Peter Olsen

Using Random Response Input in Ibrahim Time Domain

In this paper the time domain technique Ibrahim Time Domain (ITD) is used to analyze random time data. ITD is known to be a technique for identification of output only systems. The traditional formulation of ITD is claimed to be limited, when identifying closely spaced modes, because of the technique being Single Input Multiple Output (SIMO). It has earlier been showed that when modifying ITD with Toeplitz matrix averaging. Identification of time data with closely spaced modes is improved. In the traditional formulation of ITD the time data has to be free decays or impulse response functions. In this article it is showed that when using the modified ITD random time data can be analyzed. The application of the technique is displayed by a case study, with simulations and experimental data.

Comparison of Two (Geometric) Algorithms for Auto OMA

In this paper we compare two geometric algorithms for automatic Operational Modal Analysis(OMA). The compared algorithms are the Shortest Path Algorithm (SPA) that considers shortest paths in the set of poles and the Smallest Sphere Algorithm (SSA) that operates on the set of identified poles to find the set of smallest spheres, containing physical poles. Both algorithm are based on sliding filter stability diagrams recently introduced by Olsen et al. We show how the two algorithms identify system parameters of a simulated system, and illustrate the difference between the identified parameters. The two algorithms are compared and illustrated on simulated data. Different choices of distance measures are discussed and evaluated. It is illustrated how a simple distance measure outperforms traditional distance measures from other Auto OMA algorithms. Traditional measures are unable to discriminate between modes and noise.

Modal participation in multiple input Ibrahim time domain identification

The Ibrahim time domain (ITD) identification technique was one of the first techniques formulated for multiple output modal analysis based on impulse response functions or general free decays. However, the technique has not been used much in recent decades due to the fact that the technique was originally formulated for single input systems that suffer from well-known problems in case of closely spaced modes. In this paper, a known, but more modern formulation of the ITD technique is discussed. In this formulation the technique becomes multiple input by adding some Toeplitz matrices over a set of free decays. It is shown that a special participation matrix can be defined that cancels out whenever the system matrix is estimated. The participation matrix becomes rank deficient if a mode is missing in the responses, but if any mode is present in one of the considered free decays, the participation matrix has full rank. This secures that all modes will be contained in the estimated system matrix. Finally, it is discussed how correlation functions estimated from the operational responses of structures can be used as free decays for the multiple-input ITD formulation, and the estimation errors of the identification technique are investigated in a simulation study with closely spaced modes. The simulation study shows that the multiple-input formulation provides estimates with significantly smaller errors on both mode shape and natural frequency estimates.

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