Damage Localisation Using Principal Component Analysis of Distributed Sensor Array

The spatial information given by the distributed sensors (e.g., piezoelectric laminates) can be used to forecast structural damage on localised critical spot. It is well known that a localised structural damage with relative small amplitude does not affect significantly the modal response of the structure, at least at low frequencies. Nevertheless, a local delamination or electrode deterioration at the distributed sensor level will show significant changes on the response of the sensor by modifying its apparent electromechanical coupling. Assuming that the number of sensors is greater than the number of involved structural modes, a local structural damage, with relative small amplitude, will only affect a particular distributed sensor without affecting significantly the response of the others. By applying a principal component analysis (PCA) on the sensor time responses, it is possible to see that any change of one particular sensor electromechanical coupling factor will affect the subspace generated by the complete sensor response set. The subspace generated with the damaged structure can then be compared with the subspace of an initial state in order to diagnose damage or not. INTRODUCTION This paper investigates the problem of structural health monitoring by means of distributed piezoelectric sensors. These last ones are very well convenient for applications on plate like structures. The success of piezoelectric materials comes from their relative low-cost and lightweight properties and from the fact that piezoelectric laminas can be used as well _____________ Pascal De Boe, Jean-Claude Golinval, LTAS-VIS, Université de Liège, 1, Chemin des Chevreuils, B52, B-4000 Liège, Belgium Email : [email protected], [email protected] http://www.ulg.ac.be/ltas-vis/ in actuator mode as in sensor mode (Lee [1]). Most of the damage detection methods, with piezoelectric lamina sensors, are based on the impedance structural health monitoring. The basic principle is to track the high frequency electrical point impedance of a piezoelectric material bounded onto a structure (Kabeya et al. [2]). However, this technique presents some difficulties to locate damages, needs high frequency (typically > 50 kHz) data acquisition system and, in general, has to be applied on demand. Fatigue cracks resulting from permanent vibrations due to, e.g., seismic excitations, can lead to a severe reduction of the structural integrity. It is then useful to have an on-line monitoring system in order to warn an operator of the structural damages. A preventive maintenance phase could then be initiated before the cracks achieve a critical damage level. The problem is not an easy task. Indeed, it is well known that a localised structural damage with relative small amplitude does not affect significantly the modal response of the structure, at least at low frequencies (Friswell and Penny [3]). For example, if a cantilever beam contains a crack, the first bending mode will look very much like the first mode of the undamaged structure. Model-based techniques are then very difficult to be implemented to detect a low damage level. Compared to classical accelerometer sensors, piezoelectric laminas have the advantage to cover an appreciable surface. A strategically positioned lamina, at a zone with high probabilities of failure, has then the ability to 'catch' damages: a local de-lamination (or an electrode deterioration) at the sensor level will then show significant changes on the response of the sensor by modifying its apparent electromechanical coupling. Assuming that the number of sensors is greater than the number of involved structural modes, a local damage, with relative small amplitude, will only affect a sensor without affecting significantly the response of the others. By applying a Principal Component Analysis (PCA) on the sensor time responses, any change of one particular sensor electromechanical coupling factor will then affect the subspace generated by the complete sensor response set. While the control and chemical engineering communities have considered the PCA for the sensor validation problem, it had not caught the attention of structural dynamics community until recently. Principal Component Analysis, also know as Karhunen-Loeve decomposition and Proper Orthogonal Decomposition (POD), is emerging for the parameter identification of nonlinear mechanical systems (Lenaerts et al. [4]). By inspecting subspace angles, Friswell and Inman [5] have studied the problem of sensor validation for smart structures. This paper will present an on-line, low amplitude damage detection technique by using PCA of piezoelectric lamina responses. This method does not require the knowledge of neither the structural excitations nor a structural model. The damage detection and localisation technique is illustrated on a plate instrumented by several piezolaminates and excited by external loads. DYNAMICS OF PIEZO-STRUCTURES In the case of a structure instrumented with piezoelectric sensor/actuator, electromechanical relationships are added to the dynamics of the system to represent the contributions of the electrical degrees of freedom linked to the piezoelectric actuator and sensor (Saunders et al. [6]): q v C x v f x K x D x M