Multiactuator Piezoelectric System for Structural Damage Localization

In initial studies, it has been shown that the combination of Principal Component Analysis (PCA) and the contribution plots of Q and T-statistics can be considered an efficient technique to detect, distinguish and localize damages in structures that are equipped with several piezoelectric transducers (PZT’s). In those previous works, the specimen (aircraft turbine blade) was excited using just one of the set of PZT’s bounded on the surface. This paper studies the advantage of using the whole set of PZT’s as actuators as well as sensors. An active piezoelectric system is developed. At each phase of the diagnosis procedure, one PZT is used as actuator (a known electrical signal is applied) and the others are used as sensors (collecting the wave propagated through the structure at different points). A data-driven model for undamaged structure is built applying PCA to the data collected by several experiments. The current structure (damaged or not) is subjected to the same experiments, and the collected data are projected into the baseline PCA model. The indices Q, T, φ and I determine whether the structure is healthy or not. In addition, the contribution of each sensor to these indices supplies information about the localization of the damage. Introduction Nowadays, the application of Structural Health Monitoring (SHM) in aerospace and aircraft industry has been growing up due to the need for: (i) reducing maintenance costs and, (ii) improving the safety of the components, structures and users. SHM is a multidisciplinary activity that includes different technical knowledge: instrumentation, advanced data processing, strategies for damage identification, prognosis, among others. There are several potentially useful techniques, and their applicability to a particular situation depends on the size of critical damage admissible in the structure. All of these techniques follow the same general procedure: the structure is excited using actuators and the dynamical response is sensed at different locations throughout the structure. Any damage will change this vibrational response, as well as the transient by a wave that is spreading through the structure. The state of the structure is diagnosed by means of the processing of these data (Worden and Farrar, 2007). 5 World Conference on Structural Control and Monitoring 5WCSCM-10150 2 Lately, several researchers from different fields have been using techniques based on Principal Components Analysis -PCA(Jolliffe, 2002) as diagnosis methods for process monitoring with potentially promising results (B. Mnassri et al, 2009; Y. Yinghua et al, 2002; J. Qin, 2003). Recently, authors of this work have been applying PCA for SHM in aeronautical structures. This statistical method, some extensions and some damage indices have been used to distinguish different defects and to localize their positions in the structure. In those works an aircraft turbine blade was used to show that the formulation of indices T and Q based on PCA are successful indices to detect and distinguish damages (Mujica et al. 2009; Mujica et al. 2010). In these experiments, just one Piezoelectric transducer (PZT) was used as actuator and the others as sensors. Despite that encouraging results were obtained, it was shown that the detectability depends of the distance from the damage to the actuator. To solve this problem, and seizing on the main characteristic of PZT’s (actuator/sensor device), authors propose the application of the mentioned methodology adding new indices to assess the same structure but using an active piezoelectric system that can be considered as multiactuator/multisensor system. In this way, each PZT is used as much as actuator as sensors in several phases. In each phase, one of the PZT’s is used as actuator and the rest as sensors. By using the indices mentioned before (Q and T) and the new ones (φ and I), different damages can be detected and distinguished form the others (depending of its location). Besides, calculating the contribution of each sensor to each index, a region of the localization of the damage could be determined. Finally, when all phases have been accomplished (one per each PZT’s), a general diagnosis must be performed in order to localize and identify the damage considering the diagnosis in each phase. Principal Component Analysis Introduction Principal Component Analysis (PCA) (Jolliffe, 2000), or equivalently Proper Orthogonal Decomposition (POD) (Chatterjee, 2000) may provide arguments for how to reduce a complex data set to a lower dimension and reveal some hidden and simplified structure/patterns that often underlie it. The goal of Principal Component Analysis is to discern which dynamics are more important in the system, which are redundant and which are just noise. This goal is essentially achieved by determining a new space (coordinates) to re-express the original data filtering that noise and redundancies based on the variance– covariance structure of the original data. PCA can be also considered as a simple, non-parametric method for data compression and information extraction, which finds combinations of variables or factors that describe major trends in a confusing data set. Among their objectives it can be mentioned: to generate new variables that could express the information contained in the original set of data, to reduce the dimensionality of the problem that is studied, to eliminate some original variables if its information is not relevant. Projection on the Principal Components Analyzing a physical process by measuring several variables (sensors) at a number of time instants (or experimental trials), considering that each measurement is an individual sample in the data set (just one value, e.g. load, voltage, pressure, etc). The collected data are arranged in a matrix as follows: € X = x11 x12 ... x1 j ... x1m ... ... ... ... ... ... xi1 xi2 ... xij ... xim ... ... ... ... ... ... xn1 xn2 ... xnj ... xnm 