Anders Skafte

A general procedure for estimating dynamic displacements using strain measurements and operational modal analysis

Measurement systems are being installed in more and more civil structures with the purpose of monitoring the general dynamic behavior of the structure. The instrumentation is typically done with accelerometers, where experimental frequencies and mode shapes can be identified using modal analysis and used in health monitoring algorithms. But the use of accelerometers is not suitable for all structures. Structures like wind turbine blades and wings on airplanes can be exposed to lightning, which can cause the measurement systems to fail. Structures like these are often equipped with fiber sensors measuring the in-plane deformation. This paper proposes a method in which the displacement mode shapes and responses can be predicted using only strain measurements. The method relies on the newly discovered principle of local correspondence, which states that each experimental mode can be expressed as a unique subset of finite element modes. In this paper the technique is further developed to predict the mode shapes in different states of the structure. Once an estimate of the modes is found, responses can be predicted using the superposition of the modal coordinates weighted by the mode shapes. The method is validated with experimental tests on a scaled model of a two-span bridge installed with strain gauges. Random load was applied to simulate a civil structure under operating condition, and strain mode shapes were identified using operational modal analysis.

Estimation of Unmeasured DOF’s Using the Local Correspondence Principle

This paper will present a new method to estimate unmeasured Degrees of Freedom (DOF’s) in a structure using only a limited amount of sensors. The method applies the Locale Correspondence Principle (LCP) to estimate a linear transformation between experimentally determined mode shapes, and mode shapes from a Finite Element (FE) Model. Mode shapes from the FE model are then altered to fit the real mode shapes of the structure, creating a set of estimated mode shapes covering all nodes.

Expansion of Mode Shapes and Responses on the Offshore Platform Valdemar

There is a need in the future for maintaining and increasing oil and gas production in the Danish North Sea. Related to this are studies for exploring the potential for extending the lifetime of offshore platforms by implementation of Structural Monitoring Systems (SMS). The project, which this paper is based on, uses an expansion technique as a first step in the sequence of assessing the actual lifetime of a platform. Mode shapes and natural frequencies are estimated using operational modal analysis. The mode shapes are then expanded by expressing each experimental mode shape as an optimal linear combination of selected modes from a finite element model. The offshore platform, Valdemar, which is fully instrumented with accelerometers, GPS, strain gauges and wave radars, is chosen as a case study. Results show that the measured response can be expanded with high precision, which provides valuable information when assessing the actual lifetime of the platform. Also it is shown that the expansion technique can be used for assessment of measurement uncertainties.

Strain Estimation in a Glass Beam Using Operational Modal Analysis

A potential application of operational modal analysis is the prediction of strain or stress time histories which, on the other hand, are one of the most important sources of uncertainty in fatigue design and remaining fatigue life calculations. This is due to the difficulty of estimating the stiffness, mass and damping properties with accuracy, as well as the use of simplified loading models.

Estimation of Rotational Degrees of Freedom by EMA and FEM Mode Shapes

In this paper a new technique is presented to estimate the rotational degrees of freedom of a flexural structure, using only a limited number of sensors that measure the translational DoFs of the system. A set of flexural mode shapes in a limited number of nodes is obtained by modal testing, while a different set of approximated mode is calculated by a Finite Element Model (FEM) at all the nodes and degrees of freedom of the structure. The technique is based on the classical assumption that the response can be determined by a linear combination of the structure’s mode shapes. The structure’s mode shapes are approximated by using the local correspondence principle for mode shapes, i.e. by using an optimally selected set of finite element mode shapes as Ritz vectors for the true mode shapes. This allows to obtain the rotational response at unmeasured DoFs. The technique is validated by comparing predicted and experimental results.

Shock of Vibration-based Technologies, Part II: Detection

Several different approaches to structural damage detection are compared in a study of both numerically simulated and experimental data, acquired from trials in the laboratory. Structural damage detection is decision making under uncertainty and is the process of discriminating a data point of a selected feature vector from the reference population of the feature vector in the undamaged state. In the study four types of parametric features, all linked to modal properties, are investigated. At the same time, four discrimination algorithms from the field of unsupervised machine learning are applied and compared using detection theory metrics. The study attempts to clarify how global information of mode shapes and eigenfrequencies compare to a simpler scalar time-series model. To compare the feature models, four types of discrimination algorithms from the unsupervised machine learning regime were applied. A simulation study and an experimental validation were carried out and the results presented. The study shows that both the choice of feature model and the choice of discriminant algorithm are important to damage detection. Furthermore, the increased performance of the sensor-array models over a single-sensor model was shown. doi: 10.12783/SHM2015/183

Study of Vibration Based SHM Technologies, Part IV: Localization Using Physical-based Methods

In this paper the performance of various vibration-based damage localization methods have been investigated using a simulated as well as an experimental test case. In general, the validity of most damage localization methods is demonstrated on academic cases such as truss structures, and often with well-defined local stiffness alterations that has a significant impact on the modal properties. Due to the simplicity of the test cases the Finite Element (FE) model dependent methods seldom addresses the challenges related modelling damage in FE. The content of this paper is prompted by a genuine curiosity on the performance of these methods in the event of a more realistic test case, e.g. using a rather complex FE model and experimentally obtained data. In the paper the results from two test cases are presented; 1) A simulation case of a small structure to validate the utilized methods and 2) An experimental case of a wooden structure with inherent uncertainties such as FE modelling errors, measurement noise and ambient influences. The purpose of the latter case is to investigate the usability of the various methods under semi realistic conditions. A well-known as well as some novel localization methods is applied in the investigation. This paper is the final contribution to a series of 4 papers that present experimental SHM investigations with focus on value of detection and value of localization using statistical and physical methods for modal based SHM. doi: 10.12783/SHM2015/171

Shock of Vibration-based Technologies, Part I: Experimental Setup and Automated Identification

Feature extraction is essential in vibration-based Structural Health Monitoring (SHM). In this paper a special focus is on how features are extracted and conditioned. The first case is a numerical simulation study of a small test structure. The second case is an experimental case where two test subjects of a scaled wooden blade structure are investigated. In the experimental case the measurements are performed over a month in an environment with changing temperature and relative humidity. Two different damage types are made, with increasing severity of the damage. All methods dealing with vibration based SHM are using the changes in the dynamic behavior as an indicator for damage. In the test cases the modal parameters of the structure are used as features and are extracted using operational modal analysis (OMA) in a framework of modal tracking. This paper is part 1 of a series of 4 papers that present experimental SHM investigations with focus on value of detection and value of localization using statistical and physical methods for modal based SHM. doi: 10.12783/SHM2015/184

Study of Vibration Based SHM Technologies, Part III: Localization Using Statistical Learning Theory

A novel approach for damage localization, based on covariance equivalent synthesized data and multi-class pattern recognition is presented. The approach combines the data acquired from the structure in the baseline state with data from an FE model but avoids the task of FE model updating. The method is presented as the second half of a two-step approach to damage detection and localization, but it’s capability of performing one-step detection & localization is demonstrated. The technique is tested on simulated data and it is verified on experimental data of two separate laboratory structures. Three types of modal features, AR coefficients, eigenfrequencies and mode shapes, were combined with four types of classifiers. All three types were found to hold information for damage localization, but frequencies were found to have the best noise rejection. Lastly, the value of detection and localization is discussed and calculated for both the one-step approach, the two-step approach, and for a no-localization approach. Based on the experimental data, the twostep approach outperforms the others. doi: 10.12783/SHM2015/305

Cross Orthogonality Check for Structures with Closely Spaced Modes

Structures with closely spaced modes can often be hard to correlate with numerical models due to the high sensitivity of the eigenvectors. Even the smallest change in either mass or stiffness can have a large influence on the eigenvectors, and makes it hard to fit a numerical model so its modal parameters matches those obtain from measurements. This paper introduces a robust method for calculating the cross orthogonality check for structures with closely spaced modes. The method utilizes the fact that a cluster of closely spaced eigenvectors from an experiment and from a well correlated numerical model will span the same subspace, although the experimental mode is badly correlated with its corresponding numerical mode. A new basis of numerical modes is created by redefining the closely spaced numerical modes as a linear combination of one another, based on their projection upon the experimental mode. This will enable a more robust calculation of the cross orthogonality check. The method is validated using simulation cases where the errors are evaluated using simulated responses for the different sets of modal parameters.