Subspace System Identification via Weighted Nuclear Norm Optimization

We present a subspace system identification method based on weighted nuclear norm approximation. The weight matrices used in the nuclear norm minimization are the same weights as used in standard subspace identification methods. We show that the inclusion of the weights improves the performance in terms of fit on validation data. As a second benefit, the weights reduce the size of the optimization problems that need to be solved. Experimental results from randomly generated examples as well as from the Daisy benchmark collection are reported. The key to an efficient implementation is the use of the alternating direction method of multipliers to solve the optimization problem.Comment: Submitted to IEEE Conference on Decision and Contro

Localisation 2D d'une fissure sur une poutre par subspace fitting

La localisation de défauts dans les structures mécaniques est une tache cruciale pour de nombreuses applications industrielles. Prédire de manière précoce un endommagement permet alors de réduire considérablement les coûts liés à la maintenance. Dans cette optique de nombreuses méthodes basées sur l’analyse vibratoire ont émergé ces dernières années [1]. Plus particulièrement, les méthodes basées sur le recalage de modèles Eléments Finis (EF) visent à corréler un modèle numérique avec des données expérimentales issues de la structure surveillée [2]. La corrélation est effectuée en ajustant les paramètres incertains du modèle. Lorsque ces paramètres sont sensibles aux défauts, il est alors possible de les diagnostiquer

Застосування зваженого методу найменших квадратів для оцінювання параметрів математичних моделей коливань ротора

Перманентне підвищення робочих параметрів роторних машин пов’язане із сучасними викликами щодо інтенсифікації робочих процесів у машинах і апаратах. При цьому актуальною постає проблема забезпечення вібраційної надійності роторних машин як одних з найбільш уживаних у сучасному високотехнологічному виробництві. При цьому коливання роторів є однією з основних проблем динаміки роторних машин. Застосування достовірних математичних моделей вільних і вимушених коливань дозволяє ефективно контролювати та прогнозувати вібраційні характеристики ротора. Основні завдання дослідження полягають у визначенні вхідних даних та параметрів математичної моделі, розроблені процедури оцінювання параметрів моделі з використанням зваженого методу найменших квадратів та аналізі результатів оцінювання порівняно з традиційним методом найменших квадратів

Analysis of State Space System Identification Methods Based on Instrumental Variables and Subspace Fitting

Subspace-based State Space System IDentification (4SID) methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification. The advantages are that the user has simple and few design variables, and that the methods have robust numerical properties and relatively low computational complexities. Though subspace techniques have been demonstrated to perform well in a number of cases, the performance of these methods is neither fully understood nor analyzed. Our principal objective is to undertake a statistical investigation of subspace based system identification techniques. The studied methods consist of two steps. The subspace spanned by the extended observability matrix is first estimated. The asymptotic properties of this subspace estimate are derived herein. In the second step, the structure of the extended observability matrix is used to find a system model estimate. Two possible methods are considered. The simplest one only u..

Variance estimation of modal parameters from output-only and input/output subspace-based system identification

International audienceAn important step in the operational modal analysis of a structure is to infer on its dynamic behavior through its modal parameters. They can be estimated by various modal identification algorithms that fit a theoretical model to measured data. When output-only data is available, i.e. measured responses of the structure, frequencies, damping ratios and mode shapes can be identified assuming that ambient sources like wind or traffic excite the system sufficiently. When also input data is available, i.e. signals used to excite the structure, input/output identification algorithms are used. The use of input information usually provides better modal estimates in a desired frequency range. While the identification of the modal mass is not considered in this paper, we focus on the estimation of the frequencies, damping ratios and mode shapes, relevant for example for modal analysis during in-flight monitoring of aircrafts. When identifying the modal parameters from noisy measurement data, the information on their uncertainty is most relevant. In this paper, new variance computation schemes for modal parameters are developed for four subspace algorithms, including output-only and input/output methods, as well as data-driven and covariance-driven methods. For the input/output methods, the known inputs are considered as realizations of a stochastic process. Based on Monte Carlo validations, the quality of identification, accuracy of variance estimations and sensor noise robustness are discussed. Finally these algorithms are applied on real measured data obtained during vibrations tests of an aircraft

Structural Identification and Damage Identification Using Output-Only Vibration Measurements

This dissertation studied the structural identification and damage detection of civil engineering structures. Several issues regarding structural health monitoring were addressed. The data-driven subspace identification algorithm was investigated for modal identification of bridges using output-only data. This algorithm was tested through a numerical truss bridge with abrupt damage as well as a real concrete highway bridge with actual measurements. Stabilization diagrams were used to analyze the identified results and determine the modal characteristics. The identification results showed that this identification method is quite effective and accurate. The influence of temperature fluctuation on the frequencies of a highway concrete bridge was investigated using ambient vibration data over a one-year period of a highway bridge under health monitoring. The data were fitted by nonlinear and linear regression models, which were then analyzed. The substructure identification by using an adaptive Kalman filter was investigated by applying numerical studies of a shear building, a frame structure, and a truss structure. The stiffness and damping were identified successfully from limited acceleration responses, while the abrupt damages were identified as well. Wavelet analysis was also proposed for damage detection of substructures, and was shown to be able to approximately locate such damages. Delamination detection of concrete slabs by modal identification from the output-only data was proposed and carried out through numerical studies and experimental modal testing. It was concluded that the changes in modal characteristics can indicate the presence and severity of delamination. Finite element models of concrete decks with different delamination sizes and locations were established and proven to be reasonable. Pounding identification can provide useful early warning information regarding the potential damage of structures. This thesis proposed to use wavelet scalograms of dynamic response to identify the occurrence of pounding. Its applications in a numerical example as well as shaking table tests of a bridge showed that the scalograms can detect the occurrence of pounding very well. These studies are very useful for vibration-based structural health monitoring