Validation of Damage Identification Using Non-Linear Data-Driven Modelling

Validation of Damage Identification Using Non-Linear Data-Driven Modelling

Miguel Angel Torres Arredondo (MAN Diesel and Turbo SE, Germany), Diego Alexander Tibaduiza Burgos (Universidad Santo Tomás, Colombia), Inka Buethe (University of Siegen, Germany), Luis Eduardo Mujica (Department of Applied Mathematics, Universitat Politècnica de Catalunya, Spain), Maribel Anaya Vejar (Universidad Santo Tomás, Colombia & Universitat Politècnica de Catalunya, Spain), Jose Rodellar (Department of Applied Mathematics, Universitat Politècnica de Catalunya, Spain) and Claus-Peter Fritzen (University of Siegen, Germany)
Copyright: © 2015 |Pages: 13
DOI: 10.4018/978-1-4666-5888-2.ch094
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Theoretical Background

The innovative data driven approach used in for the experimental evaluation in this chapter uses scale-frequency analysis, multiway hierarchical nonlinear principal component analysis (h-NLPCA), squared prediction error statistic (SPE) and self-organizing maps (SOM) to achieve the identification of damages in structures. It is based on the use of signals collected from a distributed piezoelectric transducer network which is permanently attached to the structure. Within this transducer network each transducer can work either as a sensor or actuator. The inspection of the structure is performed in several actuation steps. Within each step, one transducer is used as actuator while the rest acts in turn as sensors to collect the structural dynamic responses included in the ultrasonic waves propagated throughout the structure. To process the data, in a first step, the discrete wavelet transform (DWT) is used for feature selection and extraction from the structural dynamic responses at different frequency scales. Neural Networks are then used to build a probabilistic model from these features for each actuation step with the data from the healthy structure by means of sensor data fusion. Next, the features extracted from the dynamic responses in different structural states (damaged or not) are projected into the probabilistic models of each actuation step in order to obtain the non-linear principal components, and then the SPE metrics are calculated. Finally, these metrics together with the projections onto the non-linear principal components (scores) are used as input feature vectors to a SOM. A sketch of the single steps of the methodology is given in Figure 1. Results show that with the proposed approach all the damages were detectable and classifiable, and the selected features proved capable of separating all damage conditions from the undamaged state. For an extensive description including also a large number of references, which describe the theoretical background of the single components used in this method, the reader is referred to the chapter “Damage Identification using Non-linear Data-Driven Modelling – Methodology” within this book.

Figure 1.

Proposed methodology fusing all the actuation steps for pattern recognition and structural damage determination

Key Terms in this Chapter

Damage Detection: Damage detection makes up the first level in damage diagnosis. Its objective is to determine whether there is any change in the structure and if this change is related to damage.

Receiver Operating Characteristics (ROC) Curves: A tool for diagnostic test evaluation and they are well-known for describing the performance of diagnostic and detection systems in medical decision, signal processing and communications. These curves allow analyzing the balance between the false positive rate and the sensitivity for different cut-off points of a parameter.

Self-Organizing Maps (SOMs): The group of Artificial Neural Networks (ANN) and can be described as a nonlinear, ordered, smooth mapping of high-dimensional input data on the elements of a regular, low-dimensional display. They use an unsupervised algorithm and are also known as Kohonen Maps (see Kohonen, 2001 ).

Acousto-Ultrasonics: A highly sophisticated and advanced technique using digital signal processing and pattern recognition algorithms. The method consists of monitoring and analyzing the acoustic signals received in order to find the presence of a discontinuity (delaminations, debonding, etc.) inside the tested structure.

Structural Health Monitoring (SHM): The process of acquiring and analysing data from a set of permanently installed sensors to determine the health of a structure in a non-destructive way.

Damage Classification: Damage Classification makes up a higher level of damage diagnosis and requires prior damage detection. It allows identifying and classifying the kind of damage using signal processing tools.

Nonlinear Principal Component Analysis (NLPCA): Is commonly seen as a nonlinear generalization of standard principal component analysis (PCA). It generalizes the principal components from straight lines to curves (nonlinear). Thus, the subspace in the original data space which is described by all nonlinear components is also curved.

Wavelet Transform: Capable of revealing aspects of data that other signal analysis techniques miss, aspects like trends, breakdown points, discontinuities in higher derivatives, and self-similarity. It will provide accurate location of the transient signals while simultaneously reporting the fundamental frequency and its low-order harmonics.

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