On the reliability of error localization indicators (original) (raw)
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Significance of modeling error in structural parameter estimation
Computer‐Aided Civil …, 2001
Structural health monitoring systems rely on algorithms to detect potential changes in structural parameters that may be indicative of damage. Parameterestimation algorithms seek to identify changes in structural parameters by adjusting parameters of an a priori finiteelement model of a structure to reconcile its response with a set of measured test data. Modeling error, represented as uncertainty in the parameters of a finite-element model of the structure, curtails capability of parameter estimation to capture the physical behavior of the structure. The performance of four error functions, two stiffness-based and two flexibility-based, is compared in the presence of modeling error in terms of the propagation rate of the modeling error and the quality of the final parameter estimates. Three different types of parameters are used in the parameter estimation procedure: (1) unknown parameters that are to be estimated, (2) known parameters assumed to be accurate, and (3) uncertain parameters that manifest the modeling
A Method for Determining Model‐Structure Errors and for Locating Damage in Vibrating Systems
1999
A method is proposed for the determination of natural frequencies and mode shapes of a system which is constrained so that unknown stiffnesses are replaced by rigid connections. The constraint is not imposed physically but only in mathematics so that the behaviour of the constrained system is inferred from the unconstrained measurements. Since stiffnesses which are made rigid cannot experience any elastic strain they can have no effect on the inferred measurements. A procedure for comparing the inferred measurements with similarly constrained finite element predictions can be used to determine model-structure errors. Damage, such as a crack in a beam, can be located by comparing the inferred measurements from the structure in its undamaged and current states. It is demonstrated how unmeasured rotations may be constrained by using rigid-body modes and a reduction/expansion transformation from a finite element model.
Identification of imperfections by means of dynamic response
Journal of physics, 2018
The idea of using the changes of the characteristics of natural or forced vibrations (natural frequency, natural modes, damping) for the determination of the position and magnitude of damage to building structures originated in the 70s [1]. The achievement of ever higher accuracy of developing dynamic displacement sensors and evaluation instruments has made this idea increasingly applicable. Identification is a process defining the properties of a structure and the characteristics of its design model. The often required identification task of determining the rate of deterioration of structures by means of their dynamic response has been numerous lately. The paper sums up the experience of the Institute of Theoretical and Applied Mechanics (ITAM) of the Czech Academy of Sciences, with laboratory tests of large models and in-situ measurements.
Uncertainty Quantification in Structural Health Monitoring
50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2009
Structural health monitoring (SHM) involves detection, isolation and quantification of damage in engineering systems. This paper focuses on methods for the quantification of uncertainty in each of these procedures, in the context of continuous online monitoring. Sources of uncertainty include, but are not limited to, physical variability, measurement uncertainty and model uncertainty. Damage detection is based on statistical hypothesis testing whose uncertainty can be captured easily. Isolation is based on the comparison of fault signatures and sometimes the observed signatures may not uniquely isolate faults, thus causing uncertainty in fault isolation. A metric based on least squares is proposed to assess the confidence in fault isolation, when the fault signatures fail to isolate faults uniquely. The uncertainty in damage quantification is evaluated through statistical non-linear regression and confidence limits for the damage parameter are calculated. The procedures are then illustrated using two types of example problems, a structural frame and a hydraulic actuation system. 1. Motivation Fault diagnosis of an engineering system comprises of three steps: damage detection, damage isolation (localization) and damage quantification. Model-based diagnosis involves the use of a mathematical model which attempts to capture the behavior of the system. Fault diagnosis techniques and system identification techniques form the components of a health monitoring system. While the former aids in damage detection and damage isolation, the latter aids in damage quantification. Diagnosis methods can be broadly classified into two groups, data-driven methods and model-based methods. The authors have previously developed a model-based diagnosis technique using the bond graph modeling language to achieve real time diagnosis. In this technique, the residuals (differences between measurements and model predictions) are measured continuously online and used in diagnosis. Damage detection is based on statistical significance testing of the residuals. Damage isolation is done qualitatively, based on the fault signatures developed from causal relationships between system measurements and system parameters. Damage quantification is based on the method of least squares in non-linear regression. The focus of this paper is to address the issue of uncertainty in the results of this diagnosis technique, coming from each of the three stages. There can be several sources of uncertainty in the diagnosis procedure and can be broadly classified into three different types. System responses are measured through sensors which are noisy in nature. This leads to measurement uncertainty. Any model-based approach to diagnosis would be prone to modeling errors, represented by model uncertainty. Uncertainty also arises from the physical variability in the parameters of the model. All these sources lead to uncertainties in fault detection, fault isolation and damage quantification and this paper develops methods to quantify these uncertainties. This paper demonstrates these approaches by employing a bond graph based model. However, the methods are general and can be adapted to any type of model-based diagnosis approach. Any model-based approach to structural health monitoring brings into the question the validity of the mathematical models and hence, the accuracy of the diagnosis. Noisy sensor measurements contribute additional uncertainty in the diagnosis. Non-destructive evaluation techniques often use the terminology "Probability of Detection" which addresses the uncertainty in detection 1. However, such techniques are only applicable to offline testing and are not directly applicable to real time diagnosis. System identification techniques combine damage isolation and damage quantification into one procedure and so, the individual uncertainties are not separated. This paper uses separate methods for detection and isolation, and quantifies the uncertainty in each of them through well established statistical procedures. The uncertainty in damage quantification is equivalent to that of estimating
Using Modal Parameters for Structural Health Monitoring
Structural Health Monitoring & Damage Detection, Volume 7, 2017
In two recent papers, we introduced the idea of numerically comparing currently acquired operating data with archived data to identify faults in rotating machinery (Ganeriwala et al.: Using operating deflection shapes to detect unbalance in rotating equipment. In: IMAC XXVII. Orlando, FL (2009); Richardson et al.: Using operating data to locate and quantify unbalance in rotating machinery. In: IMAC XXXIV, January 25-28, 2016). We introduced a new metric for comparing two operating deflection shapes called the Shape Difference Indicator (SDI). In another previous paper (Richardson et al.: A new measure of shape difference. In: IMAC XXXII, February 3-6, 2014), we used SDI to measure the difference in modal frequencies from before and after a stiffness change was made to a mechanical structure. In this paper we provide more details of how experimental modal frequency and damping parameters can be used together with the SDI metric as a means of detecting and quantifying changes in the physical properties of a structure. Also, we have implemented SDI together with a search method for ranking the differences between currently acquired modal parameters and archived modal parameters. We call this new method Fault Correlation Tools (FaCTs™). FaCTs™ can be used in multiple applications, including structural health monitoring, production qualification testing, and recertification of machinery in field maintenance applications.
Health monitoring of operational structures - Initial results
36th Structures, Structural Dynamics and Materials Conference, 1995
Translational and Rotational Error Checking-STRECH and MAtriX COmpletioN-MAXCON) are described and applied to operational structures. The structures include a Horizontal Axis Wind Turbine (HAWT) blade undergoing a fiitigue test and a highway bridge undergoing an induced damage test. STRECH is Seen to provide a global damage indicator to assess the global damage state of a structure. STRE.CH is also Seen to provide damage localization for static flexibility shapes or the first mode of simple structures. MAXON is a robust damage localization tool using the higher order dynamics of a structure. Several options are available to allow the procedure to be tailored to a variety of structures. Two techniques for damage localization (Structural Three bodies of research have been instrumental in the development of a health monitoring capability at
Mechanical Systems and Signal Processing
This paper presents a novel Optimal Sensor Placement (OSP) strategy that is dedicated to model updating problems based on the modified Constitutive Relation Error (mCRE) functional in low-frequency dynamics. The mCRE is a credible alternative to model updating functionals that stands out by searching structural parameters alongside mechanical fields as the best trade-off between all available information from measured data, without any further a priori assumption. Considering damage detection problems, due to possible discrepancies in terms of parameters sensitivity with respect to mCRE, sensor locations provided by standard OSP algorithms may be irrelevant. The proposed approach uses the concept of Information Entropy by formulating a modified Fisher information matrix, in which the sensitivity of the mCRE mechanical fields with respect to the updated parameters is involved. The approach is legitimated by the strong connection between mCRE and Bayesian inference. A proof-of-concept involving an earthquake engineering inspired academic case study, where accelerometers are positioned on a two-story frame structure subjected to random ground motion, permits to illustrate the soundness and efficiency of the proposed methodology compared to other classical OSP techniques. The influence of critical mCRE parameters is shown, as well as the benefits of taking multiple scenarios into account so as to get an OSP that is relevant for a wider range of possible damage occurrences.
Structural health monitoring via stiffness update
2010
ABSTRACT The performance of an updated time-domain least-squares identification method for identifying a reduced-order linear system model in case of limited response measurements and its use in structural health monitoring is evaluated. It is shown that the incorporation of a mass-invariability constraint enhances the robustness of the parametric identification procedure.
Time and frequency domain regression-based stiffness estimation and damage identification
Modal analysis and system identification are popular methods for obtaining insight into structural properties from vibration signals. The associated algorithms, however, often require responses from a large group of representative DOFs of the structure to produce accurate and consistent results. In addition, their direct output, which is generally a set of estimated modal properties, does not explicitly reflect possible structural damage locations and extent. In this paper, two novel regression-based techniques that use local acceleration responses of a frame structure to estimate its local stiffness are proposed. One employs displacement simulation methods; the other is based on spectral estimates. Both methods are proven effective in their application to data collected from two laboratory specimens that are subjected to white noise excitation. the structural stiffness matrix because they are associated with large system eigenvalues, are often outside the measured bandwidth. In , a damage detection strategy using measured flexibility matrix is introduced, but its implementation requires an analytical model of the structure to be known beforehand. Thus, for a general understanding of the structural vibration characteristics on a macro scale, system identification techniques are useful, but for local structural damage identification, more efficient methods are needed . In this paper, two explicit methods for damage localization and severity estimation that are computationally more efficient than many system identification and model updating techniques are developed and validated. The algorithms are more competent in the sense that they employ standard linear regression techniques and require data from only a few sensing channels.
Nuclear Engineering and Design, 2004
In general, the structures are submitted during their useful life to deterioration processes that, depending on the intensity, may affect their performance and load capacity and consequently their safety. In this case, it is necessary to accomplish an inspection in order to evaluate the conditions of the structure and to locate and quantify the intensity of the damage. In this study, a method to identify and to quantify damage in structures, called Residual Error Method in the Movement Equation [Localização e quantificação de danos em estruturas por meio de suas características dinâmicas. Universidade de Brasília, Brasília, DF, 2000] is evaluated, by a numerical analysis, to verify its efficiency when applied to continuous beams and frame structures. This method is based on the alteration, produced by damage, in the dynamic properties of the structures. The location of the damage is done observing the error in the movement equation of the intact structures. The structures are discretized in finite elements and the damage is introduced by a stiffness and area reduction of the elements' cross-sections. Other two methods of damage detection used in this paper are: the Damage Detection from Changes in Curvature Mode Shapes [J. Sound Vibration 145 (1991) 321] and the indexes MAC [Proc. 1st Int. Modal Anal. Conf. 1 (1982) 110] and COMAC [Proc. 6th Int. Modal Anal. Conf. 1 (1988) 690]. Observing the obtained results, the Residual Error Method in the Movement Equation is efficient in the damage location and quantification of the studied structures.