Dynamic Mode Decomposition for Compressive System Identification

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, we integrate and unify two recent innovations that extend DMD to systems with actuation [Proctor et al., 2016] and systems with heavily subsampled measurements [Brunton et al., 2015]. When combined, these methods yield a novel framework for compressive system identification [code is publicly available at: https://github.com/zhbai/cDMDc]. It is possible to identify a low-order model from limited input-output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data is available, it is possible to dramatically accelerate downstream computations by first compressing the data. We demonstrate this unified framework on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, we explore this architecture on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test-case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data

COST-EFFECTIVE PROGNOSTICS AND HEALTH MONITORING OF LOCALLY DAMAGED PIPELINES WITH HIGH CONFIDENCE LEVEL

Localized pipeline damages, caused by degradation processes such as corrosion, are prominent, can result in pipeline failure and are expensive to monitor. To prevent pipeline failure, many Prognostics and Health Monitoring (PHM) approaches have been developed in which sensor network for online, and human inspection for offline data gathering are separately used. In this dissertation, a two-level (segment- and integrated-level) PHM approach for locally damaged pipelines is proposed where both of these degradation data gathering schemes (i.e., detection methods) are considered simultaneously. The segment-level approach, in which the damage behavior is considered to be uniform, consists of a static and a dynamic phase. In the static phase, a new optimization problem for the health monitoring layout design of locally damaged pipelines is formulated. The solution to this problem is an optimal configuration (or layout) of degradation detection methods with a minimized health monitoring cost and a maximized likelihood of damage detection. In the dynamic phase, considering the optimal layout, an online fusion of high-frequency sensors data and low-frequency inspection information is conducted to estimate and then update the pipeline’s Remaining Useful Life (RUL) estimate. Subsequently, the segment-level optimization formulation is modified to improve its scalability and facilitate updating layouts considering the online RUL estimates. Finally, at the integrated-level, the modified segment-level approach is used along with Stochastic Dynamic Programming (SDP) to produce an optimal set of layouts for a long pipeline consisting of multiple segments with different damage behavior. Experimental data and several notional examples are used to demonstrate the performance of the proposed approaches. Synthetically generated damage data are used in two examples to demonstrate that the proposed segment-level layout optimization approach results in a more robust solution compared to single detection approaches and deterministic methods. For the dynamic segment-level phase, acoustic emission sensor signals and microscopic images from a set of fatigue crack experiments are considered to show that combining sensor- and image-based damage size estimates leads to accuracy improvements in RUL estimation. Lastly, using synthetically generated damage data for three hypothetical pipeline segments, it is shown that the constructed integrated-level approach provides an optimal set of layouts for several pipeline segments

Numerical Prediction of Turbulent Non-Premixed Forced Ignition in Altitude Relight

Fast and reliable altitude relight performance is one of the end goals of aircraft engine design. Relight involves the use of an external heat source (a kernel, for instance), to ignite a cold mixture of fuel and air in a turbulent flow environment. Due to the variabilities in spark kernel formation, its transport in a turbulent flow environment, and the mixing and chemical reactions that are influenced by turbulent mixing, ignition is described statistically in terms of a probability of success. Currently, full-engine tests remain the most direct approach to evaluating relight probability at relevant conditions. However, this approach is expensive both in terms of time and monetary cost. Computational models that can accurate predict ignition processes in a statistical sense can vastly accelerate engine design, and significantly reduce cost. The objective of the dissertation is to develop a predictive computational framework that addresses this key need. Forced ignition, due to the nature of turbulent flow, exhibits complex flame structure. To describe the combustion processes, a novel hybrid tabulation approach is formulated. This method combined a conventional flamelet-progress variable tabulation with a homogeneous reaction model to capture the spark transition from a homogeneous volumetric reaction process to a diffusion-controlled flame. Since the success of kernel ignition or failure has to be described statistically, a procedure for introducing uncertainties from spark discharge and the turbulent flow is developed. The resulting computational model involves an ensemble approach, where a large set of realizations of a detailed large eddy simulation (LES) based description of the flow along with the hybrid tabulation model is used to determine ignition probabilities The proposed framework is thoroughly validated using a stratified forced ignition experiment designed to replicate high altitude relight. The model is found to successfully reproduce the fundamental physics, including the evolution of the spark kernel, and the entrainment of the fuel-air mixture into the hot kernel discharge. A particular experiment using methane as fuel is used to calibrate the spark discharge model, which is then used without modification in the study of alternative jet fuels. It is shown that the prediction framework capture the ignition probability for different fuels and operating conditions. This new computational framework provides the first rigorous approach to modeling high altitude relight.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168027/1/yhtang_1.pd

The data concept behind the data: From metadata models and labelling schemes towards a generic spectral library

Spectral libraries play a major role in imaging spectroscopy. They are commonly used to store end-member and spectrally pure material spectra, which are primarily used for mapping or unmixing purposes. However, the development of spectral libraries is time consuming and usually sensor and site dependent. Spectral libraries are therefore often developed, used and tailored only for a specific case study and only for one sensor. Multi-sensor and multi-site use of spectral libraries is difficult and requires technical effort for adaptation, transformation, and data harmonization steps. Especially the huge amount of urban material specifications and its spectral variations hamper the setup of a complete spectral library consisting of all available urban material spectra. By a combined use of different urban spectral libraries, besides the improvement of spectral inter- and intra-class variability, missing material spectra could be considered with respect to a multi-sensor/ -site use. Publicly available spectral libraries mostly lack the metadata information that is essential for describing spectra acquisition and sampling background, and can serve to some extent as a measure of quality and reliability of the spectra and the entire library itself. In the GenLib project, a concept for a generic, multi-site and multi-sensor usable spectral library for image spectra on the urban focus was developed. This presentation will introduce a 1) unified, easy-to-understand hierarchical labeling scheme combined with 2) a comprehensive metadata concept that is 3) implemented in the SPECCHIO spectral information system to promote the setup and usability of a generic urban spectral library (GUSL). The labelling scheme was developed to ensure the translation of individual spectral libraries with their own labelling schemes and their usually varying level of details into the GUSL framework. It is based on a modified version of the EAGLE classification concept by combining land use, land cover, land characteristics and spectral characteristics. The metadata concept consists of 59 mandatory and optional attributes that are intended to specify the spatial context, spectral library information, references, accessibility, calibration, preprocessing steps, and spectra specific information describing library spectra implemented in the GUSL. It was developed on the basis of existing metadata concepts and was subject of an expert survey. The metadata concept and the labelling scheme are implemented in the spectral information system SPECCHIO, which is used for sharing and holding GUSL spectra. It allows easy implementation of spectra as well as their specification with the proposed metadata information to extend the GUSL. Therefore, the proposed data model represents a first fundamental step towards a generic usable and continuously expandable spectral library for urban areas. The metadata concept and the labelling scheme also build the basis for the necessary adaptation and transformation steps of the GUSL in order to use it entirely or in excerpts for further multi-site and multi-sensor applications