as the use of advanced materials to reduce structural weight, it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs. From experience gained in the machinery health monitoring field, one would expect the vibration signature of the structure, either frequency response functions and/or modal parameters, to provide useful information in determining the location and extent of structural damage. Assume that a refined finite element model (FEM) of the structure has been developed before damage has occurred. By refined, we mean that the measured and analytical modal properties are in agreement. Next, assume that at a later date some form of structural damage has occurred. If significant, the damage will result in a change in the structures modal parameters. The question is: can the discrepancy between the original FEM modal properties and postdamage modal properties be used to ascertain structural damage? Most prior work in damage detection has used the general framework of FEM refinement (system identification) in the development of damage assessment algorithms. The motivation behind the development of FEM refinement techniques is based on the need to validate engineering FEMs before their acceptance as the basis for final design analysis. The standard problem has been to seek a refined FEM that is as close to the original FEM and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation. A considerable amount of work in this area has been