Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian

The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The traditional spectral clustering algorithm, which relies on the leading $K$ eigenvectors to detect $K$ clusters, fails in such cases. In this paper we propose the {\it spectral embedding norm} which sums the squared values of the first $I$ normalized eigenvectors, where $I$ can be significantly larger than $K$. We prove that this quantity can be used to separate clusters from the background in unbalanced settings, including extreme cases such as outlier detection. The performance of the algorithm is not sensitive to the choice of $I$, and we demonstrate its application on synthetic and real-world remote sensing and neuroimaging datasets

Spectral diffusion map approach for structural health monitoring of wind turbine blades using distributed sensors

Distributed Sensor Networks (DSN) has emerged as a sensing paradigms in the structural engineering field due to the application of Structural Health Monitoring (SHM) for large-scale structures which results in accurately diagnosing the health of structures and enhancing the reliability and robustness of monitoring systems. The multisensor network greatly enhances the feasibility of applying SHM and also provides awareness of structural damage. In this work, we develop data-driven method for the diagnosis of damage in mechanical structures using an array of distributed sensors. The proposed approach relies on comparing intrinsic geometry of data sets corresponding to the undamage and damage state of the system. This approach assumes no knowledge of underlying models of the different data sources. We use spectral diffusion map approach for identifying the intrinsic geometry of the data set. In particular, time series data from distributed sensors is used for the construction of diffusion map. The low dimensional embedding of the data set corresponding to different damage level is done using singular value decomposition of the diffusion map to identify the intrinsic geometry. We construct appropriate metric in diffusion space to compare the low-dimensional data set corresponding to different damage cases. The developed algorithm is applied for damage diagnosis of wind turbine blades. Towards this goal we developed a detailed nite element-based model of CX-100 blade in ANSYS using shell elements. The damage in the blade is modeled by degrading the material property which in turn results in change of stiffness. One of the main challenges in the development of health monitoring algorithms is the ability to use sensor data with relatively small signal to noise ratio. Our developed diffusion map-based algorithm is shown to be robust to the presence of sensor noise. The proposed diffusion map-based algorithm can not only account for data from different sensors but also different types of sensor in the form of sensor fusion hereby making it attractive to exploit the distributed nature of sensor array. The distributed nature of sensor array is further exploited to determine the location of damage on the wind turbine blade. Our extensive simulation results show that our proposed algorithms can not only determine the extend of damage but also the location of the damage

Damage detection on mesosurfaces using distributed sensor network and spectral diffusion maps

In this work, we develop a data-driven method for the diagnosis of damage in mesoscale mechanical structures using an array of distributed sensor networks. The proposed approach relies on comparing intrinsic geometries of data sets corresponding to the undamaged and damaged states of the system. We use a spectral diffusion map approach to identify the intrinsic geometry of the data set. In particular, time series data from distributed sensors is used for the construction of diffusion maps. The low dimensional embedding of the data set corresponding to different damage levels is obtained using a singular value decomposition of the diffusion map. We construct appropriate metrics in the diffusion space to compare the different data sets corresponding to different damage cases. The developed algorithm is applied for damage diagnosis of wind turbine blades. To achieve this goal, we developed a detailed finite element-based model of CX-100 blade in ANSYS using shell elements. Typical damage, such as crack or delamination, will lead to a loss of stiffness, is modeled by altering the stiffness of the laminate layer. One of the main challenges in the development of health monitoring algorithms is the ability to use sensor data with a relatively small signal-to-noise ratio. Our developed diffusion map-based algorithm is shown to be robust to the presence of sensor noise. The proposed diffusion map-based algorithm is advantageous by enabling the comparison of data from numerous sensors of similar or different types of data through data fusion, hereby making it attractive to exploit the distributed nature of sensor arrays. This distributed nature is further exploited for the purpose of damage localization. We perform extensive numerical simulations to demonstrate that the proposed method can successfully determine the extent of damage on the wind turbine blade and also localize the damage. We also present preliminary results for the application of the developed algorithm on the experimental data. These preliminary results obtained using experimental data are promising and is a topic of our ongoing investigation

Bridge damage detection using spatiotemporal patterns extracted from dense sensor network

The alarmingly degrading state of transportation infrastructures combined with their key societal and economic importance calls for automatic condition assessment methods to facilitate smart management of maintenance and repairs. With the advent of ubiquitous sensing and communication capabilities, scalable data-driven approaches is of great interest, as it can utilize large volume of streaming data without requiring detailed physical models that can be inaccurate and computationally expensive to run. Properly designed, a data-driven methodology could enable fast and automatic evaluation of infrastructures, discovery of causal dependencies among various sub-system dynamic responses, and decision making with uncertainties and lack of labeled data. In this work, a spatiotemporal pattern network (STPN) strategy built on symbolic dynamic filtering (SDF) is proposed to explore spatiotemporal behaviors in a bridge network. Data from strain gauges installed on two bridges are generated using finite element simulation for three types of sensor networks from a density perspective (dense, nominal, sparse). Causal relationships among spatially distributed strain data streams are extracted and analyzed for vehicle identification and detection, and for localization of structural degradation in bridges. Multiple case studies show significant capabilities of the proposed approach in: (i) capturing spatiotemporal features to discover causality between bridges (geographically close), (ii) robustness to noise in data for feature extraction, (iii) detecting and localizing damage via comparison of bridge responses to similar vehicle loads, and (iv) implementing real-time health monitoring and decision making work flow for bridge networks. Also, the results demonstrate increased sensitivity in detecting damages and higher reliability in quantifying the damage level with increase in sensor network density