Sparse and low-rank methods in structural system identification and monitoring

This paper presents sparse and low-rank methods for explicit modeling and harnessing the data structure to address the inverse problems in structural dynamics, identification, and data-driven health monitoring. In particular, it is shown that the structural dynamic features and damage information, intrinsic within the structural vibration response measurement data, possesses sparse and low-rank structure, which can be effectively modeled and processed by emerging mathematical tools such as sparse representation (SR), and low-rank matrix decomposition. It is also discussed that explicitly modeling and harnessing the sparse and low-rank data structure could benefit future work in developing data-driven approaches towards rapid, unsupervised, and effective system identification, damage detection, as well as massive SHM data sensing and management

Mathematical modelling ano optimization strategies for acoustic source localization in reverberant environments

La presente Tesis se centra en el uso de técnicas modernas de optimización y de procesamiento de audio para la localización precisa y robusta de personas dentro de un entorno reverberante dotado con agrupaciones (arrays) de micrófonos. En esta tesis se han estudiado diversos aspectos de la localización sonora, incluyendo el modelado, la algoritmia, así como el calibrado previo que permite usar los algoritmos de localización incluso cuando la geometría de los sensores (micrófonos) es desconocida a priori. Las técnicas existentes hasta ahora requerían de un número elevado de micrófonos para obtener una alta precisión en la localización. Sin embargo, durante esta tesis se ha desarrollado un nuevo método que permite una mejora de más del 30\% en la precisión de la localización con un número reducido de micrófonos. La reducción en el número de micrófonos es importante ya que se traduce directamente en una disminución drástica del coste y en un aumento de la versatilidad del sistema final. Adicionalmente, se ha realizado un estudio exhaustivo de los fenómenos que afectan al sistema de adquisición y procesado de la señal, con el objetivo de mejorar el modelo propuesto anteriormente. Dicho estudio profundiza en el conocimiento y modelado del filtrado PHAT (ampliamente utilizado en localización acústica) y de los aspectos que lo hacen especialmente adecuado para localización. Fruto del anterior estudio, y en colaboración con investigadores del instituto IDIAP (Suiza), se ha desarrollado un sistema de auto-calibración de las posiciones de los micrófonos a partir del ruido difuso presente en una sala en silencio. Esta aportación relacionada con los métodos previos basados en la coherencia. Sin embargo es capaz de reducir el ruido atendiendo a parámetros físicos previamente conocidos (distancia máxima entre los micrófonos). Gracias a ello se consigue una mejor precisión utilizando un menor tiempo de cómputo. El conocimiento de los efectos del filtro PHAT ha permitido crear un nuevo modelo que permite la representación 'sparse' del típico escenario de localización. Este tipo de representación se ha demostrado ser muy conveniente para localización, permitiendo un enfoque sencillo del caso en el que existen múltiples fuentes simultáneas. La última aportación de esta tesis, es el de la caracterización de las Matrices TDOA (Time difference of arrival -Diferencia de tiempos de llegada, en castellano-). Este tipo de matrices son especialmente útiles en audio pero no están limitadas a él. Además, este estudio transciende a la localización con sonido ya que propone métodos de reducción de ruido de las medias TDOA basados en una representación matricial 'low-rank', siendo útil, además de en localización, en técnicas tales como el beamforming o el autocalibrado

Dictionary Learning for Sparse Representations With Applications to Blind Source Separation.

During the past decade, sparse representation has attracted much attention in the signal processing community. It aims to represent a signal as a linear combination of a small number of elementary signals called atoms. These atoms constitute a dictionary so that a signal can be expressed by the multiplication of the dictionary and a sparse coefficients vector. This leads to two main challenges that are studied in the literature, i.e. sparse coding (find the coding coefficients based on a given dictionary) and dictionary design (find an appropriate dictionary to fit the data). Dictionary design is the focus of this thesis. Traditionally, the signals can be decomposed by the predefined mathematical transform, such as discrete cosine transform (DCT), which forms the so-called analytical approach. In recent years, learning-based methods have been introduced to adapt the dictionary from a set of training data, leading to the technique of dictionary learning. Although this may involve a higher computational complexity, learned dictionaries have the potential to offer improved performance as compared with predefined dictionaries. Dictionary learning algorithm is often achieved by iteratively executing two operations: sparse approximation and dictionary update. We focus on the dictionary update step, where the dictionary is optimized with a given sparsity pattern. A novel framework is proposed to generalize benchmark mechanisms such as the method of optimal directions (MOD) and K-SVD where an arbitrary set of codewords and the corresponding sparse coefficients are simultaneously updated, hence the term simultaneous codeword optimization (SimCO). Moreover, its extended formulation ‘regularized SimCO’ mitigates the major bottleneck of dictionary update caused by the singular points. First and second order optimization procedures are designed to solve the primitive and regularized SimCO. In addition, a tree-structured multi-level representation of dictionary based on clustering is used to speed up the optimization process in the sparse coding stage. This novel dictionary learning algorithm is also applied for solving the underdetermined blind speech separation problem, leading to a multi-stage method, where the separation problem is reformulated as a sparse coding problem, with the dictionary being learned by an adaptive algorithm. Using mutual coherence and sparsity index, the performance of a variety of dictionaries for underdetermined speech separation is compared and analyzed, such as the dictionaries learned from speech mixtures and ground truth speech sources, as well as those predefined by mathematical transforms. Finally, we propose a new method for joint dictionary learning and source separation. Different from the multistage method, the proposed method can simultaneously estimate the mixing matrix, the dictionary and the sources in an alternating and blind manner. The advantages of all the proposed methods are demonstrated over the state-of-the-art methods using extensive numerical tests

Eigen-spectrograms: an interpretable feature space for bearing fault diagnosis based on artificial intelligence and image processing

The Intelligent Fault Diagnosis of rotating machinery proposes some captivating challenges in light of the imminent big data era. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open issues. Models' interpretation is still buried under the foundations of data driven science, thus requiring attention to the development of new opportunities also for machine learning theories. This study proposes a machine learning diagnosis model, based on intelligent spectrogram recognition, via image processing. The approach is characterized by the introduction of the eigen-spectrograms and randomized linear algebra in fault diagnosis. The eigen-spectrograms hierarchically display inherent structures underlying spectrogram images. Also, different combinations of eigen-spectrograms are expected to describe multiple machine health states. Randomized algebra and eigen-spectrograms enable the construction of a significant feature space, which nonetheless emerges as a viable device to explore models' interpretations. The computational efficiency of randomized approaches further collocates this methodology in the big data perspective and provides new reading keys of well-established statistical learning theories, such as the Support Vector Machine (SVM). The conjunction of randomized algebra and Support Vector Machine for spectrogram recognition shows to be extremely accurate and efficient as compared to state of the art results.Comment: 14 pages, 13 figure

Sensor Signal and Information Processing II

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing

Application of PCA to Cardiac Optical Mapping

Structural remodeling of the heart due to pathologies such as hypertension and myocardial infarction leads to the appearance of myofibroblasts, a phenotype largely absent in physiologic myocardium. While myofibroblasts are responsible for wound healing and structural repair of damaged myocardium, they are thought to have deleterious effects on electrical and mechanical properties of the heart. Understanding these effects is critical to developing effective treatments, and has motivated the development of a series of in vitro engineered heart tissues and cardiomyocyte-myofibroblast co-cultures whose mechanical and electrophysiological function can be deduced from video analysis. Electrophysiological properties are evident from changes in intensity of a fluorescent calcium assay, mechanical properties are evident from deformations apparent in the video, and both are used to study excitation-contraction coupling properties. This thesis contributes efficient mathematical tools for denoising and analyzing videos of contracting, vibrating, and flashing structures

30th International Conference on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2017)

Proceedings of COMADEM 201

Use of the continuous wavelet tranform to enhance early diagnosis of incipient faults in rotating element bearings

This thesis focused on developing a new wavelet for use with the continuous wavelet transform, a new detection method and two de-noising algorithms for rolling element bearing fault signals. The work is based on the continuous wavelet transform and implements a unique Fourier Series estimation algorithm that allows for least squares estimation of arbitrary frequency components of a signal. The final results of the research also included use of the developed detection algorithm for a novel method of estimating the center frequency and bandwidth for use with the industry standard detection algorithm, envelope demodulation, based on actual fault data. Finally, the algorithms and wavelets developed in this paper were tested against seven other wavelet based de-noising algorithms and shown to be superior for the de-noising and detection of inner and outer rolling element race faults